AIX-MARSEILLE UNIVERSITE

Transcription

1 AIX-MARSEILLE UNIVERSITE Ecole doctorale de physique et sciences de la matière THESE Présentée pour l obtention du grade de DOCTEUR EN SCIENCES D AIX-MARSEILLE UNIVERSITE Spécialité: Physique Interaction laser femtoseconde - diélectrique à intensité modérée: analyse du dépôt d énergie et application à l ablation de la silice fondue et de la cornée Nadezda VARKENTINA Soutenue le 5 juin 2012 à Marseille devant le jury composé de Dr. Stéphane GUIZARD, Ecole Polytechnique, Rapporteur Prof. Lionel CANIONI, Université Bordeaux I, Rapporteur Dr. Karsten PLAMANN, LOA ENSTA, Examinateur Dr. Tatiana ITINA, Université Jean Monnet, Examinateur Dr. Nicolas SANNER, Aix-Marseille Université, Examinateur Dr. Olivier UTEZA, Aix-Marseille Université, Directeur de thèse Dr. Louis HOFFART, Aix-Marseille Université, Co-directeur de thèse

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3 Cette thèse est particulièrement dédiée à ma mère Elena, à mon père Vasily, à ma sœur Svetlana, à un très cher ami.

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5 Remerciements J ai effectué ma thèse au laboratoire LP3 en collaboration avec le CHU La Timone et l Institut Fresnel. Aussi, j aimerais exprimer ma gratitude à toutes les personnes qui ont rendu ce travail possible. Je tiens tout d abord à remercier mon directeur de thèse, le Dr. Olivier UTEZA, pour la grande confiance et le soutien permanent qu il m a accordés tout au long de ces trois années, pour sa disponibilité, son aide, son enseignement et sa patience, ainsi que pour tous les bons moments partagés. Que soient également remerciés le Dr. Marc SENTIS et le Dr. Philippe DELAPORTE de m avoir accueillie dans leur laboratoire. Je remercie le Dr. Louis HOFFART et le Dr. Nicolas SANNER d avoir suivi mes travaux de thèse de bout en bout. Je voudrais exprimer ma profonde reconnaissance au Dr. Tatiana ITINA, du Laboratoire Hubert Curien (Saint Etienne, France), pour sa confiance, son aide et pour avoir bien voulu présider mon jury de soutenance. Je tiens à remercier vivement le Pr. Lionel CANIONI, du Laboratoire Ondes et Matière d Aquitaine (Bordeaux, France), d avoir accepté d être rapporteur et d avoir fait partie de mon jury de thèse, mais aussi pour ses remarques et pour l intérêt qu il a porté à mon travail. Je tiens à dire ma gratitude au Dr. Stéphane GUIZARD, du Laboratoire des Solides Irradiés (Palaiseau, France), d avoir accepté d expertiser mes travaux de thèse et d avoir fait partie de mon jury. J adresse aussi mes remerciements au Dr. Karsten PLAMANN, du Laboratoire d Optique Appliquée (Palaiseau, France), d avoir accepté de faire partie de mon jury de soutenance. Je voudrais tout particulièrement exprimer ma reconnaissance à Madame Simone ESCOFFIER pour sa gentillesse, son soutien, ses sourires et aussi ses cours de français depuis mes premiers jours en France. Qu il me soit permis ici de remercier Monsieur Joël GARREAU DE LOUBRESSE de m avoir appris le français, d avoir corrigé mes fautes pendant la préparation de mon oral, mais aussi de m avoir fait grandir et aidée à retrouver confiance en moi. Merci également pour son soutien et sa disponibilité constante pendant la rédaction de ce manuscrit. Je tiens à remercier mes trois amies que j ai rencontrées au laboratoire LP3 et qui restent toujours dans mon cœur: Vanessa VERVISCH, toujours très attentionnée et gentille, à l écoute et qui a été présente pour v

6 Remerciements vi me soutenir et m aider, ainsi que pour tous les bons moments partagés; Ksenia MAXIMOVA, mon amie avec qui je partageais le bureau, le laser et beaucoup de moments agréables et inoubliables; Chaimah BIJAOUI, ma petite stagiaire qui m a supportée pendant la rédaction et m a énormément soutenue et redonné confiance en moi. Je remercie Thierry SARNET pour sa bonne humeur et son humour et de m avoir appris à skier et jouer à la Pétanque. J adresse mes remerciements à mes collègues, Thibault DERRIEN, Emeric BIVER, SEDAO, Benoit BUSSIERE, Julie AILUNO, Yannick LARMANDE, Rémi TORRES et Ludovic RAPP, ainsi qu aux autres membres du laboratoire pour tous les bons moments passés ensemble. Je voudrais exprimer aussi ma reconnaissance au Dr. Patricia ALLONCLE, à Laurent CHAR- MASSON, Max ROLLAND, Gaëlle COUSTILLIER et tous les membres et ex-membres de LP3 qui ont rendu la vie de tous les jours agréable. Je souhaite à tous les doctorants de LP3 de bien réussir leurs thèses et garder l ambiance agréable et chaleureuse de laboratoire. Enfin, ma reconnaissance du fond du cœur va à ma famille et mes amis pour la foi, l amour et le soutien qu ils m ont accordés.

7 "Le mal existe, mais pas sans le bien, comme l ombre existe, mais pas sans la lumière." Alfred de Musset. "Ce n est pas parce que les choses sont difficiles que nous n osons pas, c est parce que nous n osons pas qu elles sont difficiles." Sénèque. "One never notices what has been done; one can only see what remains to be done." Marie Curie.

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9 Conformément à la demande de la Scolarité d AIX-MARSEILLE UNIVERSITE cette thèse écrite en anglais contient la traduction en français de l introduction et la conclusion et un résumé long qui précèdent le sommaire.

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11 Abstract (french) Introduction L évolution des systèmes laser stimule inévitablement le développement d applications pratiques et vice-versa. Cette stimulation se fait aussi en réponse aux demandes sociétales et économiques poussant la technologie laser à sans cesse progresser et s adapter. Au début de leur histoire, les lasers femtosecondes étaient installés seulement dans des laboratoires de grande taille et envergure, en raison de leur complexité, de leur faible fiabilité et de la difficulté de leur maintenance. Les développements et réalisations continuels dans les domaines de la technologie et science des impulsions ultra-courtes, soutenus par une forte concurrence internationale, exigent des compétences dans différents domaines de recherche tels que la physique du solide, la science des matériaux, ainsi qu un savoir-faire important dans les technologies optiques. Cela implique en particulier une bonne connaissance de l interaction laser-matière et le maintien d un niveau élevé de développement technologique et industriel associé. Panorama d ensemble et tendances du micro-usinage laser Selon Laser Focus World [1], après une baisse importante dans le monde entier de leur chiffre d affaires en 2009, on observe de nouveau une augmentation des demandes pour les technologies laser (voir figure 1). Les prévisions pour 2010 mentionnent un chiffre d affaires annuel total de 60% pour le marché des diodes laser et 40% pour le reste des lasers. Les technologies laser couvrent un large spectre d applications comme cela est présenté dans la figure 2. Les domaines d application les plus importants sont: la communication et le stockage optique de données et le traitement des matériaux. Dans l industrie des communications et du stockage optique, les lasers sont utilisés pour les télécommunications et l échange de données, dans les systèmes émetteurs-récepteurs et dans les amplificateurs optiques. Le traitement des matériaux xi

12 xii Figure 1: Evolution du chiffre d affaires mondial des lasers pour la période: Figure 2: Répartition des revenus commerciaux par application laser. adresse des industries telles que le traitement des métaux (soudage, découpe, recuit, perçage), des semi-conducteurs et de manière générale le domaine de la microélectronique (lithographie, inspection et contrôle, analyse de défauts et réparation, perçage de vias ou trous), le marquage de tout type de matériaux (plastique, métaux, silicium), le prototypage rapide, la fabrication des ordinateurs, le micro-usinage, la réalisation d hologrammes et de réseaux. D autres segments moins importants sont les suivants: la thérapie médicale (ophtalmologie, photo coagulation, thérapies diverses, applications cosmétiques comme par exemple l enlèvement des rides et l épilation), la recherche scientifique et militaire (recherche fondamentale et développement de grands projets laser dans les universités et laboratoires nationaux comme le NIF (National Ignition Facility) ou

13 xiii le LMJ (Laser MégaJoule), les lasers à électrons libres émettant dans le domaine des rayons X (Stanford SLAC, etc.), l instrumentation et les capteurs (sciences de la vie, secteur biomédical, nouveaux médicaments, diagnostic, spectroscopie, contrôle des wafers et masques dans le domaine de la micro-électronique, scanners, métrologie, LIDAR, lecteurs codes barres), l enregistrement et la projection d images et les systèmes d impression (imprimantes laser pour usage privé et commercial, écrans, pointeurs laser, vidéoprojecteurs, hologrammes, téléviseurs), le divertissement (spectacles de lumière) et bien d autres applications. Micro-usinage laser de la silice fondue SiO 2 et des diélectriques amorphes. Applications Un matériau d une importance primordiale et très largement utilisé est la silice fondue (figure 3). La silice fondue (voir annexe A) est un matériau diélectrique mis en œuvre dans des applications exigeant une précision élevée. Figure 3: La silice fondue est par exemple utilisée dans la fabrication de têtes de club de golf (secteur des loisirs), de composants pour l industrie automobile (chemises, etc.), de lentilles, hublots et miroirs (industrie optique), d outils de formage, etc. (industrie du verre), de creusets pour la production de cellules solaires (industrie photovoltaïque), d instruments chirurgicaux (secteur médical). Source: World Wide Web. En particulier du fait de leur extrême précision, les lasers femtosecondes sont le point clé de nombreuses applications exigeantes [2 8]. Les lasers femtosecondes permettent en effet de communiquer sous forme de photons, de réaliser des systèmes de traitement des signaux à l intérieur des matériaux transparents, d écrire des guides d ondes dans un solide, etc. [2, 5]. Les processus non linéaires qui sont facilement accessibles avec des lasers femtosecondes (conduisant à une intensité élevée localement et avec une énergie modérée) induisent une modification de la matière dans des volumes d ordre micrométrique, ouvrant ainsi une nouvelle ère pour l usinage

14 xiv de la matière. Des réalisations tridimensionnelles (3D) consistant en la réalisation de guides d onde, de micro canaux pour la micro fluidique, de coupleurs, de dispositifs de stockage binaires et de dispositifs optiques ou photoniques complexes à l intérieur et à la surface d un solide transparent par écriture laser directe et indirecte 1 sont les nombreuses applications d un laser femtoseconde [3]. Le stockage optique 3D de données peut ainsi être produit par ablation locale dans la matière en régime monotir (formation de zones «vides», ou de densité plus faible que la densité moyenne du matériau, entourées de zones plus denses), conduisant à l écriture d un 1 en code binaire, tandis que l absence d un trou (ou zone vide) est lue comme un zéro binaire [2]. La sélection «zone vide» peut éventuellement être modifiée par le système laser femtoseconde, s il est permis de réécrire sur le même substrat. Des guides d ondes peuvent être fabriqués localement point par point en modifiant l indice de réfraction et, en déplaçant le point focal dans le sens transversal ou latéral, l inscription de lignes est également possible. Une autre approche est d utiliser la filamentation du faisceau qui produit un changement d indice de réfraction suffisant pour la réalisation de guides d onde, cette technique ne demandant pas de plus la mise en mouvement du point focal du faisceau. L écriture laser directe permet d introduire des modifications de l indice de réfraction et/ou de la biréfringence, consistant en des variations périodiques de la composition des matériaux, ou l alternance de régions avec une masse volumique légèrement supérieure à la valeur nominale et de régions avec une plus faible densité. Ces régions sont d échelle submicrométrique et imprimées dans le volume irradié. Selon les caractéristiques d irradiation, des réseaux micrométriques peuvent aussi être écrits dans le volume des verres. Une autre méthode de production de réseaux consiste à utiliser l holographie (au moyen d interférence de deux faisceaux), en enregistrant une distribution d interférences sur un échantillon photosensible. Des canaux micro fluidiques peuvent être facilement fabriqués à l aide d un laser femtoseconde sur la surface et dans le volume d un diélectrique à large bande interdite. Tout d abord, un réseau avec des modifications locales du matériau, éventuellement de caractéristiques variables, est usinée par laser. Ensuite, il est gravé en utilisant une solution diluée d acide fluorhydrique permettant une attaque acide et ainsi l obtention d un réseau structuré en 2D ou 3D. Une seconde approche pour produire des canaux micro fluidiques consiste à utiliser l écriture directe par laser. Pour éviter le redépôt des débris induits par l ablation du matériau, le procédé de perçage au laser incorpore le plus souvent un fluide permettant leur évacuation. Les applications de type «lab-on-a-chip» sont ensuite réalisées par l intégration de canaux micro fluidiques et guides d ondes optiques dans un système unique et compact. Les lasers femtosecondes sont aussi 1 Résultat de deux techniques de micro-usinage indépendants, par exemple la combinaison d attaque laser et chimique [2, 9, 10].

15 xv largement utilisés pour la fabrication de cristaux photoniques à partir de la structuration d une grande variété de substrats transparents, cristaux, etc. [5]. Parmi les applications de pointe concernant les lasers femtosecondes, on peut citer le lissage de surface, la réparation des masques ou l enlèvement de défauts, le micro-usinage sélectif de matériaux complexes comme par exemple des systèmes multicouches, des lentilles de petite taille ou des composants d optique diffractive [6,7]. L étude présentée dans cette thèse met ainsi l accent sur la silice fondue, tout d abord d un point de vue fondamental. Cependant, nous pensons que la connaissance et la compréhension des mécanismes d absorption de l impulsion laser (obtenues au cours de ces travaux) pourraient être sûrement étendues à tous les diélectriques. En analysant attentivement le processus de dépôt d énergie laser dans la matière et ses conséquences, l ablation de matière, nous déterminerons également des informations importantes pour les applications de micro-usinage. Cela constituera la seconde partie de nos travaux. En conclusion de nos recherches, nous aimerions répondre en particulier à la question portant sur l intérêt (et dans quelle mesure) d utiliser un laser femtoseconde pour des applications telles que le micro-usinage à la surface d un matériau diélectrique (silice fondue) et la chirurgie au laser. Cette thèse de doctorat se compose de 4 chapitres, une conclusion générale et quelques annexes: Le premier chapitre décrit l état de l art de l interaction laser femtoseconde - diélectrique et présente une vue générale de l ablation laser d un solide, accompagnée d une modélisation de l absorption de l impulsion laser dans la matière. Le deuxième chapitre présente la méthodologie utilisée lors des travaux expérimentaux et des mesures préliminaires. Nous présentons également les mesures de seuils de dommage et d ablation d une cible diélectrique que nous distinguons en introduisant des définitions et des techniques de détection appropriées. Le chapitre trois est d abord dédié à une expérience pompe-pompe pour déterminer l absorption laser à la surface d un diélectrique et analyser la morphologie des cratères créés lors de l interaction. Les premières conclusions sont appuyées par une analyse théorique de l interaction laser-matière. Puis une expérience pompe-sonde révèle les mécanismes en jeu lors de l absorption de l impulsion laser à la surface du matériau. L objectif ici est de mesurer à la fois l évolution temporelle de la réflexion et de la transmission afin d analyser finement l évolution de l absorption du matériau.

16 xvi Cela nous permet enfin de proposer un scénario éclaircissant le dépôt d énergie d une impulsion laser femtoseconde dans un matériau et de définir une plage de fonctionnement (en termes de fluence incidente), optimale pour le traitement de surface d un matériau diélectrique. Le quatrième chapitre illustre les résultats sur l endommagement et l ablation de surface d un matériau diélectrique inerte pour des applications industrielles (perçage, rainurage). Nous montrons ensuite quelques résultats de l étude de la dissection d un tissu biologique (la cornée) par laser femtoseconde, dans le but d améliorer l application des systèmes laser femtosecondes à la chirurgie de greffe de cornée. Les annexes sont consacrées à la description des matériaux étudiés dans cette thèse et à un calcul d accord de phase non linéaire. Conclusion Le but de cette thèse a consisté à étudier et à faire la lumière sur les mécanismes de dépôt d énergie d une impulsion laser femtoseconde dans un diélectrique. La compréhension de l ablation locale d un matériau par laser femtoseconde a exigé une approche systématique concernant les différents aspects du processus: dépôt d énergie et dissipation, éjection de la matière et enfin la caractérisation des structures obtenues. La méthodologie précise et les nombreuses expériences développées au cours de cette étude ont ainsi permis d obtenir et de comparer un ensemble important de résultats concernant le processus d ablation par laser d un matériau diélectrique transparent. En particulier, la compréhension du phénomène de dépôt d énergie laser à la surface d un diélectrique a été obtenue dans le cadre de ce travail et a aussi permis de mettre en évidence l intérêt d un laser de durée d impulsion courte (subpicoseconde en l occurrence) pour le micro-usinage et la médecine. À notre connaissance, très peu d études ont porté sur autant d aspects de l interaction laser matière sur un matériau (silice fondue). Cela a notamment été réalisé au moyen de nombreuses et diverses expériences (pompe-pompe et pompe-sonde) accompagnées par une modélisation précise. Les principaux résultats obtenus au cours de cette étude sont maintenant listés ci-dessous. Mécanismes d ablation laser

17 xvii Les lasers femtosecondes permettent d accéder à l absorption non linéaire d un matériau initialement transparent (diélectrique) par ionisation multiphotonique suivie par le phénomène d avalanche électronique (ionisation par impact). La formation d une densité d électrons libres élevée dans la bande de conduction est nécessaire pour initialiser l endommagement ou l ablation par laser des matériaux à large bande interdite. Au moyen de mesures de transmission et de réflexion, nous avons observé la dépendance de l absorption laser à l énergie incidente ainsi que la dynamique de l absorption de l impulsion laser au sein du matériau. Un temps minimum et une énergie minimale (fluence), déterminés au cours de cette étude, sont ainsi nécessaires pour créer un matériau absorbant (transformation d un diélectrique initialement transparent en matière absorbante) mais présentant aussi un comportement «métallique» (matériau partiellement réfléchissant). De manière concomitante au déclenchement d une forte absorption lors du dépôt d énergie, une réflexion importante de l impulsion est également initiée. La réflexion, fortement dépendante de la partie réelle de la fonction diélectrique, augmente en effet fortement dès lors que la densité critique est atteinte et arrête temporairement (et partiellement) le dépôt d énergie. Cependant, l augmentation contrôlée de la densité d électrons libres autour de la valeur critique permet de trouver un compromis entre une absorption élevée de l impulsion laser et une réflexion accrue (mais loin d être totale). Nous avons ainsi montré que, pour des lasers de durée d impulsion subpicoseconde ( 500 fs), le dépôt d énergie se déroule pendant toute la durée d impulsion pour des fluences modérées et élevées (F > 3F th ). Nous avons aussi noté que le temps minimal pour créer un milieu absorbant se déplace vers le début de l impulsion avec l augmentation de la fluence incidente. En outre, l énergie laser déposée dans le sous-système des électrons suivie par le transfert d énergie au réseau (ions), processus qui se termine après la fin d impulsion, provoque des modifications matérielles. Dans le cas des lasers femtosecondes de durée d impulsion "longue" ( 500 fs), l ablation consiste en une succession d effets électroniques (explosion Coulombienne ou ablation électrostatique), qui se produisent pendant ou juste après la fin d impulsion, et d effets thermomécaniques, qui se produisent sur des échelles de temps plus longues par rapport à la durée d impulsion. Ces effets sont fortement localisés dans un volume micrométrique. Ils donnent ainsi accès à des procédés de micro-usinage et de dissection de tissus biologiques précis et avec des effets collatéraux faibles. Application des lasers femtosecondes au micro-usinage Pour de nombreuses applications des lasers femtosecondes, les points clés sont le contrôle du procédé, la résolution micrométrique et la reproductibilité. Nous avons démontré qu un laser

18 xviii subpicoseconde est un outil précis pour réaliser localement l ablation d un matériau diélectrique. Le mécanisme principal de l ablation laser est d origine thermique (thermomécanique), mais une mince couche de surface peut être ablatée par effet électronique. Par ailleurs, la qualité de l ablation dépend fortement de la fluence du laser appliquée à la fois en termes d efficacité d ablation (exprimée en µm 3 /µj) et de qualité du cratère d ablation final (aspect lisse des parois et du fond du cratère). Avec un système laser très stable, il est possible d atteindre une répétabilité élevée avec des caractéristiques choisies. La sélectivité élevée d ablation est obtenue grâce au caractère fortement déterministe de l interaction et par un réglage minutieux de la fluence incidente du laser. Dans notre cas, la résolution transversale et axiale est respectivement environ 1 µm et 20 nm. Enfin, l analyse des données expérimentales et théoriques fournit un outil important pour dégager des idées de mise en forme spatio-temporelle du faisceau et ainsi optimiser le dépôt d énergie laser et son utilisation lors d un procédé d interaction laser-matière. Application des lasers femtosecondes à la greffe de cornée La dissection laser ou photo disruption est basée sur les effets thermomécaniques induits par le dépôt d énergie laser. C est pourquoi les lasers femtosecondes de longue durée d impulsion (régime subpicoseconde) sont bien adaptés aux procédés de dissection des tissus. Les lasers femtosecondes ont ainsi été utilisés pour la chirurgie par laser, comme par exemple le procédé LASIK depuis 1989, pour corriger la vision (correction à faible profondeur de propagation). Aujourd hui, cette procédure est reproductible et bien adaptée aux exigences de la chirurgie. En s appuyant sur la procédure LASIK, les lasers femtosecondes possèdent un excellent potentiel pour la chirurgie lamellaire profonde, utilisée dans le cas de la greffe de cornée. Dans notre étude, nous avons ainsi cherché à améliorer la qualité (résultat fonctionnel) d un procédé laser clinique commercial de dissection et donc à satisfaire les exigences de la chirurgie ophtalmologique. Nous avons ainsi entrepris de minimiser la dose d énergie injectée laser pour accélérer le rétablissement postopératoire de la vision et un meilleur confort du patient tout en ayant le même résultat fonctionnel de découpe (voire son amélioration). Nos résultats ont ainsi permis de démontrer l amélioration de la dissection laser à forte profondeur de la cornée sans augmentation de la dose d irradiation par laser et en obtenant une surface résultante plus régulière et plus lisse, en augmentant seulement le nombre de passages laser. Perspectives

19 xix Les perspectives de cette étude s inscrivent tout d abord dans la poursuite de la recherche et de la compréhension des mécanismes d interaction d un laser femtoseconde ultra court avec un diélectrique. Aujourd hui, les lasers ultra courts sont un domaine très actif de la recherche scientifique et des systèmes laser de durée d impulsion 10 fs peut très probablement ouvrir des possibilités de résolution axiale et transversale encore plus élevées pour l ablation et la micro structuration de la matière. Les mécanismes de dépôt d énergie laser et de relaxation, tels que le couplage électron-électron et électron-phonon, pourraient être accessibles et avantageusement étudiés avec un laser femtoseconde ultra court. Cette étude pourrait aussi aider à faire la lumière sur l applicabilité des modèles théoriques existants. En effet, nous avons noté par exemple que l approche théorique largement acceptée, basée sur le modèle de Drude, devrait être probablement affinée ou révisée selon les observations relatives à la dépendance de la fréquence de collision électron phonon à la concentration et à la température des électrons et aussi en raison de la différence des conditions initiales pendant l interaction laser avec un matériau tout d abord de type diélectrique puis évoluant vers un état métallique. Aller vers une meilleure définition du comportement de la fonction diélectrique d un matériau transparent sous irradiation intense est à notre sens un domaine d étude théorique et expérimental très intéressant. En ce qui concerne l étude du procédé de greffe de cornée par laser femtoseconde, il est nécessaire de collecter davantage de données, concernant par exemple l absorption d éléments chimiques tels que le sodium, le potassium, ou le soufre dans la région du proche infrarouge, afin de mieux comprendre l absorption laser dans un tissu biologique transparent comme la cornée. Déterminer précisément l influence de l élasticité et de la concentration en eau des tissus sur le mécanisme de dissection par laser sera aussi instructif pour perfectionner le processus de photo disruption laser. Ensuite, il sera important de mener à bien des études cliniques supplémentaires afin de déterminer le niveau optimal de l énergie laser en mode de fonctionnement clinique (en termes d efficacité de coupe, de régularité de surface postopératoire et de temps et qualité de récupération visuelle des patients). Cette étude viserait à augmenter la fiabilité du procédé, le confort et la rapidité de la guérison du patient, et la qualité de reproductibilité des résultats cliniques en utilisant des conditions d opération permettant la minimisation des effets collatéraux induits lors de l acte chirurgical. Enfin, si l on tient compte des avantages d un laser femtoseconde, en particulier dans le domaine de la biologie, la compréhension des mécanismes d interaction avec la matière vivante et le dépôt de dose minimale d irradiation laser permettraient d étudier l ADN de manière non-thermique et donc non-destructive (analyse quantitative de l ARN, etc.), et de réaliser l impression laser de biomatériaux et la fabrication de biosystèmes.

20 xx Résumé long De nombreux processus fondamentaux d interaction laser - matière ont lieu sur des échelles de temps de l ordre de quelques femtosecondes à plusieurs centaines de picosecondes. Dans le cadre de cette thèse, nous étudions plus particulièrement l interaction d un laser femtoseconde avec une cible diélectrique. La partie fondamentale de ces travaux vise à décrire le processus de dépôt d énergie laser au sein de la matière, sa redistribution au réseau et l éjection de matière (ablation). Dans ce contexte, nous mettons aussi en évidence l intérêt des lasers femtosecondes pour la modification précise et locale d un matériau (notamment en termes d endommagement et d ablation de la surface) pour des applications telles que le micro-usinage des diélectriques et la chirurgie de la cornée par laser. L ablation laser est une suite de phénomènes complexes constituée des phases suivantes: excitation des porteurs libres (électrons) suivie de leur thermalisation, transport, diffusion et relaxation des porteurs, effets thermiques et structurels. Lorsque l énergie d un laser femtoseconde est déposée à la surface d un matériau diélectrique, les électrons de valence sont excités vers la bande de conduction par l intermédiaire de deux phénomènes: la photo ionisation (ionisation multi photonique et/ou effet tunnel selon les caractéristiques d interaction définies dans le cadre du paramètre de Keldysh) suivie par un chauffage des porteurs libres (électrons) par effet Joule et la mise en place d un mécanisme d avalanche électronique (ionisation par impact). D un point de vue thermodynamique, le processus de dépôt d énergie en régime femtoseconde est fortement hors-équilibre pour les sous-systèmes électronique et ionique (T e T i ). Cela signifie que le plasma d électrons libres est «chaud» et le réseau (matrice des ions) "froid" ou en d autres termes "gelé" («frozen» en anglais) lors de l interaction. Le processus de thermalisation (dépôt d énergie dans la matrice) se déroule ensuite de la manière suivante: la diffusion électron - électron conduit à l équilibre thermique de la population d électrons au cours de l impulsion, puis la diffusion électron - phonon conduit au transfert de l énergie du sous-système électronique au sous-système des ions, cette phase étant complètement réalisée après la fin de l impulsion incidente, à l échelle de quelques picosecondes dans un grand nombre de matériaux selon les caractéristiques de couplage électron-phonon. A l issue de cette phase de thermalisation, l équilibre thermique des sous-systèmes électronique et ionique est atteint (T e T i ). L élimination complète des porteurs est approximativement obtenue lorsque l équilibre thermique est atteint. Ce processus inclut la recombinaison non-radiative (recombinaison Auger, génération de défauts en volume et en surface et recombinaison de surface), la recombinaison radiative et la diffusion des porteurs. En outre, dans l état d équilibre thermique, si la température du réseau dépasse le

21 xxi point de fusion, d ébullition ou de sublimation, les processus de fusion, évaporation ou ablation peuvent avoir lieu. Le panache d ablation (contenant électrons, ions, agrégats et autres produits d ablation) se forme et se développe au dessus de la surface du matériau. Dans le même temps, la localisation du dépôt d énergie et, par conséquent la modification de température extrêmement locale ainsi que la présence de conditions initiales fortement hors équilibre (présence d électrons «chaud» des électrons et d un réseau «froid» lors de l impulsion laser) provoque la création d ondes de pression de forte amplitude et de dynamique rapide. Le mouvement hydrodynamique est le fruit de deux ondes de pression (ondes de compression et de raréfaction) se déplaçant dans des directions opposées. Dans les matériaux diélectriques, l action combinée des effets de température et de pression conduisent à la création d un cratère d ablation entouré par une zone fondue. Dans cette zone, le chauffage n est pas suffisant pour faire fondre la matière mais peut provoquer des changements réversibles ou irréversibles. Dans cette étude, nous essayons de progresser dans la compréhension de la toute première étape de l interaction, en particulier, la phase de dépôt d énergie laser dans la matière (phase d ionisation), et ensuite de bien appréhender les mécanismes de redistribution au réseau. Nous portons ainsi une attention approfondie à ces mécanismes afin de mieux définir les domaines d application des lasers femtosecondes de longue durée d impulsion (plusieurs centaines de femtosecondes) et de définir leur zone d efficacité maximale. En outre, les résultats expérimentaux notamment obtenus à partir d expériences pompe-pompe et pompe-sonde, et accompagnés par une modélisation théorique, nous permettent de mieux comprendre l ablation de matériaux diélectriques par laser. Dans un premier temps, nous établissons la différence entre endommagement et ablation. Il est en effet important de distinguer ces deux modifications résultant de l interaction lasermatière, comme cela est montré dans ce travail. Souvent, dans la littérature, ces deux types de modifications matérielles (énergétiquement proches par rapport à la fluence appliquée) sont confondus en régime femtoseconde, les techniques de détection et/ou les définitions de seuil (lorsque celles-ci sont données) utilisées ne permettant pas de les discerner. Selon la fluence du laser appliquée et par ordre croissant, on distingue: des modifications structurelles transitoires ou permanentes telles qu un changement local de phase ou d indice de réfraction, mais ne conduisant à aucun changement visible de la topographie de surface. des dommages irréversibles accompagnés par un changement de morphologie de surface sans aucune variation significative de la masse de la cible (c est-à-dire sans enlèvement de matière). Le dommage résultant peut être une compression la matière, ou de manière plus générale, sa réorganisation (fusion, resolidification, etc.).

22 xxii l obtention d une ablation (enlèvement de matière), modification substantielle 3D de la matière, caractérisée par des caractéristiques géométriques telles que le diamètre, la profondeur et le volume du cratère obtenu. Nous proposons donc une méthodologie pour mesurer précisément les seuils de dommage et d ablation de matériaux diélectriques. Le seuil de dommage est défini par microscopie optique au moyen d une analyse statistique. Pour cela, nous réalisons une matrice d impacts laser sur le matériau de N M points (N est le nombre d essais, généralement au nombre de 20, M est le nombre de fluences testées, généralement une quinzaine). Nous déterminons ensuite le seuil en comptant le nombre de sites endommagés pour chaque fluence donnée. Chaque essai correspond à un tir laser unique (1025 nm, 500 fs, ω 0 = 6.3 µm), réalisé chaque fois sur un site frais (sans aucune irradiation laser préalable). La fluence maximale pour laquelle la probabilité d endommagement est nulle définit la valeur du seuil de dommage (4.4 J/cm 2 dans nos conditions, test sur silice fondue SiO 2 de qualité Suprasil). Le seuil d ablation est défini par microscopie à force atomique (AFM) en étudiant l évolution de la mesure du volume ablatée et/ou du diamètre du cratère en fonction de la fluence appliquée. L interception de la courbe au volume (ou diamètre) nul permet de déterminer le seuil d ablation (5,9 J/cm 2 en utilisant la courbe de régression utilisant la donnée du volume et 6 J/cm 2 au moyen du diamètre). En outre, la même technique (étude du diamètre ablatée) mais utilisant un diagnostic différent (microscopie optique) conduit à une valeur similaire (incertitude totale d environ 15%) par rapport à celle déterminée par AFM. Cette technique (microscopie optique) diminue le temps de traitement des données, mais ne permet pas de disposer des caractéristiques tridimensionnelles du cratère et, de plus, elle est considérée comme moins précise que celle reposant sur l utilisation d un AFM, ce dernier possédant une meilleure résolution spatiale et définissant sans aucune ambigüité la topologie de surface à l échelle nanométrique. Nous décrivons et discutons aussi la méthodologie pour effectuer des mesures précises au moyen d un banc expérimental, spécifiquement dédié aux études d endommagement et d ablation. Nous montrons que les effets non-linéaires (autofocalisation, ionisation de l air) et les aberrations sont réduits en raison du choix pertinent de la longueur focale de la lentille utilisée et du contrôle de l intensité locale (énergie incidente). En outre, nous estimons l incertitude totale des mesures expérimentales de seuil (somme des incertitudes liées à la détermination de la taille du faisceau ou «beamwaist», à la mesure d énergie, à la stabilité tir à tir des impulsions laser, à la composition du matériau et au traitement post mortem) à environ 20 à 25% pour nos expériences. Par la suite, une légère modification du banc d essai expérimental nous permet d étudier la dépendance de l énergie absorbée en fonction de la fluence du laser appliquée. Nous mesurons

23 xxiii ainsi l énergie laser incidente, réfléchie et transmise (E inc, E refl, E trans ) au moyen de trois photodiodes. Dans cette expérience, seule la composante spéculaire de la réflexion et la transmission (R spec, T spec ) est prise en considération. L absorption laser est ensuite déduite de la formule suivante: A = E abs /E inc = 1 R spec T spec = 1 E refl /E inc E trans /E inc Pour une meilleure compréhension de l évolution expérimentale de la réflexion, de la transmission et de l absorption du laser par la matière dans une large gamme d énergie incidente, nous développons une modélisation basée sur la propagation de l impulsion laser dans un milieu diélectrique et l équation d ionisation de ce dernier par le laser. La propagation est définie par l équation de Helmholtz à une dimension qui donne la répartition du champ électromagnétique dans la cible avec un profil temps-espace de la permittivité calculé en chaque point. La solution de cette équation donne immédiatement l absorption de l énergie laser en chaque point du maillage (espace et temps) et les coefficients complexes de réflexion et transmission. En outre, le modèle à deux températures décrit précisément le processus fortement non-équilibre du dépôt d énergie (T e T i ). L évolution de la densité d électrons libres est calculée à partir de la formulation exposée dans [11] et déduite de la théorie cinétique. Les calculs monodimensionnels sont ensuite complétés par une approche bidimensionnelle grossière afin de mieux reproduire les résultats expérimentaux. L intégration sur le diamètre du faisceau permet de prendre en compte la variation locale de la densité d électrons libres et de la permittivité, et donc par suite de la transmission et de la réflexion. Les courbes théoriques et expérimentales (voir figure 4) de la réflexion, transmission et absorption en fonction de la fluence incidente mettent en évidence: Au seuil d endommagement (F th ), l absorption est égale à quelques pour cent ( 2%) de la fluence incidente définissant l énergie minimale devant être déposée pour transformer le diélectrique en milieu absorbant. Au seuil d ablation (1,3 F th ), l énergie absorbée atteint presque 25% de l énergie incidente définissant l énergie pour créer un milieu fortement absorbant. L absorption sature à environ 60% à fluence élevée. L énergie restante est divisée entre énergie réfléchie et partiellement transmise par le plasma. La différence de pente observée lors des variations de réflexion de transmission en fonction de la fluence met en évidence l évolution des modifications du matériau, qui, initialement transparent, évolue ensuite vers un état fortement absorbant puis réfléchissant (en particulier à haute fluence). Nous pensons qu un temps et une dose d énergie minimums sont nécessaires pour convertir le matériau diélectrique en milieu absorbant opaque, possédant des propriétés similaires à celles d un métal.

24 xxiv La modélisation reproduit fidèlement l évolution de la réflexion et la transmission pour des fluences faibles (< 10 J/cm 2 ). Par contre, nous observons un écart significatif entre la réflexion théorique et expérimentale à fluence incidente élevée (> 10 J/cm 2 ). Cela peut s expliquer par une mauvaise collection ou perte partielle du signal expérimental, une surestimation théorique de la réflexion ou la combinaison de ces deux effets. En ce qui concerne le premier aspect, nous avons apporté le plus grand soin à l obtention de nos mesures expérimentales. En outre, nous vérifions que l expansion du plasma (source de diffusion) et la perte de signal consécutive lors de la mesure sont négligeables. Figure 4: Courbes expérimentales de réflexion R, transmission T et absorption A en fonction de la fluence normalisée (par rapport au seuil de dommage F th ). Les barres d erreur représentent l écart-type des données correspondant à une moyenne sur 20 essais environ. La courbe du bas montre l évolution de R, T et A à proximité des seuils de dommage et ablation.

25 xxv A fluence élevée, la vitesse d expansion de plasma est probablement comprise entre v = cm/s (vitesse observée à fluence incidente faible, F = 5 J/cm 2, et mesurée à une échelle de temps nanoseconde) et v = cm/s (vitesse observée à fluence élevée, F = 50 J/cm 2, pour une impulsion de durée τ L = 60 fs). La distance d expansion du plasma à la fin de l impulsion laser est ainsi estimée entre 15 nm (à faible fluence) à 50 nm (à fluence élevée). Ces valeurs sont négligeables par rapport à la profondeur de champ de l optique de collection. En outre, l expansion du plasma aux temps courts (à l échelle de l impulsion) est largement monodimensionnelle et la perte de signal expérimentale est donc probablement très faible. On peut également s interroger sur la validité du modèle théorique et, en particulier, l applicabilité du modèle de Drude. Ce modèle «fonctionne» bien lorsque la fonction diélectrique est constante dans chaque couche mais se révèle beaucoup moins précis lorsque le gradient de densité et de la fonction diélectrique en chaque point (temps et espace) change rapidement. Nous pensons que l expression de la fonction diélectrique devrait prendre en compte de manière plus complexe les gains et pertes de l énergie électromagnétique à travers une formulation améliorée et plus précise afin de mieux décrire l interaction d une cible diélectrique avec une impulsion laser incidente. En outre, la réflexion est très sensible au choix du paramètre de la fréquence de collision électron-phonon. Dans nos calculs, ce dernier est recalculé, à chaque pas de temps et pour chaque cas de fluence, en fonction de la fluence réellement appliquée (prise en compte de la déplétion de la pompe) permettant d appréhender la dépendance temporelle de ce paramètre. Cependant, nous pensons que les approximations théoriques, qui sont faites ici, pourraient être rediscutées et précisées (en particulier en utilisant des mesures et modélisations spécifiques toutefois en dehors du champ d application de cette thèse) pour mieux prendre en compte l évolution temporelle du paramètre de collision électron-phonon, en particulier à des fluences élevées. En outre, la modélisation ne prend pas en compte la transition entre un plasma essentiellement composé d électrons libres et un plasma en expansion contenant un nombre croissant (en particulier à haute fluence) de différentes espèces (électrons, ions, neutres) et particules (agrégats). Par conséquent, il ne définit pas, complètement et exactement, les modifications du matériau par l impulsion laser. En outre, nous supposons aussi que d autres phénomènes physiques, non pris en compte dans la modélisation, peuvent éventuellement devenir significatifs à fluence élevée. Pour compléter notre étude de l absorption d énergie laser par une cible diélectrique, nous effectuons une expérience pompe-sonde. De même que lors de l expérience pompe-pompe, nous mesurons la réflexion et la transmission et en déduisons ensuite l absorption (voir figure 5 et figure 6). Nous obtenons ainsi des informations supplémentaires sur la dynamique d absorption et du dépôt d énergie laser sur une large plage de retards temporels (- 3 ps à 100 ps) et pour une large gamme de

26 xxvi fluences. L instant de retard (ou délai) «zéro» t 0 correspond au maximum de l impulsion pompe. L impulsion sonde est en incidence oblique (26 ) et l instant t 0 est déterminé à l aide de la génération de second harmonique en mode non colinéaire. Il est important de noter que les résultats expérimentaux sont le produit de convolution d une pompe (durée totale de 1000 fs) avec une sonde (durée totale de 1120 fs). Les courbes de réflexion et de transmission se comportent différemment avec en particulier des dynamiques et pentes différentes pour revenir à leurs valeurs initiales au repos. L ensemble des courbes théoriques et expérimentales permet tout d abord de conclure que la dynamique de l absorption est sensible à l énergie (fluence). La transmission expérimentale décroît en douceur après avoir atteint son minimum et, pour des fluences faibles, retourne à sa valeur initiale en suivant une forme analogue à celle du faisceau (forme gaussienne). A fluences élevées, après la fin du faisceau pompe, la transmission sature en dessous de sa valeur initiale et reste constante jusqu à plusieurs centaines de picosecondes. La valeur minimale de transmission résiduelle à des fluences élevées est égale à 0,45, très largement en dessous de la valeur initiale de transmission. L augmentation de la réflexion expérimentale est retardée par rapport à la transmission et la valeur maximale est égale à environ 7%. Nous définissons le temps d apparition du miroir plasma par une augmentation de la réflexion de 10% par rapport à sa valeur initiale. Ce temps passe du front descendant de l impulsion à sa partie avant au fur et à mesure de l accroissement de la fluence. En outre, le temps de construction d un plasma réfléchissant (ou écranteur, effet de «miroir plasma») est déterminé en prenant le critère d augmentation de la réflexion de 1,5 fois la réflexion initiale. Il s établit pendant le front descendant de l impulsion à faible fluence et sature à environ 150 fs avant le maximum de l impulsion aux fluences élevées. Dans nos conditions, l effet de miroir plasma n est pas très élevé (loin d être total) et retardé par rapport à la fenêtre d absorption efficace de l énergie incidente. En résumé et pour schématiser, la partie avant de l impulsion est transmise et le reste de l impulsion est partiellement absorbé et partiellement réfléchi dans nos conditions, en conformité avec les références [12, 13]. Cela valide notre hypothèse sur l existence d un temps minimal pour créer un milieu absorbant puis réfléchissant, définissant ainsi une "fenêtre" temporelle où le dépôt d énergie est efficace. Le temps de retard pour créer un matériau très absorbant et réfléchissant est sensible à la fluence appliquée et suit un comportement non linéaire (exponentiel, selon une loi du type a + bexp(cf), avec c < 0) en fonction de la fluence. Avec l augmentation de la fluence laser incidente, le temps minimal pour créer un milieu très absorbant diminue jusqu à 50 fs ( 10% de la durée d impulsion FWHM). La durée d absorption de l énergie laser incidente augmente avec la fluence et est égale à quasiment la totalité de

27 xxvii Figure 5: Évolution de la réflexion en fonction du délai pompe-sonde. a) Réflexion sur de longs délais pompe-sonde (- 3 ps à + 10 ps). b) Evolution de la réflexion lors de l impulsion pompe incidente (- 1 ps à + 1 ps). l impulsion incidente à fluence élevée. Un autre point intéressant est que, à haute fluence, la réflexion décroît beaucoup plus rapidement qu à faible et moyenne fluence. Des mesures supplémentaires de transmission et le calcul de l épaisseur de matière ablatée par effet électronique permettent de mettre en évidence des preuves d ablation électronique rapide (explosion Coulombienne ou ablation électrostatique). Cet effet se produit rapidement après la fin de l impulsion (échelle ps) et explique ainsi les ruptures de pente observées sur les courbes de réflexion et transmission à haute fluence. En outre, nous constatons que l ablation électronique constitue environ 10% de la matière ablatée totale quelle que soit la fluence et atteint environ 30 nm à fluence élevée. Ensuite, dans le but de reproduire les profondeurs d ablation obtenues expérimentale-

28 xxviii Figure 6: Évolution de la transmission en fonction du délai pompe-sonde. a) Transmission sur de longs délais pompe-sonde (- 3 ps à + 10 ps). b) Evolution de la transmission lors de l impulsion pompe incidente (- 1 ps à + 1 ps). ment et mesurées par l AFM, nous estimons l importance énergétique du dépôt d énergie dans la matière selon la profondeur. Les critères thermodynamiques utilisés, à titre de comparaison avec le régime d un dépôt d énergie constamment à l équilibre, sont les enthalpies de fusion ( H f = 0,28 kj/cm 3 ) et sublimation ( H sub = 21,4 kj/cm 3 ) ainsi que l énergie de liaison ( E = 54 kj/cm 3 ). Nous reproduisons ainsi l évolution relative de la profondeur ablatée, mais d un point de vue quantitatif, les valeurs obtenues en considérant H sub ou E sont sous-estimées. En fait, si l on considère la décomposition totale de la matière (critère basée sur l énergie de liaison), nous ne parvenons pas à reproduire les profondeurs expérimentales par un facteur important. L écart est cependant plus faible si l on considère le critère de sublimation. La comparaison des

29 xxix mesures expérimentales avec les calculs théoriques montre ainsi que l ablation est un processus présentant des effets thermiques importants pour des impulsions laser subpicosecondes. Le procédé d ablation est ainsi majoritairement le résultat de processus de fusion, évaporation et de propagation d ondes de pression (effet mécanique, non estimé dans ce travail) dans le matériau sur des échelles de temps plus longues (> 10 ps) que la durée d impulsion. Par ailleurs, les calculs théoriques et le traitement des données expérimentales mettent en évidence le processus hautement non-équilibre du dépôt d énergie. La température électronique atteint ainsi 60 ev et la température du réseau environ 11 kk à la fin de l impulsion laser (F = 53,2 J/cm 2, couche de surface). Dans ces conditions, l énergie incidente est absorbée de manière importante (jusqu à 60%) et durant à peu près la totalité de l impulsion. La comparaison de l enthalpie de sublimation et de l énergie absorbée par le diélectrique considérant le volume défini par le diamètre d ablation confirme qu une grande quantité d énergie ( 5 fois l énergie de sublimation près du seuil) est déposée localement pour transformer le matériau initialement transparent en un milieu très absorbant. En outre, à fluence élevée, l énergie absorbée par la cible augmente de manière importante jusqu à près de 75 fois l énergie de sublimation! Nous supposons donc que, à fluence élevée, le panache d ablation contient des particules très énergétiques. Le contexte applicatif de ce travail est dédié au micro-usinage par laser femtoseconde de matériaux diélectriques (Si0 2 à titre d exemple) et à la chirurgie oculaire par laser (greffe de cornée). L intérêt des lasers femtoseconde pour le micro-usinage réside dans la capacité de prédire les résultats finaux d ablation (en termes de diamètre, forme et profondeur du cratère). Ainsi, nous analysons les caractéristiques d ablation en fonction de la fluence normalisée (par rapport au seuil de dommage). En outre, la qualité de l ablation et la résolution de gravure obtenue avec notre système laser est déterminée. L étude du dépôt d énergie laser montre qu il existe un régime optimal de travail (en termes d une plage de fluence permettant de maximiser l efficacité d enlèvement de matière, exprimée en µm 3 /µj), produisant un rendement élevé du dépôt d énergie et de l ablation laser. Ce régime optimal d efficacité d ablation est situé entre 2,8 F th et 12,5 F th (13 et 55 J/cm 2 ) pour nos conditions laser (500 fs, 1030 nm). L augmentation de la fluence laser au-dessus de la fluence minimale pour créer un milieu absorbant conduit à une croissance rapide de l efficacité d ablation jusqu à 2,8 F th. L efficacité d ablation diminue ensuite de manière importante lorsque la fluence incidente est supérieure à 12,5 F th. Cela est dû à l effet d écrantage par le plasma qui se forme rapidement au cours de l impulsion, affectant le dépôt d énergie. En dessous de 2,8 F th, l efficacité d ablation est faible pour le micro-usinage, en raison de la nature fortement non-linéaire de l absorption. De plus, la qualité de gravure (ou d écriture) est faible: la forme et la morphologie du cratère d ablation est ainsi par exemple

30 xxx fortement irrégulière à 1,7 F th (proche du seuil d ablation). La forme du cratère est gaussienne avec une rugosité élevée des parois et du fond du cratère. La profondeur maximale atteinte à cette fluence est de l ordre de 65 nm et le diamètre du cratère est 4,5 µm. Lorsque la fluence incidente augmente, la profondeur et le diamètre du cratère s accroissent, mais une faible qualité de micro-usinage (irrégularités en fond de trou) est toujours observée à 2,8 F th. Dans la plage de fluence correspondant à une efficacité optimale (2,8 F th < F < 12,5 F th ), la forme du cratère évolue d une forme Gaussienne vers un aspect «top-hat» et les parois et fonds de cratère deviennent lisses et régulières (faible rugosité). Pour une durée d impulsion donnée, si la fluence appliquée est soigneusement sélectionnée, un laser supbicoseconde peut permettre une haute sélectivité d enlèvement de matière (ablation) en termes de profondeur ( 20 nm) et de diamètre ( 1 µm). En outre, les valeurs maximales pour la profondeur d ablation atteignent 300 nm ( 0,003 fois la zone de Rayleigh) et pour le diamètre 13 µm (environ 2 fois la taille du col du faisceau). La résolution axiale (profondeur du cratère) dépend principalement de la fluence locale (intensité locale) et la résolution transversale de la fluence totale. Nous supposons que la forme temporelle de l impulsion la plus efficace pour le micro-usinage consisterait en une courte ( 50 fs ou moins) et forte (haute fluence) pré impulsion pour créer un milieu très absorbant, suivie par un plateau de longue durée et d énergie (fluence) moyenne à faible pour une absorption efficace de l énergie et des caractéristiques de micro-usinage (perçage, gravure, etc.) optimales. L aspect médical de ce travail vise à optimiser la dissection cornéenne profonde par laser (cadre d application : greffe de cornée), en étudiant l influence de paramètres susceptibles de minimiser la force d enlèvement du capot et la rugosité de surface du substrat résiduel après traitement laser. Cette procédure de greffe est aujourd hui réalisée, mais de manière non optimale, dans les hôpitaux et cliniques au moyen de systèmes commerciaux ayant des caractéristiques similaires à celui du laboratoire. La dissection laser des couches antérieures ( 200 µm) et postérieures (> 400 µm) de la cornée sans altération de la surface et des couches sous la surface est destinée à augmenter le confort et la sécurité du patient ainsi que la qualité du résultat fonctionnel (procédé). Cette partie de l étude regroupe 3 laboratoires (CHU La Timone, LP3 et Institut Fresnel). Les résultats, obtenus sur 15 cornées exploitables (30 cornées traitées au total), permettent de dégager des tendances, qui devront être confirmées dans un proche avenir. Nous observons tout d abord que l augmentation du nombre de passages par laser, en accroissant l énergie totale déposée (effets cumulatifs), simplifie la séparation du greffon du substrat cornéen. En outre, cela procure une surface tissulaire résultante plus lisse facilitant ainsi la récupération de la vision et une guérison totale, ainsi que la diminution des complications postopératoires. Nous démontrons aussi la diminution de la force et de l énergie de traction nécessaire pour sé-

31 xxxi parer le greffon du substrat cornéen (reproduction en laboratoire du geste du chirurgien pendant l intervention) avec la profondeur de la cornée. Nous supposons que cela est dû à la différence de structure des couches antérieures et postérieures de la cornée. En outre, le niveau plus élevé d hydratation dans le stroma postérieur peut augmenter l absorption laser et conduire à une séparation plus facile du capot cornéen de son substrat. Il serait également intéressant d étudier de manière spécifique l absorption des éléments biochimiques composant le stroma cornéen dont la composition varie fortement en fonction de la profondeur (couches postérieures et supérieures de la cornée). Le but de cette thèse a donc consisté à étudier de manière précise et, par suite, de faire la lumière sur les mécanismes de dépôt d énergie laser dans un diélectrique. La méthodologie développée et le nombre d expériences réalisées au cours de cette étude ont aussi permis d obtenir et de comparer différents résultats concernant le processus d ablation laser d un milieu diélectrique transparent. En particulier, la compréhension de la phase de dépôt d énergie obtenue dans ce travail a permis de définir des conditions optimales d utilisation des lasers femtosecondes de longue durée d impulsion (500 fs) pour le micro-usinage des matériaux solides transparents inertes (SiO 2 ) et tissulaires (chirurgie de la cornée).

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33 Contents Introduction 1 1 State of the art/background and review of earlier works Introduction Material ionization with femtosecond laser pulse Carrier excitation Optical field ionization Avalanche ionization Carrier scattering, transport/transfer of the laser energy, lattice thermalization Hydrodynamic motion, thermomechanical effects, structural modification, resolidification Modelling of the ionization of transparent dielectric Description of the model Electron density, material excitation Material response Electron and ion temperatures. Two temperature model Laser energy absorption, reflection and transmission Conclusion Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses Introduction Structural modification: damage or ablation. Experimental techniques for estimation of ablation and damage threshold values Introduction Classification of material modifications Diagnostics, methodology and definitions Technique of damage detection Technique of ablation detection Experimental set-up Laser parameters Sample positioning and diagnostics Remarks on the choice of the lens focal length Aberrations Self-focusing and air ionization Precision of measurement and error bar estimation Single experiment Choice of the number of experimental trials Error bar related to laser parameters Postmortem treatment xxxiii

34 CONTENTS xxxiv Reproducibility of results Conclusion Damage and ablation thresholds of fused silica Conclusion Analysis of energy deposition Introduction Pump depletion. Energy balance as a function of incident fluence Pump-pump experimental test-bench Pump-pump experiment Measurement Results Analysis Choice of the constants and input data. Influence of the effective electron background collision frequency Comparison of theoretical and experimental curves Conclusion Temporal dynamics of energy deposition: pump-probe experiment Some relevant previous results Pump-probe experimental test-bench Sample positioning. Focusing pump and probe beams. Preliminary experiments Spatial overlapping of the laser spots on the sample surface Second harmonic generation for superposing two laser beams temporally Measurement of reflection and transmission strongly below the threshold of material modification: correct alignment of delay line Reflection, transmission and absorption during the pulse Time resolved analysis of energy deposition Timing of absorption process Reflection, transmission and absorption on long temporal delays Energetic considerations Conclusion Experimental observation of the evolution of reflection, transmission and absorption signals as a temporal response on the laser irradiation (Pump-probe experiment) Introduction Pump-probe experimental test-bench Sample positioning. Focusing pump and probe beams Spatial overlapping of the laser spots on the sample surface Generation of the second harmonic of the laser for superposition two laser beams temporarily Estimation of the phase matching angle for non-collinear SHG Estimation of the interaction area for non-focused and focused beams Reflection, transmission and absorption as functions of time in theory and experiment Energy balance. Distinction between damage and ablation thresholds Moment of the beginning and end of absorption. Absorption duration Comparison of the theoretical and experimental time scales for energy deposition

35 CONTENTS xxxv Efficiency of the 500 fs laser, optimal F Conclusion Applications: micromachining of dielectrics and biological tissues Introduction Application of femtosecond lasers for drilling Experimental study of the femtosecond laser interaction with the corneal tissue Corneal diseases History of treatment of corneal disease and interest of laser-based process Measurement of laser induced modifications of biological tissue Study of laser fluence yielding tissue modification Damage threshold measurement and interpretation Study of the clinical corneal graft process Corneal dissection (CHU La Timone) Traction measurement: laser parameter optimization for corneal graft surgery (LP3) Measurement of the resultant surface roughness (Fresnel Institute) Results and discussion Conclusion Conclusion 167 Annex A: Structural characteristics of fused silica 171 Annex B: Estimation of phase matching angle for non-collinear SHG 177 Annex C: Human eye 181 Bibliography 186

36 CONTENTS xxxvi

37 Introduction The evolution of laser systems inevitably stimulates the development of practical applications and vice-versa. As applications and social and economical requests evolved, laser technology requirements evolved in response to them. At the beginning of their history femtosecond lasers were installed only in large-scale laboratories, because of their complexity, their low reliability and maintenance difficulty. Developments and achievements of ultra-short pulse technologies allowed the international competition for production of industrial femtosecond lasers and development of new applications demanding competences in different research fields such as solid state physics, material science as well as know-how in optical technologies. That implies a good knowledge of laser-matter interaction and maintenance of a high level of associated industrial technological development. General overview of laser micromachining, tendencies According to Laser Focus World [1] after an important decrease in world wide commercial revenues in 2009, there is again an increase on demands of laser technologies (see fig. 1). Figure 1: Evolution of worldwide revenues of commercial lasers in the period:

38 Introduction 2 The forecast for 2010 assume a total annual revenue of 60 % for diode and 40 % for nondiode lasers. presented in fig. 2. Demands of laser technologies cover a large spectrum of applications as Figure 2: Distribution of commercial interest in laser applications. The most important are: communications and optical storage and material processing. In the industry of communications and optical storage, lasers are used for tele- and data communication, for transceivers and in optical amplifiers. Material processing includes such industries as metal processing (welding, cutting, annealing, drilling), semiconductor and microelectronic manufacturing (lithography, inspection, control, defect analysis and repairing, via drilling), marking of all types of materials (plastic, metals, silicon), rapid phototyping, desk-top manufacturing, micromachining, embossed holograms, grating manufacture. Other less important segments are: medical therapy (ophthalmology, photocoagulation, therapy, cosmetic applications including wrinkle removal and hair removal); scientific and military research (fundamental research and development at universities and large laboratories as National Ignition Facility or NIF, free electron x-ray laser - Linac Coherent Light Source, etc.); instrumentation and sensors (life-science sectors, biomedical instruments, drug-delivery, diagnostics, spectroscopy, wafer and mask inspection, scanners, metrology, LIDAR, barcode readers); image recording (pre-press systems and laser printers for private and commercial use); displays and entertainment (light shows, televisions, laser pointers, video projectors, holograms) and others. Laser micromachining of SiO 2 and amorphous dielectrics. Applications A material of paramount importance that is used all over is fused silica (fig. 3). Fused silica

39 Introduction 3 (see Annex A) is a dielectric material implemented in applications demanding high precision. Figure 3: For instance, fused silica is used to make: golf club heads in the recreational industry; casting water jackets for core stability in the automotive industry; lenses, mirrors, windows, forming tools, etc. in the glass industry; crucibles that produce solar cells in the photo-voltaic industry; surgical instruments and inserts in the medical industry. Source: World Wide Web. In particular, as they give extreme precision, femtosecond lasers are the key point to many high demanding applications [2 8]. Femtosecond lasers are of interest to produce photonics communications, signal processing systems inside transparent materials, to write waveguides in a bulk solid [2, 5]. Nonlinear processes that are easily accessible with femtosecond lasers are responsible for the material modification due to the high intensity focused in a small micrometric volume opening a new era of material machining. Three dimensional achievements for waveguiding, microchanelling, microfluidics, couplers, binary storage devices, integration of photonic and three-dimensional (3-D) optical devices inside and at the surface of a transparent solid by directand indirect 2 -writing are the numerous applications of a femtosecond laser [3]. Optical 3D data storage could be produced by single shot material ablation (void formation), that will represent 1 in binary code and the absence of a hole reads as a binary zero [2]. The void position could be changed by the same femtosecond laser system allowing information to be rewritten on the same substrate. Waveguides could be fabricated by localized point-by-point modification of refractive index while moving the focal point in transversal or lateral direction for line inscription. Another approach is beam filamentation that produces refractive index change sufficient for waveguides and does not demand for the focus moving. Direct-writing allows birefringence and refractive index changes consisting in a periodic laserinduced variation in material composition, the alternation of regions with slightly higher or nominal density with regions of much lower density. Those regions are of submicrometric-scale and imprinted in the irradiated volume. Depending on irradiation characteristics they can also 1 Result of two independent micromachining techniques, for instance combination of laser and chemical attack [2, 9, 10].

40 Introduction 4 present micrometer gratings in the bulk of glasses. Another method of grating production resides in holography (by means of interference of two beams), when storing the interference pattern on a photosensitive sample. Microfluidic channels could be easily fabricated with the help of femtosecond laser on the surface of a wide bandgap dielectric and in bulk. First, a grating with changed density stripes is machined by laser. Then it can be etched by diluted solution of hydrofluoric acid, producing 2D or 3D hollows along stripes. A second approach to produce microfluidic channels is laser direct-writing. To avoid debris caused by optical breakdown, a wetting fluid most often accompanies the process of laser drilling. Lab-on-a-chip applications are further enhanced by the integration of microfluidic channels and optical waveguides into a single device. Femtosecond lasers are widely used for photonic crystal fabrication from large variety of transparent substrates such as different glasses, crystals and etc. [5]. Among cutting edge applications for femtosecond lasers, one can mention surface smoothing, photomasks repairing or defects removing; the selective micromachining of complex multi-layer devices and small size lenses or diffractive optical elements [6, 7]. The present study focuses on fused silica, first, from the fundamental point of view. The knowledge and comprehension of the mechanisms of laser pulse absorption could be further extended for all dielectrics. By analyzing carefully the laser energy deposition process and its consequences, the material ablation, we will also determine important information, that will address the second part of our work focused on micromachining applications. In particular, we would like to answer the question whether it is interesting to use a subpicosecond laser for such applications as material micromachining and laser surgery. The PhD thesis consists of 4 chapters, a general conclusion and a few annexes: The first chapter describes the state of the art in femtosecond laser solid interaction and presents a general view of laser ablation of a solid, accompanied by a modelling of laser absorption in matter. The second chapter presents the methodology of experimental work and preliminary measurements. We also introduce the measurements of damage and ablation thresholds of a dielectric target and the distinction in their definition and detection. The chapter three is first dedicated to a pump-pump experiment to determine the laser ab-

41 Introduction 5 sorption at the surface of a dielectric and the analysis of morphology of the craters fabricated during the interaction. The first conclusions are supported by a theoretical analysis of lasermatter interaction. Then a pump-probe experiment uncovers the mechanisms at play during the laser pulse absorption. The objective here is to measure both temporal evolution of reflection and transmission together with consequent analysis of the absorption change during the pulse. Finally, the scenario of energy deposition and the optimal working fluence range for laser surface treatment are proposed. The fourth chapter further illustrates the results on surface damage and ablation of inert dielectric for industrial application (hole drilling, grooving). We then show some results of the clinical study of biological tissue (cornea) dissected by femtosecond laser for improving the application of femtosecond laser systems to corneal graft surgery. The annexes are devoted to the description of the materials studied in this thesis and nonlinear phase-matching calculation.

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43 Chapter 1 State of the art/background and review of earlier works Contents 1.1 Introduction Material ionization with femtosecond laser pulse Carrier excitation Carrier scattering, transport/transfer of the laser energy, lattice thermalization Hydrodynamic motion, thermomechanical effects, structural modification, resolidification Modelling of the ionization of transparent dielectric Description of the model Electron density, material excitation Material response Electron and ion temperatures. Two temperature model Laser energy absorption, reflection and transmission Conclusion

44 "Bertie, le monde est fait de simples d esprit et d esprits confus, et je te laisse le soin de décider de quel côté tu te trouves" Gerald M. Edelman, Prix Nobel de médecine Biologie de la conscience, Edition Odile Jacob (1992)

45 Chapter 1: State of the art/background and review of earlier works Introduction The advances in decreasing the pulse duration has brought us from the picosecond timescale a generation ago, to the femtosecond timescale [5,11,14,15] in the past decades, and now into the attosecond (1 as = s) regime [16 19]. Those advances allow us to observe fundamental processes such as chemical reactions, phase transitions, and surface processes that are established on timescales comparable to the oscillation periods of atoms and molecules, those taking place from several femtoseconds to hundreds of picoseconds. In this context, femtosecond lasers are a nice tool to modify, observe and study the processes occurring while light is interacting with a target. Those lasers are well suited for observing ultrafast electron and lattice dynamics in solids making possible the study of matter modification induced by the laser pulse. The laser energy can be considered as a sequence of photons with energy ν, defined by the laser wavelength λ. The photons propagating into the target interact with the electrons of the material, giving them their energy and promoting them to higher energy states, or in other words exciting them. It is widely known that in solids the electronic structure consists of available energy states for electrons, which form bands. According to band theory, dielectrics 1, have completely filled valence band and entirely empty conduction band, separated by a large gap (band gap with energy states forbidden for electrons, > 4 ev) at 0 K. The electrons of the valence band (possessing higher energies in the valence band) are weakly bounded to the lattice and could interact with the photons. The interaction of a femtosecond laser with a transparent solid is a sequence of complex phenomena as shown in fig Figure 1.1: Mechanisms of laser ablation of solids [20]. 1 Materials with electrical resistance Ohm/m in a constant electric field at room temperature.

46 Chapter 1: State of the art/background and review of earlier works 10 When the fluence is sufficiently high, it can yield structural modification, damage or ablation of initially transparent material. Processes of laser damage or ablation include absorption or carrier excitation, carrier scattering, photoelectron emission and surface charging, electron trapping, defect generation [21], followed by electron-phonon inelastic scattering and lattice heating, phase transformation and shock wave formation [22 25], melting, melt propagation [26], boiling, evaporation, permanent damage or ablation [15,27] and resolidification. Those processes are relatively temporally separated and divided on 4 main consecutive phases as described in fig The phases are accompanied by an ensemble of macroscopic transformations as presented in fig Figure 1.2: Processes of laser ablation of solid materials [28]. The main phases of laser ablation are: 1. Carrier excitation. Absorption of the incident beam by the electrons and ionization of the material is produced in a micrometrical volume (fig. 1.2a). The duration of this phase equals to the pulse duration. This phase is a highly non-equilibrium process for the electronic and

47 Chapter 1: State of the art/background and review of earlier works 11 ionic subsystems (T e T i ). It is characterized by "hot" free electron plasma and "cold" or "frozen" lattice. The time required for electron-electron equilibrium given by the Fermiliquid theory [29] depends on the free electron density. For instance, for 1.21 ev (1025 nm) of absorbed energy and a solid carrier density of cm 3 (corresponding to a single atom ionization), the thermal equilibrium for the electron population is obtained in a time less than 20 femtoseconds that is much lower than the pulse duration in most laser systems. 2. Carrier scattering, transport/transfer of the laser energy, lattice thermalization. Thermal equilibrium of the electronic and ionic subsystems is achieved (T e T i ) via electron phonon scattering within the region of energy deposition (fig. 1.2a and b). The required time amounts to 5-20 ps in dielectrics [15]. Another process occurring is the electron diffusion that removes carriers from the excited region. 3. Hydrodynamic motion, thermomechanical effects, structural modification. When the free electron and lattice temperatures come to an equilibrium, hydrodynamic ion motion settles adiabatically in a small thermally-insulated volume. Indeed, due to the extremely short time ( ps), there is no opportunity for significant heat exchange with the surrounding zone. As a consequence, it provokes the initiation of a high magnitude compressive wave that upon loosing its intensity becomes an acoustic wave. The amplitude of rarefaction wave decreases quickly while it is moving in the opposite direction in respect to the compressive wave. Thus, regions with lower density are created. The high temperature plasma (containing electrons, ions and atoms, T e = T i ) is formed in the direction perpendicular to the sample surface. The plasma plume, typically, could carry out up to 80 % of absorbed energy, causing together with the rarefaction wave low collateral damage of the material [12]. If the lattice temperature exceeds the melting, boiling or sublimation point, melting, vaporization or ablation can establish. The plasma containing ablation products that was homogeneously expanding above the sample surface is ejected far from the target, leaving an ablated crater surrounded by a melted zone (see fig. 1.2b and c). The total time of the processes is in the order of nanoseconds after the end of the pulse. 4. Resolidification. Expansion of the liquid region is limited by the thermal diffusion due to cooling of the excited region. Resolidification or condensation follows melting, vaporization or ablation, caused by the temperature decrease. However, the material does not necessarily return back to its original structural or phase characteristics (fig. 1.2d). The temperature reaches the ambient value on timescale of microseconds.

48 Chapter 1: State of the art/background and review of earlier works 12 In the context of our work, we would like to get more insights on these complex phenomena occurring during laser ablation of transparent dielectrics. In particular, we will pay thorough attention to the very first stage of the interaction. In that context, we now describe precisely the fundamental mechanisms of laser ionization and define the important points of our modelling accounting for laser absorption in dielectric materials. 1.2 Material ionization with femtosecond laser pulse Carrier excitation A laser pulse propagating into a medium can induce free electron excitation, heat them and cause laser-induced optical breakdown. When the energy of a single photon is enough for the excitation of one electron, in other words the laser energy is enough to overcome the bandgap, the mechanism called linear absorption is considered to be the dominant mechanism of laser-matter interaction. When the energy of one photon is not sufficient for promoting an electron from the valence band to the conduction band, the electron becomes free by simultaneous absorption of a series of photons. The building up of high free electron density in the conduction band is necessary in order to initialize laser damage or ablation of wide bandgap materials. For materials ablated by lasers, the critical density, n cr = ωl 2m eε 0 /e 2 (n cr = cm 3 at λ = 1025 nm), is defined as the free electron density, at which the plasma oscillation frequency is equal to the laser frequency. It is widely assumed to be a criterion for the optical breakdown [30 34]. Once the critical density is created, the originally transparent material becomes "at the same time" 2 highly reflecting and opaque. A large percentage of the absorbed laser energy is deposited in a very thin surface layer within a short period of time, leading to the ablation of this layer. For the radiation absorption, that means to render the material highly absorbing, the first free carriers are created by photoionisation or optical field ionization Optical field ionization For classical femtosecond laser (visible and IR range), a single photon energy is not sufficient to overcome the large band gap in dielectrics and create the first free electrons at intermediate intensities (around 50 TW/cm 2 ). Now, when high intensity is applied, nonlinear absorption can take place. Depending on laser frequency and intensity, two regimes are possible: multiphoton ionization and electron tunnelling through the potential barrier. 2 A balance is found between the increased reflection and high absorption due to the modified dielectric function (the decrease of the real and increase of the imaginary parts).

49 Chapter 1: State of the art/background and review of earlier works 13 L.V. Keldysh [35] examined optical field ionization and introduced a general expression for the ionization rate and approximate expression for both limiting cases (γ 1; γ 1) in terms of adiabatic parameter γ: γ = ω L e [ m e n ] rcε 0 E 1/2 gap (1.1) I where E gap is the energy gap (9 ev for SiO 2 ), e the electron charge, m e the reduced mass of electron, ω L the laser pulsation, I the laser intensity at the focus, c the velocity of light and n r the real part of the refractive index of the material. In fig. 1.3 different types of optical field ionization (photoionization) are shown introducing the main mechanisms of laser absorption by the electrons of the valence band. For values γ 1, the Figure 1.3: Optical field ionization. Modified from [34]. process is called tunnelling and is responsible for ionization (fig. 1.3a). The electric field of the laser suppresses the Coulomb well that binds valence electron to its parent atom. If the electric field is strong enough to distort the potential well, the bound electron tunnels through the short barrier and, thus escapes from the atom. The process is characterized by extremely strong laser field and low laser frequency, for example, when the laser pulse is very short (τ< 10 fs). If we take the laser wavelength of 1025 nm, tunnelling ionization will be dominant at intensities 10 PW/cm 2. For γ 1, there is an intermediate (transition) regime and both effects compete (fig. 1.3b). This transient case for λ = 800 nm is obtained at field strengths of about MV/cm. This corresponds to intensities of W/cm 2 [36,37] at 100 fs pulse duration. For instance calculation of γ for our case gives 3.9 for λ = 1025 nm, pulse duration 500 fs and for intensity W/cm 2. According to Keldysh, for γ 1 (fig. 1.3c), common for high laser frequency and moderate field strengths, but below the single photon absorption, the first seed electrons are created by multiphoton ionization. Bonded valence electrons simultaneously absorb enough photons to

50 Chapter 1: State of the art/background and review of earlier works 14 overcome the band gap of the material (n ph = λegap hc ). The probability of the process increases with laser intensity. For instance, calculation of γ gives 20 for λ = 1025 nm, the pulse duration 500 fs and for intensity W/cm 2. In our works MPI is thus supposed to be the dominant mechanism of photoionisation. Once the electron is situated in the conduction band of the solid, its energy can be increased by free carrier absorption (See ). Note that it does not alter the number of free carriers Avalanche ionization Upon ionization process, more and more electrons promoted into the conduction band of the material 3 linearly absorb several laser photons sequentially via non-resonant process called "inverse Bremsstrahlung absorption" (also called Joule heating) moving to higher energy states in the conduction band. This process is accomplished only in the course of collisions with heavy charged particles (ions or atomic nuclei). A third particle (ion/ atom, impurity) is necessary in order to conserve both energy and momentum as they cannot be both conserved if only an electron and a photon interact. Collisional (also known as impact) ionization takes place for free electrons of high kinetic energy when the energy to transfer is comparable to the potential well 4. One electron can thus ionize another electron from the valence band, resulting in two excited electrons at the conduction band minimum (fig. 1.4). Each of them can then absorb laser irradiation through free carrier absorption and subsequently ionize additional electrons from the valence band [38]. This process is efficient as long as a large quantity of high kinetic energy free electrons is present in the conduction band. Moreover, the energy gain through inverse Bremsstrahlung must be more rapid than the energy loss by collisions with heavy particles (phonon scattering, recombination, STE) and diffusion out of the focal volume. These free electrons can again and again be heated by the laser field through free carrier absorption and, once they have enough energy, impact more valence band electrons. This process can repeat itself as long as the laser field is present and intense enough yielding exponential growth of the number of free electrons. It is thus called "electronic avalanche" (see fig. 1.4). 3 In case of a metal we talk about initial number of free electrons. 4 Fermi level in a metal.

51 Chapter 1: State of the art/background and review of earlier works 15 Figure 1.4: Avalanche ionization [34]. Recently, for ultra short laser pulses (less then 40 fs) variations of classical avalanche process were preposed theoretically [39,40]. The mechanism describes a hole-assisted ionization.when an electron is promoted to the conduction band, it leaves a positively charged hole. All the adjacent molecules and atoms experience the combined effect of applied laser field and the electrostatic field of the hole. This process is most efficient in the laser polarization direction. The total field increases and the hole exponentially enhances the ionization rate and promotes the creation of a new hole adjacent to the existing one. As long as new holes are created, the process leads to "collision-free" electron avalanche or "forest fire" ionization [39, 40] Carrier scattering, transport/transfer of the laser energy, lattice thermalization Dissipation of the energy absorbed by the electrons occurs on a timescale longer than the laser pulse duration. When highly excited electron plasma is produced, the thermal equilibrium is broken (T e T i ) and the system drives to return to an equilibrium state. Electron - electron and electron - phonon collisions or scattering are the mechanisms to settle again the carriers to a Fermi-Dirac distribution within tens to hundreds of femtoseconds after excitation. Figure 1.5: Free carrier scattering [20]. During the electron electron scattering (fig. 1.5a) (electrostatic interaction between two carriers), the total energy of the electron plasma is not changed neither the free electron density.

52 Chapter 1: State of the art/background and review of earlier works 16 On the contrary, the excess of the free electron kinetic energy is diminished by electron - phonon collisions. A phonon is a quantum of vibrational energy of the lattice directly connected to the material temperature. The communication of the electron energy to the crystalline lattice via phonons drives the system to thermal equilibrium (T i = T e ). In a carrier phonon scattering process, free carriers could also gain energy by absorbing a phonon and move to higher energy states. The electrons could thus remain either in the same conduction or valence band valley (intravalley scattering, fig. 1.5b) or be transferred to a different valley (intervalley scattering, fig. 1.5c). The energy transfer to the lattice via phonon emission during carrier phonon scattering decreases the energy of the carriers, without changing of their number density. Because the emitted phonons carry little energy, a large number of successive scattering events is required to relax the deposited energy. Therefore around 5 20 ps [15] are needed in dielectrics, before the free carriers and the lattice reach thermal equilibrium. In other words it corresponds to the time for "hot" electrons to transfer their energy to "cold" lattice. As the absorbed energy is transferred from the high energy electrons to the lattice through electron phonon scattering within the region of energy deposition and on a timescale longer than the pulse duration, this energy exchange is conventionally described by the two-temperature (TTM) model (see section 1.4.3). In the femtosecond regime, the complete cooling up of the electrons due to the energy transfer to the lattice, and further the heat conduction to the bulk arise after the laser pulse. It originates from not important coupling between the electrons and the lattice during the pulse. Once the carriers and the lattice are in equilibrium, the material is at a well-defined temperature. The excess carriers will be removed in the condition of thermal equilibrium by the electron recombination or by their diffusion out of the excitation region. It exists radiative and non-radiative recombination. Radiative recombination is a relaxation process, inverse to the optical excitation, where the electron looses its energy and descends (moves) to a lower energy level by emitting a photon (luminescence), decreasing the total energy of the system. The characteristic time of the process is in order of µs. Non-radiative recombination processes include three body Auger recombination, defect generation in bulk and surface and surface recombination. During Auger recombination, the electrons and holes redistributed throughout the conduction and valence bands recombine and the excess energy excites the electrons higher in the conduction band. Auger recombination decreases the carrier density, but the total energy of the free electron system is kept constant, as the average energy of the remaining carriers increases. Another mechanisms such as defect generation and surface recombination compensate this energy increase. The excess energy is indeed used to create a defect (a new energy state) at the surface or in the bulk or to increase the energy of the already existing ones. It should be also noted that during the relaxation one

53 Chapter 1: State of the art/background and review of earlier works 17 electron from the conduction band could be trapped in the bandgap, creating distortions of the crystalline lattice that is similar to a coloured center. The process is called self trapping of excitons (electron-hole pair, STE) and is widely observed in materials with low elasticity, as for SiO 2 (as compared, for instance, to polymers). The trapped exciton will recombine, first, while emitting photon (luminescence). Note, high purity fused silica luminescence spectrum lies in the blue ( ev) due to a large Stokes shift [31, 41, 42]. Second, the STE recombination is fulfilled by the creation of a permanent colour center or defect in the bandgap. It is widely assumed that STE associated with the absorption bands at 5.6 ev corresponds to the E-center of silicon [43, 44] and/or NBOHC (bond breaking) and then relaxes in a long time delay into a silicon oxygen deficient center, causing compaction of the lattice. Grojo et al. [45] in his extensive study has put in evidence avalanche ionization for ultrashort pulse duration and has shown that STE create seed electrons in fused silica bulk that causes important increase in absorption. The time of exciton self-trapping in SiO 2 is inferior to 300 femtoseconds [45, 46] followed by a decay within 400 picoseconds. The carriers can also diffuse into the material, and the electrons in excess are thus removed from the excitation region. But, in contrast to the other (Auger) recombination processes, the total number of free carriers in the material is not changed. Note, in dielectrics, Auger recombination become more important for high electron densities, while recombination with a photon emission is more prominent et low electron densities Hydrodynamic motion, thermomechanical effects, structural modification, resolidification The laser absorption yields a distribution of free electrons creating extremely localized alteration of the temperature, confined in the focal volume. In fact, the system experiences a high and swift temperature rise without any motion of the lattice (it is almost "frozen" due to high ion mass). Any energy loss is due to electron heat diffusion. The system thus behaves adiabatically inducing a huge and brutal pressure rise [22, 47 50]. Two pressure waves are required for conserving the momentum. Thus the stress wave contain compressive and tensile components moving in opposite directions. Even if the temperature rise is too small to produce a thermal damage, the tensile stress may cause fracture of the material [51]. The evolution of the thermoelastic stress distribution in the laser focus can be calculated by the three-dimensional thermoelastic wave equation [30]: p(r, t) = T2 β(t ) dt (1.2) T 1 K comp (T )

54 Chapter 1: State of the art/background and review of earlier works 18 The integral is calculated for the range of temperatures, from T 1 = 20 C the temperature before the laser pulse to T 2 (r) the plasma temperature after the laser pulse, r is the radial coordinate, β the thermal expansion coefficient, K comp the compressibility, p(r, t) the pressure distribution. The total time of the processes is determined by the sub-micrometer breakdown volume and is estimated in the order of or less than a few hundreds of picoseconds. All thermal processes occur after establishing local equilibrium, depending on the absorbed laser energy deposited in a thin layer defined by the penetration depth. A convenient approach is done by the Beer Lambert law (considering exponential attenuation of the absorbed light intensity or absorbed fluence F 0 propagating into the target) : ( ) z F (z) = AF 0 exp α eff (1.3) where A is the surface absorptivity and α eff is the effective optical penetration depth. According to the equation 1.3, assuming different fluence values, several phenomena could take place leading to one of the following processes depending on the quantity of the deposited energy [52, 53]: 1. Normal vaporization (slow heating rate). Vaporization from an outer surface is a process, which is attributed to any pulse length, when the material reaches the vaporization point. The process does not include any nucleation. Atoms are vaporized from the surface and carry away heat. The material has an exponential depth temperature profile. 2. Normal boiling. In this case, the pulse length should be sufficiently long for heterogeneous 5 nucleation to occur. Thus, the target will undergo normal boiling, from the surface into the depth defined by the absorption length or thermal length. 3. Phase explosion (Explosive boiling). The third type of thermal process requires that the laser fluence is sufficiently high and the pulse duration is short that the target reaches homogeneous 6 bubble nucleation (instead of heterogeneous nucleation as for the normal boiling). In this case the material undergoes a rapid transition from the state of superheated liquid to a mixture of vapor and liquid droplets [54]. 4. Subsurface heating. It is similar to the case of normal vaporization, but the profile is modified, thus, the highest temperature is concentrated beneath the surface. In this case the condition of the exponential depth temperature profile is not satisfied. 5 Denotes a process involving substances in different phases (solid, liquid, or gaseous). 6 Denotes a process involving substances in the same phase (solid, liquid, or gaseous).

55 Chapter 1: State of the art/background and review of earlier works 19 For femtosecond laser pulses, if the laser fluence is sufficiently high, we can distinguish 3 consecutive zones (with respect to depth): an ablated zone, a melted zone and a modified zone. In the first (ablated) zone the free electron density will be higher than the critical electron density (optical brackdown zone). In the second zone, where the fluence is too low to create optical breakdown, but the electron density is still high enough to cause high temperature rise, melting occurs. This melted layer has a constant thickness, that is independent of the incident laser fluence, even for Gaussian beam distribution [28]. The third zone characterizes the solid region where the heating is not sufficient for material melting, but the energy deposition is high enough to modify the material (reversible or irreversible changes). The ablation of the material causes the plasma expansion above the material. During the first hundreds of picoseconds to nanoseconds, the plasma plume will be distributed only in one dimension normally to the sample surface. The plasma expands further in both lateral and perpendicular directions and removes the ablated material from the surface. A huge amount of the absorbed energy is used by the expanding plasma to move into the ambient gas [28]. The small portion of the thermal energy left in the target expands into the bulk as a result of heat diffusion. The temperature decreases and the melted material starts to resolidify. During the resolidification time, a thin rim around the ablated crater appears due to the action of the forces exerted by the plasma that controls the fluid dynamics of the molten layer driving the liquid from the centre to the edges of the crater [28]. The temperature of the heated material reaches the ambient value on the timescale of microseconds. 1.3 Modelling of the ionization of transparent dielectric Modelling of ultra-short laser pulses interacting with a solid target is challenging as the generation of the plasma and partial reflection of the laser irradiation should be taken into account. The localization of the energy deposition is also one of the important points. It exists a large variety of approaches for numerical simulation of fs laser - dielectric target interaction. Most of them aim to reproduce experimental damage and ablation thresholds introducing two criteria: first, the optical breakdown is achieved when the free electron density equals to the critical density [11, 37, 55 59]; and, second, the amount of absorbed energy per unit volume reaches a critical value, which is for SiO 2 E thr = 54 GJ/m 3 (E thr = 54 kj/cm 3 ) [60]. In the literature we can find the approach of Stuart et al. [11, 56, 61] using kinetic models. In this study, the electron distribution function is based on Fokker-Planck equation considering the electron distribution stationary, but non-maxwellian. Kaiser and Rethfeld et al. [37] solve the system of Boltzmann equations. This approach is further used in numerous studies [31, 58, 62, 63]. Further Rethfeld applies the

56 Chapter 1: State of the art/background and review of earlier works 20 multiple rate equations for describing the interaction of ultrashort laser pulses with solids [64,65]. In this approach, every electron in the conduction band is considered individually and contributes (whatever its energy) to the avalanche ionization process. In fact, the total energy distribution of free electrons in the conduction band with the definition of an average energy is not used. The electrons only with high kinetic energy will impact the electrons from the valence band and a single photon absorption is only considered in the conduction band. This approach depicts nonstationarity of electron distribution and small importance of avalanche for ultrashort laser pulses and increasing influence of avalanche ionization for longer pulse durations. Belsky et al. [66] introduced multi-photon absorption in conduction band in the Rethfield model as long as the electrical field is present in the target. Surface charging that leads to microscopic Coulomb explosion is proposed by Stoian et al. [67 71] and similar effect due to the electrostatic force is used by Gamaly et al. [15]. This effect is proved to occur on the first inner layers of dielectrics due to high charge separation between electrons and ions (due to the low carrier mobility in comparison to metals and semicoductors). The value of "gently" ablated material is in order of several atomic layers (several nanometers) at the threshold [70, 71]. The "gentle" ablation is followed by the "strong" ablation that is similar to fracture in metals. Gaier et al. [39, 72] present "forest fire" model that accounts for very short fs laser pulses. The model is based on "enhanced ionization" in molecules or "ionization ignition" in clusters. When an electron is rapidly removed from its position, it leaves a positively charged hole, that participates in the overall electric field enhancement due to its electrostatic field. Thus, a positively charged hole promotes the creation of a new hole, adjacent to the existing one further producing more and more free electrons. This approach was followed by Petrov et al. [40]. Another popular approach is based on the formation of plasma and the evolution of the laser generated carriers described by the rate equation of Stuart et al. [11, 14, 32, 36, 59, 67 69] as a function of time and beam propagation inside the material. Such approach gives a good approximation for sub-picosecond laser pulses. Other approaches consider the pulse propagation into the target. For instance, Du et al. [73], Couairon et al. [62], Mermillod-Blondin et al. [74], Gulley et al. [75] take into account the spatial and temporal nonlinear propagation of ultrashort laser pulses in dielectric target including optical Kerr effect, delayed Raman-Kerr optical shock response, self-steepening, plasma absorption, plasma defocusing and energy absorption due to photoionization by solving the Schrödinger equation. Couairon et al. concluded that, in the bulk material under strong focusing conditions, the very first electrons are created by multiphoton ionization followed by avalanche. The estimation of the free electron density for irreversible damage is found below the critical density due to balancing between plasma defocusing and self-focusing. Gulley et al. [75]

57 Chapter 1: State of the art/background and review of earlier works 21 shows the importance of the Drude dispersion operator for taking into account the nonlinear effects especially for ultra-short laser pulses. It is also studied the influence of the electron background collision frequency and the importance of its value on reflection, transmission and absorption and threshold value [38, 75 77]. In his model, Feit at al. [11, 55, 56] calculates the plasma properties at a given spatial position and further advancing step-by-step the laser pulse into the material. This approach thus takes into account both the propagation and laser absorption. It shows the deviation of the damage threshold value for a wide range of pulse durations from 100 fs to 20 ps from the τ 1/2 scaling, that is widely accepted for longer pulse durations (> 20 ps) [11, 55]. This particular feature is the result of non-equilibrium low thermal regime ("cold" lattice and "hot" electrons) with low collaterally damaged zone. Gamaly et al. [59], for instance, uses exponential decay into the material depth. Some authors [62, 65, 78] use one component of the electromagnetic field propagation into material. The advantage is the two dimensional distribution of the field, but this approach does not take into account the plasma reflection. 1.4 Description of the model The choice of the model used is justified by several important reasons. Lambert-Beer law is a good approximation for metals only in which the skin layer is about tens of nanometers and the permittivity distribution is almost uniform (this assumption works for low laser intensities). It also fails when the material expansion starts and permittivity profile changes substantially. For dielectrics, this approximation is not suitable neither because of low initial electron density (n e n cr ), when dielectrics are transparent for irradiation. More complex approach with Schrödinger equation is the best suited for ultra-short laser pulses (< 10 fs) and strong focusing in the material bulk, when non-linear effects become important. Maxwell equations become non-valid (electro-magnetic field changes swiftly in a short time period), when the pulse duration is ultra short and WKB (Wentzel Kramers Brillouin) approximation (it is also known as the Liouville Green method) used in the Helmholtz equation is not suitable. But for short laser pulses (> 100 fs) the system of Helmholtz equations can be successfully solved. Thus, we choose the Helmholtz equation for modelling laser-matter interaction. It gives the electromagnetic field distribution in the target with an arbitrary time-space profile of permittivity and does not have strict condition on numerical time step in comparison with the approach based on solving the Maxwell equations. Solution to the Helmholtz equation immediately gives the laser energy absorption in each point (space and time) and the complex reflection and trans-

58 Chapter 1: State of the art/background and review of earlier works 22 mission coefficients. Non-equilibrium states with different temperatures of electron and lattice subsystems are taken into account by the two-temperature model. The rate equation of Stuart et al. [11] deduced from kinetic theory is used for modelling the free electron density change Electron density, material excitation The equation for the electron density evolution is: n e (z, t) t = n v n e (z, t) n v (σ n I n (z, t) + αi(z, t)n e (z, t)) n e(z, t) τ trap (1.4) The two terms on the right-hand side represent sources and losses of free electron generation n e (z,t) respectively composed of: (i) multiphoton ionization term for n-photon absorption σ n I n (z, t) [79], where n ω L E 7 gap, ω L is the photon energy; (ii) avalanche term α I(z,t)n e (z,t); and (iii) the free electron losses (electron-plasma lifetime) due to recombination and trapping τ trap [45,46]. The laser intensity is I(z,t); the number of valence electrons is n v = cm 3. Here z is the direction perpendicular to the target surface (depth). Keldysh [35] used the perturbative theory to derive the ionization probability of solids for strong electromagnetic waves. This formula was adapted to fit multiphoton ionization in our model. The cross section of optical field ionization yields σ n = σ 8 in m 13 /sw 8. The avalanche ionization rate is α (expressed in cm 2 /J) and is deduced from our parametric study of input data and confirmed by the value found in literature in similar conditions (see chapter 3) Material response The material response to the laser action is based on the oscillation of electrons in the laser field. We use the expression for the dielectric constant based on Drude model [80]: ( ε = 1 + (ε gω 1) 1 n ) e(z, t) n v n e(z, t) n cr iν col /ω L, (1.5) where ε gω is the dielectric function in normal conditions and ν col is the effective frequency of collisions. The imaginary part of the dielectric function determines laser pulse absorption. The expression (1.5) used for the dielectric permittivity correctly describes the dielectric properties in both conditions: in normal conditions (without ionization) which are known from experimental measurements at rest; and in conditions of strong ionization, when the classical Drude model for electron gas is valid [68,81]. In other words, the dielectric acquires metallic-like properties (for free electron densities cm 3 ). 7 the number of photons for n-photon absorption is n = 1 + int {E gap/( ω L)}.

59 Chapter 1: State of the art/background and review of earlier works 23 The electron background collision time τ col =1/ν col is variable during the process of energy deposition as the free electron density and the electron temperature grow rapidly during the laser pulse, while lattice temperature changes slowly. In our case we estimate the changes of ν col by taking it as the harmonic mean of the following contributions [76, 82, 83]: ν 2 col = (ν e ph + ν ee ) 2 + (ν en + ν ei ) 2 + ν 2 c (1.6) The electron background collision frequency for low electron temperature takes into account the electron-phonon ν e ph = A e ph T i /ne 1/3 and electron-electron ν ee = A ee Te 2 /ne 2/3 collisions [83, 84]. For high electron temperature (the electron has a high energy level in the conduction band, T e strongly superior than Fermi level T F for metals), the collision frequency is described by electron-neutral ν en = (n v n e (z, t))t 1/2 e and electron-ion collisions ν ei = Zn e (z, t)λt 3/2 e [32,83]. The parameters are: A e ph = K 1 cm 1 s 1 and A ee = K 2 cm 2 s 1 (these values will be commented during the study of the modelling parameters in chapter 3), T e and T i are the electron and ion temperatures respectively; Z = n e /n i the mean ion charge with concentration of ions n i, Λ the Coulomb logarithm { Λ = max 2, ln ( bmax b min )}, (1.7) where b max = max { r 0, } kb T e 4πn e e 2 { } Z e 2 b min = max,. k B T e me k B T e In order to avoid unphysical behaviour of the collision frequency in the intermediate regime (for the case of intermediate electron temperatures), it is required that the frequency of electron collisions is not smaller than the ion sphere radius [82]. Thus, cutoff collisions define the electron background collision frequency in the intermediate regime: ν c = v e V 1/3. V = 4πn a /3, where n a is the atom density, v e the electron velocity Electron and ion temperatures. Two temperature model The absorbed energy is transferred from conduction band electrons to the lattice through electronphonon scattering within the region of energy deposition yielding temperature increase and matter reorganization (STE,...). This energy transfer is described by the two-temperature (TTM)

60 Chapter 1: State of the art/background and review of earlier works 24 model 8 as the time of their equilibration is long compared to pulse duration [85, 86]: E e t = C e T e t = g(t e T i )/ρ + Q(z, t)/ρ (1.8) E i t = C i T i t = g(t e T i )/ρ (1.9) The specific energy of electrons and ions is respectively E e and E i, Q(z,t) is the laser heating source term, ρ the material density. The heat capacities (per unit volume) of the electron and ion/lattice subsystems are C e and C i respectively, the parameter characterizing the electronlattice coupling g = g 0 n 2/3 e with a material constant g 0. The electron heat capacity depending on electron temperature and free electron density is expressed by [83]: C e (T e, n e ) = f FD (ɛ) γ st (ɛ)ɛdɛ, T e where f FD (ɛ) is the Fermi-Dirac distribution function, ɛ the electron energy and the density of states is: γ st (ɛ) = (1/2π 2 )(2m e / 2 ) 3/2 ɛ. The femtosecond irradiation regime is characterized by non-significant coupling between the electrons and the lattice during the pulse. After the laser pulse, the electrons are cooled due to energy transfer to the lattice, and heat conduction to the bulk. Note that for picosecond and nanosecond pulse durations, the electron temperature becomes quasi-stationary during the pulse (T e T i ). The lattice heating occurs during the laser pulse and "continuous" laser absorption compensates the losses Laser energy absorption, reflection and transmission Based on classical electrodynamics, we can calculate the laser light absorption and reflection using an arbitrary permittivity profile [87]. We take a one-dimensional approximation where the material permittivity depends on z coordinate only, normal to the target surface giving ε = ε(z) and ε(z ) = 1. Then, for S- polarization of the laser field (fig. 1.6a), we hence can write Ẽ = Re{E exp( iω Lt + ik L x sin θ)}, E = {0, E y, 0}, k L = (ω L /c){sin θ, 0, cos θ} is the wave vector. Here θ is the incidence angle. The single component of the electric laser field envelope E y (z, t) slowly varying in time can be defined as follows: 2 E y z 2 + k2 L[ε(z) sin 2 θ]e y = 0. (1.10) 8 The electron and the lattice/ion subsystems are characterized by their temperatures T e and T i.

61 Chapter 1: State of the art/background and review of earlier works 25 x (a) x (b) z z B E θ E θ k 0 k 0 B Figure 1.6: Polarization of laser light: (a) s; (b) p. In the case of P-polarization (fig. 1.6b), for the single component of the magnetic field envelope B y (z, t), B = {0, B y, 0}, one obtains: 2 B y z 2 + k2 L[ε(z) sin 2 θ]b y ln ε(z) B y z z = 0. (1.11) We describe the complex permittivity of material localized in the range z 1 z z N by the piecewise-defined function (see fig. 1.7). Figure 1.7: Schematic drawing of the laser pulse propagation in the material bulk and target ionization under a femtosecond pulse. b) (colour online). A piecewise-constant distribution of permittivity in zones. The electromagnetic field amplitudes f m (in the equation (1.19)) are determined on zone boundaries [87]. Note, that every material layer is small enough to consider locally n e and T e as constants, that is imperative in Drude model. The front and back interfaces of the film (thin layers of 1 nm are taken in the calculation) 9 are located at z = z 1 and z = z N, respectively. The amplitude and phase of the incident electromagnetic wave is determined in the point z = z 0. Within this approximation, in an arbitrary zone z m z z m+1 for m = 0,..., N 1, 9 We use a mesh. The minimal step is taken close to the surface and equals to 1 nm and it further increases with the increase of depth.

62 Chapter 1: State of the art/background and review of earlier works 26 equations (1.10) and (1.11), the exact solution is found in the form: F m (z) = f m (+) e ikm(z zm) + f m ( ) e ikm(z zm), (1.12) where F = E y or B y in the case of S or P-polarization, respectively; f (+) m and f ( ) m are the amplitudes of right and left traveling waves at z = z m, respectively; and k m = k L εm sin 2 θ with k L = ω L /c. The permittivity is supposed to be constant ε(z) = ε m in the range z m z z m+1. It is known that tangential components of the field are continuous on the border of two computational cells, and the first derivative along the normal direction has jump for p-polarized components, we hence rewrite the following system of the equations: F m (z m+1 ) = F m+1 (z m+1 ), (1.13) ( F m / z) zm+1 = D m ( F m+1 / z) zm+1, (1.14) where: D m = 1, if S-polarization, ε m /ε m+1, if P-polarization. (1.15) Denoting the phase ψ m = k m (z m+1 z m ), and rewriting the conditions (1.13) and (1.14), yield to: f m (+) e iψm + f m ( ) e iψm = f (+) m+1 + f ( ) m+1, (1.16) f m (+) e iψm f m ( ) e iψm = k m+1 D m (f (+) m+1 k f ( ) m+1 ). (1.17) m In a vector form it is equivalent to: C m+1 fm+1 = P m fm, (1.18) where: C m+1 = f m = f m (+), (1.19) f ( ) m 1 1 d m+1 d m+1, (1.20)

63 Chapter 1: State of the art/background and review of earlier works 27 with d m+1 = (k m+1 /k m )D m, and: P m = eiψm e iψm e iψm e iψm. (1.21) Using (1.18) for m = 1,..., N 1 one obtains: f N = (C N ) 1 P N 1... (C 2 ) 1 P 1 (C 1 ) 1 P 0 f0 (1.22) with f 0 (+) given and f N ( ) 0, since no wave is traveling to the left for z z N. Two unknown values f 0 ( ) and f N (+) can be found from equation (1.22). Finally, the absorption term in each zone is defined as [88]: Q m = I(t)k LIm{ε m } z m+1 z m where I(t) is the incident laser pulse intensity, and zm+1 z m E(z) 2 dz, (1.23) E 2 = E y 2, if S-polarization, E x 2 + E z 2, if P-polarization. (1.24) The field components E y or B y are calculated from (1.18) for f 0 (+) 1. The relations between E x, E z and B y in P-polarization case are E x = i/(εk L )( B y / z), E z = B y sin θ/ε, and the laser energy absorption in each zone z m z z m+1 can now be determined. The coefficients of reflection R and transmission T can also be easily calculated: R = f ( ) 0 /f (+) 0 2, T = f (+) N /f (+) 0 2. In the calculations, the laser fluence is: The laser energy is: E = 0 F (r) = F (r)2πrdr = 0 I(r, t)dt. (1.25) 2πrdr I(r, t)dt (1.26) We also specify the peak laser fluence, that is used in our experiments: F peak = 2E πω 2 0 (1.27)

64 Chapter 1: State of the art/background and review of earlier works 28 In the case of the following time-space intensity distribution (Gaussian fit): I(r, t) = I 0 exp[ ln(16)t 2 /τ 2 L] exp[ 2r 2 /ω 2 0], (1.28) with the pulse duration (FWHM, see fig. 1.8) τ L = 500 fs and once the beamwaist ω 0 and the energy E are specified, we can find the peak intensity I I/I FWHM time, ps Figure 1.8: Pulse duration FWHM used for the modeling of laser ionization of dielectrics. It is represented by the formula To this end we integrate (1.29) and find: F (r) = I 0 π/ ln(16)τl exp[ 2r 2 /ω 2 0] (1.29) Substitution of this result into (1.26) gives: E = I 0 π/ ln(16)τl πω 2 0 The peak intensity is I 0 = E/(πω 2 0 τ L π/ ln(16)). 1.5 Conclusion The interaction of a femtosecond laser with a solid is a sequence of complex phenomena. It consists of a series of consequent phases which are widely studied and that we have discussed earlier. For each step of laser-matter interaction there is an active experimental and theoretical research developed [28, 89 91]. Absorption on the surface of a dielectric, ionization mechanism producing optical breakdown, thermodynamic motion of the ablation plume, shock-wave propagation are

65 Chapter 1: State of the art/background and review of earlier works 29 the fundamental aspects of the interaction. Also an extensive study of the propagation of tightly focused infrared femtosecond laser pulses and yielding to refractive index modification, filamentation driven hole drilling in the bulk of transparent materials and defect accumulation have been carried out for dielectrics. In addition, the morphology of ablated craters and the influence of the parameters listed above are the points of interest of modern research for more applicative aims such industrial repeatability, accuracy and control. But for every of those phases there are still a lot of opened questions left. In the course of the thesis, we will try to get deeper in understanding of the very first phase of the interaction (Chapter 3): i.e. the absorption of laser energy and further energy transfer and redistribution to the lattice. It will help to develop a proper and precise insight of the ablation of a dielectric material by a subpicosecond laser and to find the applications with maximal efficiency of the laser energy deposition. In this work, we principally study fused silica glass that is, nowadays, one of the mostly used material in industrial applications. We also devote one chapter to biological application (Chapter 5) of the femtosecond lasers as a promising tool for surgery and cell research. Now, the beginning of the journey into the comprehension of the mechanisms of the laser - matter interaction starts with the description of the experimental set-up followed by the measurements of damage and ablation thresholds for material processing (Chapter 2).

66 Chapter 1: State of the art/background and review of earlier works 30

67 Chapter 2 Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses Contents 2.1 Introduction Structural modification: damage or ablation. Experimental techniques for estimation of ablation and damage threshold values Introduction Classification of material modifications Diagnostics, methodology and definitions Experimental set-up Laser parameters Sample positioning and diagnostics Remarks on the choice of the lens focal length Precision of measurement and error bar estimation Single experiment Reproducibility of results Conclusion Damage and ablation thresholds of fused silica Conclusion

68 "All life is an experiment. The more experiments you make the better." Ralph Waldo Emerson

69 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses Introduction Nowadays, femtosecond lasers are extensively used for modification of dielectric materials with a particular interest to transparent glasses, crystalline quartz and fused silica. Now, as it was detailed in chapter 1, the laser pulse absorption and energy redistribution to the crystalline lattice are not completely understood. Theoretical and experimental work needs to be continued to progress in the comprehension of fundamental interaction mechanisms and laser-matter interaction and for the development of industrial applications. For that purpose, realizing precise measurements and diagnostics is essential and crucial. In this chapter we thus pay particular attention to the definition of damage and ablation thresholds for wide bandgap solids and to the techniques and methodology to precisely measure and characterize them. This chapter is also devoted to the description and choice of critical parameters for the experiments. In addition, the experimental set-up for ablation threshold measurements is instructive for dielectrics micro-machining. 2.2 Structural modification: damage or ablation. Experimental techniques for estimation of ablation and damage threshold values Introduction For a given laser system, the usual parameter to express the laser-induced change of material surface is the fluence (ratio of the energy to the beam surface, expressed in J/cm 2 ). The threshold fluence is determined as the minimal energy per unit surface to induce a detectable change of a physical property of the material (which will be precised below). We group in fig. 2.1 the threshold fluences issued from literature as a function of laser pulse duration for different set-up configurations, but in similar experimental conditions. All experiments are performed in air, in single-shot regime, on the surface of fused silica and with an operating wavelength of 800 nm.

70 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 34 Figure 2.1: Dependence of the threshold fluence on the pulse duration. Threshold values are measured by different authors [15, 36, 57, 73, 91 97] in similar experimental conditions (800 nm, material - fused silica). The pulse duration during our investigation corresponds to 500 fs (1025 nm) and, in this region, the threshold fluence is variable between 3.5 and 11 J/cm 2. To note: * - 790nm, ** nm. The fluence threshold here refers to the onset of material change as evidenced by the used technique. In some cases, it can differ from one reference to another (as we will define hereafter) depending on the material property observed and material used. We observe a strong discrepancy in the experimental results characterizing the threshold fluence. This variability of the experimental results is partly explained by the difference in description of the threshold value. Indeed, the first information to provide is the exact definition or the physical sense of the threshold and to answer the following questions: What change and how much the sample is changed? What is the minimum quantitative change that can be detected to quantify the threshold? What physical property of the sample is changed? For instance, it can be a refractive index change, the plasma formation, a change of material surface morphology or matter ejection and etc. In this context, the threshold is always material property dependent, technique dependent and diagnostic dependent. Nevertheless, the dispersion can be also attributed to: 1. The difference in set-up configuration: i.e. focusing (beamwaist size), polarization state in case of oblique incidence, number of shots, repetition rate, etc. 2. The difference in terms of diagnostics and experimental technique: for instance, one can classify between "in-situ detection" (plasma radiation monitoring from the focal region [57, 92, 93, 98], time-of-flight [67], light-scattering [34], time-resolved interference [94], transient

71 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 35 reflectivity measurements [93]) or "ex-situ detection" (visual acquisition [11,92,95,96,99]), damage [36,100] or ablation detection (ablation volume/depth measurement [14,91,97,101, 102]). 3. Material properties such as impurities, inclusions, surface roughness, amorphous or crystalline phase for different samples that vary strongly from one sample to another and are not always defined in articles. 4. The exact mathematical definitions and the methodology of exploiting the experimental data (statistical and non-statistical analysis). For instance, one should precise whether the average or peak value of the fluence is taken to define the threshold. Thus it is priceless to clarify the notion of threshold and the associated methodology used to define it Classification of material modifications There are several approaches to quantify the surface modifications induced by a laser. Depending on applied laser fluence, we can divide these modifications into 3 groups as follows (fig. 2.2): Figure 2.2: Classification of laser-induced material modifications of the surface depending on applied fluence. 1 The study describing the difference in thresholds was already done upon my arrival, but it is important to repeat it here. All experimental results shown further are the results of my work on the experimental set-up, that is introduced in [103].

72 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 36 For low fluence value, the dielectric function of the material is slightly modified that could cause some transient or permanent modifications (phase change, local refractive index change), but without any visible topography change. Note that these modifications could be detected using appropriate diagnostics. In our case and according to our objectives, we will not try to put into evidence these structural modifications. When the laser fluence is increased, a surface damage could occur. A damage is defined as a visible permanent irreversible structural modification of the material surface ( 2D modification). The damage can result in compression, lattice reorganization, melting followed by resolidification of the matter, but without any significative change of the sample mass (no matter removal). This situation is illustrated in fig. 2.3a. If the incident laser fluence is further increased (above the damage threshold), the surface of the target experiences material removal (3D modification) and an ablation crater with defined geometrical characteristics (diameter, depth and volume) is formed (see illustration in fig. 2.3b). a) F = 1.04 F th,damage b) F = 1.01 F th,ablation Figure 2.3: AFM images of material after irradiation by a single fs pulse to illustrate the conceptual difference of damage (a) and ablation (b) (taken from reference [104]). The damage threshold F th,damage is further given by the maximal fluence for which no surface topology modification is observed and the ablation threshold fluence F th,ablation corresponds to the removal of an ablated volume equal to zero Diagnostics, methodology and definitions We now present the techniques of damage and ablation detection. It is worth to note that a qualitative method suits well for damage detection and a quantitative method fits ablation

73 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 37 detection [103] Technique of damage detection In our works, the value of the damage threshold is determined by post-mortem examination of the sample with an optical microscope and through a statistical analysis of the damage occurrence. Fig. 2.4 illustrates a general view of the target surface typically obtained in an experiment of laser damaging. Figure 2.4: General view of an experiment of damage and ablation. Each line starts by a different mark to easily distinguish the applied fluence. The total number of experimental lines (MN ) finishes by a closing line. The distance between two points along a column ( y) or a line ( x) is 50 µm. The procedure is as follows. For each fixed fluence, we perform a series of trials (typically 20), each one consisting of a single laser shot on a fresh zone. The distance between two shots in line ( x = 50µm) and two separate lines ( y = 50µm) is chosen according to two reasons. Firstly, the distance between two laser shots should be much larger than the beamwaist size. It aims to avoid cumulative effects and the interaction of the following pulse with redeposited ablated matter (if there is one). Secondly, the distance between two shots should not be too large as a typical experiment requires a large area to content all fluence cases. Moreover, we typically use the double distance (2 x) between the mark (that is produced by multiple shots at high energy) and the beginning of an experimental line. The operation is repeated for a wide range of fluence values yielding a matrix (with the size FN MN ). Afterwards, the sample is examined with an optical microscope with adapted illumination and magnification and the total number of damages for each fluence is counted allowing to plot the damage probability as a function of fluence (fig. 2.5). In this analysis only the damage occurrence is of importance and there is no

74 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 38 other parameters to consider that could interfere with the analysis. We use small increments in energy close to the threshold to determine it precisely, thus reducing the error due to the increase of the number of experimental points in this delicate low fluence regime. The low and high thresholds (F th,low and F th,high ) respectively correspond to the maximum fluence for which no damage is observed (damage probability = 0) and the minimum fluence for which damage is always produced (damage probability = 1). Figure 2.5: Probability as a function of laser fluence. Illustration of the low F th,low and high F th,high thresholds and regions of interest. We notice three important zones in the graph giving essential information for the applications: 1. Region 1 : no damage (P=0) also referred "security zone". The low threshold value, or the first zone (labelled zone 1 in fig. 2.5), defines the safety zone for the applications. For example, it is indispensable to define this fluence for safe exploitation of optical elements when it is essential not to destroy optical components during the exploitation period of a laser system or in consideration of industrial applications. 2. Region 2 : erratic damage (statistic) (0<P<1) If the pulse energy is increased above F th,low, the damage starts to appear in a nonsystematic manner (labelled zone 2 in fig. 2.5). This zone called erratic should be avoided for the development of controlled, reliable and reproducible processing. 3. Region 3 : systematic damage (P=1) If the pulse energy is even more increased, we reach the zone 3 (fig. 2.5). The value of high threshold corresponds to the minimal laser fluence to produce systematical damage for all irradiated sites. The third zone describes the zone for micromachining.

75 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses Technique of ablation detection Ablation is related to material removal. It is a 3D information to recover and it is best observed by an atomic force microscope (AFM) enabling to measure ablated depth, diameter as well as ablated volume. The first method for seeking ablation threshold fluence is presented in fig. 2.6, reporting the evolution of the ablation volume as a function of fluence. Figure 2.6: Ablated volume as a function of laser fluence. a) The whole range of fluences follows logarithmic law. b) "Linear" regime close to threshold helps to determine F th,a for zero volume. The measurement of the ablated volume for numerous energies enables to determine by regression the corresponding ablation threshold. We approximate the evolution of the crater volume and crater depth by a logarithmic law. In experimental works [33, 97], the linear evolution of absorption increase close to the threshold is reported. Indeed, once significant absorption is enhanced through optical field ionization, linear absorption through impact (avalanche) ionization is expected to be dominant for long pulse durations (as it is in this work). It allows to expect a linear increase of the ablated volume with the pulse fluence. Considering low fluences, we thus define the ablation threshold by extrapolating the linear regression to zero. Another approach to estimate the ablation threshold with an AFM consists in using the diameter regression technique. This technique based on the fact that the damage size depends on incident fluence was first proposed for 20 picosecond laser pulses [105]. It is less precise for long ( ps) pulses in comparison with femtosecond ones due to the thermal character of the interaction [12]. In fact, a femtosecond laser pulse yields incredibly small or even no collaterally damaged (thermally and mechanically affected) zone, allowing a deterministic correspondence between the beam dimension and the ablated zone and thus a precise threshold definition. Mathematically it is depicted as follows. We consider the radial fluence distribution at the focal point of the

76 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 40 Gaussian beam as given by [106]: F (r) = 2E πω0 2 e 2r2 /ω0 2 = Fpeak e 2r2 /ω0 2 (2.1) where r is the radial coordinate, ω 0 the beamwaist and E the energy. The peak fluence F peak is expressed as F peak = 2E/πω0 2. This expression yields a threshold two times higher than the average value F = E/πω0 2, which is also used in literature, when the description is given. Note, that this threshold expression considers the surface correction for equivalent "top-hat" energy distribution, a uniform cylindrical beam with the same total energy and peak fluence (S = πω 2 0 /2). Afterwards, the main assumption states that, if the material is not damaged at the distance r from the beam center, the corresponding fluence value F (r) is equal to the ablation threshold F th. Therefore, the interaction of such a beam with the sample results in a damage whose diameter D scales with a logarithmic law [15, 90, 107] as a function of the incident laser pulse fluence F: D 2 = 2ω 2 0ln(F/F th ) (2.2) The fig. 2.7 plots the squared diameter D 2 measured by the AFM as a function of incident laser fluence. The numerical fit defines the ablation threshold while crossing D 2 = 0. Figure 2.7: Squared diameter D 2 measured by the AFM versus the incident fluence. Example of diameter regression technique to define the ablation threshold. It is interesting to compare the information given by the AFM with the one retrieved with an optical microscope that mainly gives a 2D information with a maximal resolution of 1µm. It is worth to note that the microscope diameter regression technique gives similar threshold

77 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 41 value compared to the AFM in our experiments. Moreover, the optical microscope regression technique is less precise due to potential ambiguity when detecting ablation craters surrounded by laser thermal or shock affected zone. The error can become more important especially close to the threshold, when the diameter size becomes comparable to the resolution of the optical microscope ( µm). Figure 2.8: a - b) A characteristic picture from the optical microscope for two different fluences. It is difficult to distinguish the thermally and shock affected zone from the ablation crater. c) The AFM profile illustrates the simplicity to measure the ablated diameter with high confidence. For instance, fig. 2.8 demonstrates two cases of diameter detection. For high and low fluences it could be ambiguous to determine precisely the diameter of the damage. For example, fig. 2.8b gives more an impression of a bump than a crater. At the same time the affected zone surrounding the crater in fig. 2.8a can interfere with the measurement, as it is difficult to say where the crater finishes. Note that we can minimize the influence of such an error if the measurement is performed by the same experimentalist and by taking constant criterion for measurement. However, optical microscopy is more simple, less expensive and faster than AFM. The difference in threshold values given by both diagnostics is less than 15 %. Nevertheless, in our study we use mostly the threshold retrieved by the AFM regression technique due to the higher resolution at the µm scale and the three dimensional aspect of the measured information. The most reliable technique of the ablation detection is thus AFM regression technique as the measurement by the atomic force microscope gives quantitative data of the amount of the ablated depth, diameter and volume. It quantifies the destruction of a very thin (theoretically up to one) atomic layer. The two techniques based on volume and diameter regression are reliable due to the unambiguous determination of the quantity of the ablated material. It is even possible to distinguish thermally and mechanically affected zone, inducing compression and resolidification of the crystalline lattice. Both methods give similar threshold values. The volume regression technique is even more precise as it considers "real" 3D crater and not 2D diameter. All the processes during laser ablation on a large time scale are three dimensional and the ablated volume characterizes better the final result of the interaction. In conclusion we point out, that we use optical microscope for determination of the damage

78 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 42 threshold (qualitative analysis of the laser-induced impacts). For the ablation detection we use the volume regression technique by AFM as a quantitative measurement of the ablation characteristics with high resolution. 2.3 Experimental set-up To obtain precise measurements and reliable information for micromachining and for understanding the basic mechanisms of laser-matter interaction, one should pay attention to all consecutive steps of experiments. We devote this part of the manuscript to the description of the conditions to perform a measurement as precise as possible and to the estimation of the error bar. For illustration, we also give the results of the damage and ablation thresholds measured by the different techniques described before. For that purpose, a damage and ablation set-up is developed (see fig. 2.9) including the laser system and optical elements for manipulating the beam, the handling and movement of the sample and the diagnostics. All experiments are produced at ambient temperature and normal pressure. Figure 2.9: Experimental damaging and ablation test-bench. M mirror; C polarizer cube; PC Pockels cell; Lift beam elevating system; λ/2 half-waveplate; Pol Brewster polarizer; L telescopic system (f 1 = 150 mm, f 2 = 500 mm); PD REF reference photodiode; L 1 focusing lens; BD beam dump, MO microscope objective, Camera visualization system.

79 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses Laser parameters A linearly s - polarized Yb:KGW laser (Amplitude Systèmes, S-pulse) provides 500 fs pulses at the central wavelength of 1025 nm ( λ = 3 nm). The pulse duration of the laser is controlled by a second order autocorrelator (model ASF-200 by Avesta or APE mini, see fig. 2.10). Figure 2.10: Laser characterization. Measurement of the pulse duration with the second order autocorrelator (APE, Avesta). The beam profile and beam energy distribution in the near-field at the exit of the laser is presented in fig. 2.11a. Figure 2.11: Laser characterization. a) Beam profile and beam energy distribution in the nearfield, beam diameter is measured at 1/e 2 ; b) Beam profile in the far-field and beam energy distribution (beamwaist size measurement at 1/e 2 ).

80 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 44 The beam is further expanded by a diverging-converging telescopic system (f 1 = 150 mm, f 2 = 500 mm) of magnification 3.3 yielding collimated laser beam of 8.0 mm on the focusing length L 1 (f = 50 mm). The choice of the focal length will be justified hereafter (see section 2.3.3). As the size of the beam defines the fluence (and thus, damage and ablation thresholds), it is very important to measure precisely the size of the beamwaist. The measurement is done for all experiments. The propagation parameters (ω 0, z r, M 2 ) 2 of the Gaussian laser beam are measured by imaging the beam focal plane on the CCD of a beam analyzer (fig. 2.9) with a 20 microscope objective. The beam analyzer is removed from the experimental installation during experiment. In order to retrieve precisely the propagation parameters, the beam size is measured in several positions along the optical z-axis as it is illustrated in fig The calibration of the CCD matrix is done with a calibration grid (200 lines/mm) in order to retrieve the value of the beam parameters. Another important point is that the stored data are further mathematically treated (calibration of the beam size in respect to the acquirement field) to minimize the induced error. Figure 2.12: The radius of the laser beam along z-axis experimentally measured and theoretically approximated with M 2 - factor. 2 The beamwaist ω 0 implies the minimal size of the focused Gaussian beam at a single position along the propagation direction - z. The Rayleigh range z r is the distance where the size of the beam increases to 2ω 0. z r = πω2 0 M 2 λ. The M 2 factor expresses the beam quality propagation factor in comparison with the perfect Gaussian beam (M 2 = 1).

81 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 45 The waist measured experimentally at 1/e 2 yields in x - direction ω 0,x = 6.6 ± 0.4 µm 3 and in y - direction ω 0,y = 6.0 ± 0.4 µm (see fig. 2.11b). The Rayleigh range z r is estimated to 95 µm (considering x-direction) and 75 µm (considering y-direction). For our laser system the laser beam is slightly astigmatic (see fig. 2.12) with a difference of 20 µm between two focal planes z r,x and z r,y. The laser beam is also slightly asymmetric as can be seen from fig We fitted the experimental distribution (fig. 2.12) with the theoretical Gaussian beam propagation law. Theoretically, for a given wavelength, the variation of the size of the focal spot along the propagation direction is: ω(z) = ω M 2 (z z ω0 ) 2 zr 2, (2.3) where z is the distance from the focal plane, z ω0 the position of the focal plane, z r the Rayleigh range. In our case M 2 x = 1.35 and M 2 y = 1.3, that characterizes the quality of the beam with respect to the "perfect" Gaussian one. For the estimation of threshold values we always take the average value of the beamwaist size (ω 0 = 6.3 µm, z r = 85 µm, M 2 = 1.33) and we are positioned almost equidistantly between ω 0,x and ω 0,y. Note, we use the formula for deriving the beamwaist in the collimated geometry: 2ω 0 = 4λ π f D M 2, (2.4) where D is the diameter of the unfocused beam, f is the focal distance. We obtain ω 0,theory = 5.5 µm, that is in accordance with our measurement. To assure single pulse picking from the 1 khz pulse train, we implement a Pockels cell (model PCD-d by BME-Bergmann) and a polarizer cube at the laser exit. The Pockels cell also enhances the contrast between the femtosecond laser pulse and nanosecond Amplified Spontaneous Emission (ASE), the pre- and post-pulses and the emission of the oscillator by thoroughly chosen delay of the optical shutter (see fig. 2.13). The Pockels cell in combination with the polarizer cube also allows to get cleaner polarization. Note that, the pulse duration is not significantly modified upon traversing the polarization elements (the Pockels cell and the polarizer cube) due to the small spectral bandwidth of the laser ( λ = 3 nm; τ L = 500 fs). 3 The error of the 0.4 µm corresponds to the uncertainty of CCD acquisition, 1 pixel.

82 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 46 Figure 2.13: Schematic presentation of Pockels cell pulse-picking. ASE is in violet, the emission of the oscillator are red lines, 1 khz laser pulse train are red pulses. The energy is measured by two power-meters: a Thorlabs detector (S120B) is used for low energy and a Coherent one (Power max, PM3) for high energy. The detector is placed before the focusing lens, measuring the energy for each position of the rotational half-waveplate and the energy correction is done with respect to the transmission of the lens. The table 2.1 summarizes the main laser parameters used in our experiments. Laser parameter Symbol Value Wavelength λ 1025 nm Bandwidth λ 3 nm Energy, max E max 180 µj Pulse duration τ L 500 fs Repetition rate R rep 1 khz Near field beam divergence (total) 200 µrad Beam quality factor M Shot to shot fluctuations E 5% Beam pointing stability < 10 % Beamwaist, f = 50mm ω µm Table 2.1: Summary of laser parameters Sample positioning and diagnostics The sample is placed perpendicularly to the laser beam. The incident laser beam has a nearly- Gaussian intensity distribution. It is focused on the target surface, using a f = 50 mm focallength, to a focal spot size of radius ω 0 = 6.3 µm measured at 1/e 2 (see 2.3.1). We obtain a precise positioning of the sample in the laser focal plane by combining energy - and z - scan procedures. The procedure consists in examining first the occurrence of laser damage on a wide range of positions along the optical z-axis. This initial experiment, performed

83 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 47 at relatively high energy, allows to define an extended zone of damage ( z) by means of the in-situ visualization system, composed of a CCD camera equipped with an objective of high magnification. The energy is further decreased as well as the magnitude of the probed z zone. Upon the repetition of this procedure with progressive decrease of the energy (close to the energy threshold) and of the z-step increment (up to 10 µm), we obtain the precise positioning of the sample in the beam focal plane. The target displacement is assured by three x, y, z - motorized translation stages (Newport MFA-CC with minimal displacement step of 0.05 µm and maximal displacement speed of 2.5 mm/s). The translation stages, the half-waveplate rotation for the energy control, the opening of the Pockels cell-based optical shutter and the recording of the different diagnostic signals (the reference photodiode, etc.) are operated by a home-made computer program using LabVIEW R and XPS Motion Controller. The target is illuminated by an incoherent white light source (Fiber-Light, DC-950 by Dolan- Jenner), so that the in-situ visualization system collects scattered and reflected light from the laser-induced permanent damages on the target surface Remarks on the choice of the lens focal length In the frame of our works, the choice of the lens focal length is a compromise between the following remarks: Applicative aspect Strong focalization with high numeric apertures is interesting for micromachining which demands micrometric and even nanometric size structures (ω 0 < µm). Aspect of detection In the case of small beamwaist size or strong focusing, the size of the damage is comparable to the resolution limit of the microscopic system (in order of 1 µm). Thus, a focal spot size ω 0 > µm is more adapted to demands of detection system (like an optical microscope). Fundamental aspect The fundamental purpose of this work is to study accurately the response of the dielectric material (fused silica) upon laser excitation. The beamwaist size ω 0 should be sufficiently large to induce detectable effects and ensure an easy collection of the signal. Aspect of ambiance During laser beam focalization, several phenomenas can distort a measurement and its interpretation. Here we consecrate our attention to the most important points: aberrations

84 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 48 and self-focusing. Geometrical (mainly spherical) and chromatic aberrations of the focusing lens can alter the spatio-temporal distribution of the beam in the focal plane (modification of its size, pulse duration and position on z-axis). Some other more important circumstances such as self-focusing or air ionization before the target can produce destructive consequences on the propagation of the laser beam and its characteristics (in case of high laser power). We analyze the experimental conditions before performing the experiments to verify if those undesired effects could influence our measurements (see section and ) Aberrations Especially, in case of femtosecond lasers, the aberrations induced by the focusing (lens, microscope objective,...) could catastrophically change the spatio-temporal distribution of the laser beam in the focal plane. Spherical aberrations induced by the difference of optical path of the beam at the center and at the periphery of the focusing lens are amplified by strong focusing. This type of aberration causes spatial and temporal enlargement of the focal spot, that is why we pay a particular attention to the choice of the focal lens. To minimize these aberrations, we use plano-convex lens. When dealing with optical lenses of small focal distance, the aberrations tend to increase ω 0. To minimize the aberrations, one needs to use a long focal lens and thus large beamwaist size (ω 0 > µm). We verify the influence of the spherical aberrations on Gaussian beam spatio-temporel distribution for a BK7PCX lens with focal distance of 50 mm. The focus spreading is expressed by [108]: f = 4Af 2 λω 2 0 2πa 4, where f is the focal distance, n the refraction coefficient of the lens and the lens parameter is: A = 2π λ n 2 (n 2 4) + 2n 8n(n 1) 2 (n + 2) ω 0 ( ) 3 ω0 f We get f = 15 nm, that is strongly inferior to the Rayleigh range. The pulse temporal spreading is given by: T 3 Aλ 4 πc ( ω0 ) 4 a We estimate T to be negligibly small compared to the pulse duration τ L. The broadening of the beam estimated in the plane of the circle of least confusion can be found

85 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 49 from: ω( f)/ω 0 = 1 + ( 3 4 ) fλ 2 πω0 2 We find ω( f)/ω 0 1. Chromatic distortions in which a lens or an objective fails to focus all the frequencies to a single point are due to refractive index dependence on the incident wavelength. Chromatic aberrations affect mainly the temporal distribution of the pulse leading to elongation of the pulse duration, but they can also cause spatial elongation. The influence of chromatic aberrations is minimized due to the laser pulse duration of 500 fs (Fourier diffraction limited spectrum corresponds to 3 nm). Nevertheless, we verify the influence of chromatic aberrations on lens focusing. The focus spreading is expressed by [109]: f = fλ2 c(n 1) dn τ L dλ, where f is the focal distance, n the refraction coefficient of the lens, τ L the pulse duration, dn dλ the dispersion for the lens (for our case, dn dλ = µm 1 ) 4. We get f = 4.1 µm, that is lower than the Rayleigh range. The pulse temporal spreading is given by: T = λ2 f (πω 0 ) 2 2c(n 1) (λdn dλ ) We estimate T to be equal to 6 fs, that is strongly lower than the pulse duration. The broadening of the beam can be found from: ω( f)/ω 0 = 0.441π τ L λ 2 (πω 0 ) 2 fλ dn c(n 1) dλ We find ω( f)/ω 0 = We thus consider these aberrations to be negligible in our experiment Self-focusing and air ionization The dependence on intensity I(x,t) of the refractive index 5 could result in self-focusing of the laser beam. As n 2 is positive for most materials, the refractive index is higher at the center than at the periphery of the beam, and thus its variation acts as a converging lens and focuses the beam. The occurrence of self-focusing depends on the ratio of beam power in respect to the 4 Calculated with a laboratory home-made software. 5 n = n 0 + n 2I(x, t), where n 0 is the index of refraction and n 2 the nonlinear index of refraction.

86 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 50 critical power defined by: P cr = 3.77λ2 8πn 0 n 2 for a Gaussian beam [110]. If P > P cr, self-focusing occurs. For fused silica (n 0 = 1.45, n 2 = cm 2 /W [111] 6, λ = 1025 nm), it gives P cr,sio2 = 3.1 MW. If we take the maximal energy in our experiment (E 70 µj), the power is P 70µJ 500fs = 140 MW. This value is strongly superior to the critical power of self-focusing. If we take the threshold energy in our experiment (E 5 µj), the power is P 5µJ 500fs of self-focusing. = 10 MW. This value is still superior to the critical power It should be noted, that the critical power defines the occurrence or not of self-focusing, and the peak laser intensity I 0 determines the length of the self-focusing L sf given by: L sf = λ 2πn 2 I 0. We, thus, calculate it for our case. For example, for the threshold intensity I(x,t) = W/cm 2 the calculation of L sf gives 15 µm. The self-focusing length L sf is much superior to the characteristic interaction zone where the effective absorption is reached. In addition, we have never detected any traces of sub-surface or bulk laser-induced damage neither below, nor above the threshold with the optical microscopy detection technique. Moreover, the value of n 2 used for these calculations is overestimated as it was measured for longer pulse duration regime, where molecular effects such as molecular reorientation, Raman and Brillouin effects are taken into account (those effects are produced on timescales longer in comparison to femtosecond ones). In femtosecond regime, only electronic effects are present. Thus, the critical power is expected to be much higher when considering femtosecond pulses. Moreover, we minimize the possibility of the occurrence of this nonlinear effect by carefully working at the surface of the dielectric and by using small focused beams (ω 0 6 µm which is obtained with f = 50 mm). The beam propagation in the incident medium (air) before the target surface should be also considered. In air, the critical power for self-focusing is P cr,air = 3.35 GW (with n0 = 1 and n 2 = cm 2 /W [111]). In our experiments, the beam power is far below the critical power in air, thus indicating the absence of self-focusing effects before the target surface. When a femtosecond pulse propagates in air, the intensity can be sufficient to provoke air ionization. In this case, the plasma can defocus the propagating beam causing, for example, the change of the ablation crater morphology 7. The condition of absence of air ionization demands intensities I < W/cm 2 before the target. We work on the target surface in the intensity range 6 The dependence of the nonlinear index of refraction n 2 on wavelength and pulse duration is neglected. 7 Note, if this phenomenon occurs, the nonlinear absorption considerably lowers the peak power before the focal region [112], thus arresting the development of self-focusing.

87 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses I W/cm 2, thus, we expect that air ionization does not influence our experiment. In addition, we develop an experiment to confirm the non-significant influence (if there is any) of the self-focusing and air ionization. The experiment is related to the beamwaist positioning or the sample positioning in the focal plane of the laser beam 8. The beamwaist is found with the standard procedure of energy and z - scan (see section 2.3.2). Figure 2.14: Experiment of damage probability for different beamwaist positions. The induced error of 50 µm is an arbitrary value corresponding to 0.6 of the Rayleigh range ( 85 µm). Then we displace the target from this position inducing an arbitrary error of ± 50 µm (fig. 2.14) and we perform the experiment of the surface damaging in three different planes (z ω0, z ω0 50µm and z ω0 +50µm) of the Rayleigh range ( 85 µm). The damage threshold value slightly increases (from F th,low = 4.4 J/cm 2 for z ω0 to F th,low = 5.2 J/cm 2 for z ω0 ±50µm) 9 as the sample is "badly" positioned in accordance with a non-perturbed propagation of the Gaussian beam (see fig. 2.15). Indeed, locally the intensity decreases due to the increase of the beamwaist size, thus, the minimal energy to produce damage respectively increases. Moreover, when examining the ablation crater dimensions at high energy (fluence) (see chapter 3), one can observe that they never exceed the beam dimensions confirming that the beam propagation is non significantly perturbed even at high energy. The low threshold values are similar for z ω0 50µm and z ω0 + 50µm. In this case, we can state that there is no significant influence of the non-linear effects such as air ionization and self-focusing close to damage threshold. The difference in high threshold for z ω0 50µm and z ω0 + 50µm is probably due to the astigmatism and asymmetry of the beam that was shown in fig We can additionally conclude that the positioning of the target is precise in respect to 8 We remark, that 50 µm is superior to the uncertainty in fixing the target position in the focal plane, and which is related to beam astigmatism ( 20 µm), the smallest z-scan increment used (10 µm) and the capacity of detection of small changes by in-situ diagnostics. 9 We recall here that the threshold is always expressed with respect to the beamwaist ω 0 = 6.3 µm.

88 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 52 the focal plane. Figure 2.15: Probability of damage as a function of incident laser fluence. beamwaist positioning on the damage threshold. Influence of the To satisfy all the delicate aspects listed above (applicative aspect, aspect of detection, fundamental aspect and minimization of the non-linear effects and aberrations), while choosing the focusing lenses, the most convenient lens focal lengths appear to be in the range between 50 mm and 100 mm. We finally choose f = 50 mm. 2.4 Precision of measurement and error bar estimation We pay special attention to the precision of measurements, because we would like to determine accurately the laser energy deposited into the material during the interaction. We are also intended to define the "optimal working fluence range" for femtosecond laser applications, notably in micro-machining and corneal surgery. That is why, it is of the paramount importance to measure the value of damage or/and ablation threshold with high precision. We have elaborated and formulated a precise methodology and developed an experimental test-bench where every component was delicately chosen. Now it is important to evaluate the uncertainty of the measurement and on the determination of damage and ablation thresholds and their characteristics (ablated volume, depth, diameter). For a given laser system, the determination of a precise threshold fluence is related to the precision of the energy and beam diameter measurement, but also to the diagnostics, methodology, experimental set-up (for instance, precision of the target positioning, beam fluctuations, etc.) and accuracy of postmortem treatment. In the following we estimate the error induced during a measurement.

89 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses Single experiment Choice of the number of experimental trials The multiplication of experimental trials reduces the error SE (relative to non-systematic class of errors) of measurements according to the following expression: SE = σ n (2.5) where σ is the sample standard deviation (in terms of chemical composition, surface state or pollution, etc.) and n the total number of observations of the sample. The number of sample observations is 20 in our experiment. This number appears to be sufficient taking into account the observed standard deviation of ablation characteristics (ablation depth, diameter, volume, see fig ) related to every fluence used and damage probability. This number is also optimized to minimize the influence of shot to shot fluctuations of the laser ( 5%) and the failure ( 4%) of the home-made synchronizing system (Laser Pulse picking Acquisition system). The number of experimental observations coupled to small energy increments close to threshold also increases the precision in the threshold fluence determination after exploiting a damage probability measurement. Note that more detailed description of this kind of error is done in ref. [113] Error bar related to laser parameters We recall that: The error bar (systematic error) for the beamwaist measurement is in order of 12 % (ω 0 = 6.3 ± 0.4 µm). The error bar for the sample positioning in the focal plane z is less then 50 µm and is in order 10 µm yielding an error of 6% considering Gaussian law for the beam propagation. The error bar for the energy measurement is related to two power-meters. We always use an adapted detector: a Coherent power-meter with the precision of 0.1 µj is used for high energy measurements and a Thorlabs power-meter with the precision of 0.05 µj measures low energy. In addition, we cross-calibrate two detectors and according to this calibration estimated the energy in the intermediate zone Postmortem treatment One of the critical point for determining the threshold value is the choice of damage and/or ablation detection technique. Optical microscopy technique is well adapted for determination of

90 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 54 the damage threshold considering a qualitative analysis of the laser-induced impacts. The AFM regression techniques are used for ablation detection through quantitative measurement of the ablation characteristics with high resolution. Now, we estimate the error that can be induced while analyzing the experimental data. Concerning the damage analysis, a damage can be not detected due to the small impact size even if it is present. This error is higher, when the damages are smaller and close to the detection resolution. To minimize this error, we recall that we use sufficiently long focal lens (f = 50 mm) yielding impacts in the range 1-20 µm easy to detect with an optical microscope. In order to further decrease this error, we also pay attention that the same user performs the measurements of the damage and ablation thresholds (statistical approach and regression technique) and in the same conditions (illumination and magnification). Concerning the ablation analysis, an important point is the choice of the number of points and the value of the coefficient of determination R 2 to determine the threshold (fig. 2.16). Figure 2.16: Ablated volume as a function of incident laser fluence. We determine the thresholds with different number of points. For red squares (respectively, green crosses) we take 5 (resp. 6) fluence points to determine the ablation threshold. In table 2.2, we show the values of the ablation threshold retrieved from the same experimental data, but taking into account different number of points. Number of points Ablation threshold, AFM volume R 2 F: J/cm F: J/cm Table 2.2: Influence of the choice of the number of points (different fluence range) on the threshold value.

91 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 55 Depending on the number of experimental points, we obtain a threshold value of F abl,1 = 5.9 J/cm 2 (5 points) and F abl,2 = 5.0 J/cm 2 (6 points). In order to limit the uncertainty, we always pay attention 10 : To use a large number of points especially close to the threshold 11 (different fluences). To consider the coefficient of determination R 2 (R ). The uncertainty of this determination is estimated to be 15% Reproducibility of results We also tested the reproducibility of the threshold measurement in order to estimate the difference, when comparing several experiments. Experiments in the same experimental conditions, but performed at different dates, yield a maximal uncertainty of ± 1 J/cm 2 on the absolute values of the threshold ( 20%) 12. These differences could be due to the variations of the local material "conditions" (local composition, pollution,...), small differences in positioning of the sample or beam parameters (beam dimensions), etc Conclusion The short review of the experimental parameters of importance in the developed damage and ablation test-bench allows to conclude, that the experimental set-up possesses a nearly optimized design and stability for obtaining precise measurements in the micrometrical range and retrieve accurate thresholds and important data for analysis of laser-matter interaction at average intensity flux (10 13 W/cm 2 ). We estimate the total uncertainty in the threshold determination to be %. 2.5 Damage and ablation thresholds of fused silica Now using our experimental set-up and the depicted methodology, we determine the damage and ablation thresholds from the impact matrix shown in fig The target consists of high-purity fused silica samples (Suprasil and HOQ 310 by Heraeus) 13. The experimental results for each 10 We use the same approach for the determination of the ablation threshold through diameter regression technique both from a microscope and an AFM. 11 Note that, the threshold is not known a priori during experiment. Now, by implementing our precise and controlled procedure of experiment (visualization, positioning,...) and methodology (multiplication of the number of points, ex-situ diagnostics,...), we always determine with a good confidence the corresponding thresholds. 12 We consider the absolute value to be the value of the threshold defined for exactly the same experimental set-up, sample and in single shot regime. 13 Suprasil, residual roughness measured with the AFM Ra=0.2 nm, impurities are negligible <0.065 ppm, total bubble cross section within the volume is mm 2 /100cm 3. HOQ 310 with residual roughness measured with the AFM Ra=1 nm, total bubble cross section within the volume is 0.5 mm 2 /100cm 3, typical trace impurities (in weight ppm): Al 20; Li 1; Ca 1, Mg 0.1; Cr 0.1; Na 1; Cu 0.1; Ti 1; Fe 0.8; OH 30; K 0.8).

92 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 56 energy case (laser fluence F) are averaged on 20 shots, each one on a fresh zone of the sample. The graph 2.17 depicts the damage probability distribution as a function of incident laser fluence for SiO 2. The low and high thresholds are respectively F low = 4.4 J/cm 2 and F high = 6.2 J/cm 2 and the fluence range, where the damage is erratic, equals to 1.8 J/cm 2. Figure 2.17: Damage probability as a function of laser fluence. The damage threshold of suprasil that is measured by statistical approach. The damage thresholds fluence is defined as the maximal fluence not to cause any surface modifications visible by an optical microscope. Fig illustrates the determination of the ablation threshold estimated by two techniques: i.e. the AFM squared diameter regression and volume regression techniques. We note, that for both of them R 2 - factor equals to A more extensive study of AFM curve behaviour will Figure 2.18: a) Ablated squared diameter as a function of incident laser fluence. The logarithmic fit allows to determine the ablation threshold. b) Ablated volume as a function of incident laser fluence. The linear fit determines ablation threshold fluence when the quantity of ablated volume equals to zero. be given in chapter 3. Here, we just point out, that, in the AFM squared diameter regression, the entire curve is approximated by a logarithmic law. The volume regression technique is fitted

93 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 57 by the liner regression close to the interception with abscissa (ablated volume 0). In table 2.3, we group the threshold values for fused silica. Material Damage threshold Ablation threshold Low High AFM, D 2 AFM, volume Suprasil 4.4 J/cm J/cm J/cm J/cm 2 Table 2.3: Recapitulation of threshold values for fused silica. The damage threshold is 2 J/cm 2 lower than the ablation threshold given by two AFM techniques. Both AFM approaches give similar values. It is worth to note, that the high damage threshold is somewhat similar to ablation threshold [103]. This high threshold value could be considered as a reference value for micro-machining processing, because it defines the lowest fluence for assured modification of the material for all irradiated sites. 2.6 Conclusion In this chapter we have put in evidence the necessity of the definition of the threshold and the importance of the distinction in damage and ablation of materials. Further, we have given the classification of the material modifications (damage and ablation) in accordance with applied laser fluence. We have developed a methodology for damage and ablation detection. The qualitative study by the optical microscopy is the best method for damage threshold determination and the AFM quantitative measurement is well suited for ablation threshold determination. We have proposed an experimental set-up for studying damaging and/or ablation of the dielectric material. We have shown and discussed the critical points to get a precise and reliable experimental results, examined the stability of our experimental set-up and estimated the error of our measurement. The interest of micro-machining considers the theoretical and experimental ability to predict the final results (in terms of diameter, shape and depth of the ablated crater). Thus, it is essential to correlate the absorbed energy with morphology of the holes. Now, in the next chapter, we will go further from the determination of the threshold values to the study of the fundamental aspect of this work: i.e. the material absorption as a function of incident fluence.

94 Chapter 2: Methodology, experimental set-up. Damage and ablation of fused silica irradiated by 500 fs laser pulses 58

95 Chapter 3 Analysis of energy deposition. Contents 3.1 Introduction Pump depletion. Energy balance as a function of incident fluence Pump-pump experimental test-bench Pump-pump experiment Analysis Conclusion Temporal dynamics of energy deposition: pump-probe experiment Some relevant previous results Pump-probe experimental test-bench Sample positioning. Focusing pump and probe beams. Preliminary experiments Reflection, transmission and absorption during the pulse Reflection, transmission and absorption on long temporal delays Energetic considerations Conclusion

96 "Nothing in life is to be feared. It is only to be understood." Marie Curie.

97 Chapter 3: Analysis of energy deposition Introduction In the previous chapter we made an overview of the measurement techniques for damage and ablation. Now we will use this precise methodology to explore the fundamental aspects of damage and ablation in dielectrics. In particular, we would like to answer several questions, among them: "How much energy is reflected, transmitted and absorbed by a target? How efficient is the laser energy deposition?" Raising these questions and answering them should shed light on the energy balance during laser-matter interaction and help for optimal processing of dielectric materials. We thus develop pump-pump and pump-probe experiments to properly measure the reflected and transmitted parts of the incident laser pulse for further estimation of the total energy absorbed and the dynamics of the absorption during the pulse for a wide range of fluences. This energy balance (here retrieved) as a function of incident fluence is further correlated to the morphology of ablation craters (see also chapter 5) and the efficiency of laser pulse absorption. As a result, the prediction of shape and depth of final craters shall become possible on the basis of the comparison of absorbed energy to ablated volume, that is of particular interest for applications in micro-machining. In addition, we devote this chapter to the theoretical study of the mechanism of laser absorption. Computation results aim to understand underlying phenomena of laser damage and ablation and to reproduce the ablation crater depth based on energetic considerations. The pump-probe experiment also allows to confront the hypothesis about the temporal delay to create an absorbing and reflecting medium. These experiments give essential information about damaging and ablation of dielectrics. 3.2 Pump depletion. Energy balance as a function of incident fluence Pump-pump experimental test-bench The standard damage and ablation set-up shown in chapter 2 is slightly modified to accommodate the measurement of reflection and transmission of the pump pulse allowing further determination of total material absorption as a function of incident laser fluence (fig. 3.1). The incident laser beam is focused normally on the sample surface, using a f = 50 mm focal lens, yielding ω 0 = 6.3 µm at 1/e 2 in the focal plane. The incident, reflected and transmitted pump signals are measured by three photodiodes allowing to determine finely the amount of energy absorbed by the sample. The lens L 2 with a focal distance of 50 mm assures the collimation of the transmitted beam. When a surface is irradiated by a laser beam, the created plasma emits light. Its broadband

98 Chapter 3: Analysis of energy deposition. 62 Figure 3.1: Pump-pump reflection and transmission experimental diagnostics. M mirror; PC Pockels cell; Lift beam elevating system; λ/2 half-waveplate; Pol Brewster polarizer; L telescopic system; F spectral band-pass (longpass cut-on filter at 1000 nm combined to a Siphotodetector of 1.1 µm cut-off frequency) and neutral density filters; PD photodiode (REF reference beam; T1, T2 transmitted beam; R reflected beam); L 1, L 3, L 4, L 5 focusing lenses; L 2 collimating lens; BD beam dump; C polarizer cube; SF spatial filter. emission is commonly centered in the ultraviolet region of the optical spectrum. For proper determination of R and T signals, it is important to ensure the collection of the light coming only from the laser beam and to minimize the influence of this "polluting" emission. For this reason, during the experiments, we implement spectral bandpass filters (coupling of a longpass cut-on filter at 1000 nm combined to a Si-photodetector of 1100 nm cut-off frequency) for optical isolation of the signals with respect to the broadband plasma emission. At the same time, the plasma emits in a wide solid angle different to the laser beam. To get optimal isolation, we also dispose spatial filters (SF) in the far-field (L i, i = 3, 4, 5 and SF) to cut the plasma spatial contribution. Moreover, we verify that the free electron plasma created by the laser pulse on the surface of the sample does not significantly change the beam polarization and influences R and T measurement. To that aim, we measure the two linear polarization states (s and p) components of the transmitted signal (measured with PD T1 and PD T2 ) as a function of fluence (fig. 3.2).

99 Chapter 3: Analysis of energy deposition. 63 Figure 3.2: Evolution of the s - and p - polarization components of the transmitted signal as a function of incident fluence. Inset shows more precisely the evolution of the s-polarized component of the beam. Two regimes ("low and high" fluences) are put in evidence and the corresponding slope of the linear fits are given in the figure. The results show that the signal collected on the residual polarization state (here the s- component) is negligible with respect to the p-component even for high incident fluence. Moreover, exercising the trendlines for both s - and p - polarization, we note that: Linear fits correctly reproduce the data. The slopes are attributed to two regimes: below the threshold (or "low fluence regime", no significant absorption) and above the threshold fluence (or "high fluence regime", high absorption or ionization). The respective slope ratios between s - and p - polarization curves in two regimes are nearly constant and equal to 100 for the low fluence regime and 10 for the "ionization" regime. The slope of the s-polarization state is always inferior to p-state. We thus conclude that there is no significant plasma-induced depolarization of the transmitted beam during the measurement (at least in the range of fluences up to 70 J/cm 2 ). After these preliminary verifications, we use the signals of photodiodes P D REF, P D R and P D T2 to establish the evolution of R and T as a function of fluence Pump-pump experiment Measurement The measurement of reflected and transmitted parts of the beam aims to calculate the absorption of the laser pulse by a target. We suppose that: R + T + A = 1, with R = R spec + R diff and T = T spec + T diff. The specular (measured in our experiment) and diffuse parts of reflection and transmission respectively noted R spec, T spec and R diff, T diff contribute in the equation. The changes in R diff and T diff can be neglected due to the pump duration, as the important

100 Chapter 3: Analysis of energy deposition. 64 variations of surface material parameters (morphology change) are supposed to take place on a timescale of picoseconds that is considerably larger than the timescale of the pump pulse. Moreover, as we are working with an initially perfectly optically polished surface (R diff R spec, T diff T spec ), we assume: A = E abs /E inc = 1 R spec T spec = 1 E refl /E inc E trans /E inc (3.1) where E inc, E refl and E trans are measured by photodiode P D REF, P D R and P D T2 signals Results Figure 3.3: Evolution of reflection, transmission and absorption as a function of normalized fluence. F th is the damage threshold. Each point is averaged on 20 laser shots and corresponding error bars representing the standard deviation of the data are shown on the graph.

101 Chapter 3: Analysis of energy deposition. 65 The experimental curves of reflection, transmission and absorption are presented in fig. 3.3 as a function of normalized incident laser fluence (normalized with respect to the damage threshold F th = 4.4 J/cm 2 as determined by the methodology described in chapter 2). The reflection, transmission and absorption curves and the damage and ablation thresholds are obtained separately and by two different measurements. Note that the onset of the transmission change roughly corresponds to the damage threshold fluence. At the damage threshold, the absorption equals to 2%. This value approximately defines the minimal energy dose to render the material absorbing. The transmission swiftly decreases with incident fluence and, at the ablation threshold F abl,th = 5.9 J/cm 2 (1.3 F/F th ), the absorbed energy roughly amounts to 25 % of the incident energy corresponding to the amount of energy to render the dielectric medium highly absorbing. The ensemble of reflection and transmission behaves differently (see fig. 3.3 and fig. 3.4). Figure 3.4: Relative change of reflection and transmission as a function of normalized fluence. The inset demonstrates the relative change of reflection and transmission close to the threshold fluence. The initiation of the significant relative change 1 of the reflection starts from 2.2 F/F th and is delayed compared to transmission (δt starts from F/F th ). The reflection does not exhibit important change up to 3 F/F th (it approximately increases twice). The relative change of the reflection is more important than the one for transmission. The reflection reaches a value that is almost 4 times its initial value. This change is rapid up to 6 F/F th and is followed by saturation. The relative transmission change is gentle and the curve progressively proceeds to saturation. 1 The change of 10 % from the maximal value is taken as a criterion of significant change.

102 Chapter 3: Analysis of energy deposition. 66 The decrease of the transmission curve in fig. 3.3 is followed by saturation from 5 F/F th. We also notice that absorption saturates at 70% and transmission at 15%. The experimental data shows low transmission and low reflection (does not exceed 20%) at high fluences. We presumably think that a part of energy of the leading edge of the incident pulse is transmitted before the material becomes highly absorbing. We also note that the fraction of the transmitted energy slowly decreases with incident fluence increase (high fluence from 7 F/F th ). As the transmission appears to be nearly saturating at very high fluences (> 5 F/F th ) and in all cases never going to zero, we suppose that there is some time needed to create the free electron density required to cause optical breakdown and to trig a highly absorbing medium. Now, as this process is laser energy consuming, the change in transmission is immediate. Another explanation could be that the medium is partly transmitting during the entire pulse duration. These hypotheses will be examined in further details with a pump-probe experiment aiming to precise the exact dynamics of laser pulse absorption. We also surmise that additional energy and time is required to make the material reflecting. That is possibly the reason of the retarded reflection change in comparison to transmission and also of the reflection saturation at high fluence 2. To verify it we also develop a pump-probe experiment (see section 3.3). The evolution of the absorbed energy as a function of incident laser fluence allows to presume that it exists an optimal fluence range where a balance between an important effective absorption and delayed plasma shielding is reached during the pulse. Another important point is the absorption dynamics (with respect to fluence) and how it influences the ablation characteristics. Experimental measurements of the fraction of reflected and transmitted energy and of ablation craters allow to correlate the absorbed energy to ablated matter. We study the morphology change considering the evolution of ablated volume, ablated depth and crater diameter as a function of incident fluence. Similar curves are obtained for two fused silica samples (suprasil and HOQ 310) 3. Figure 3.5 presents the evolution of ablated depth as a function of laser fluence. The curve exhibits two tendencies: a linear regime, where the ablated depth grows rapidly with fluence increase; and saturation of ablated depth for high fluences. We correlate this behaviour with the experimental curve of absorption dynamics and the creation of plasma at the surface of dielectric material. It is widely accepted that the threshold of optical breakdown is achieved when the electron density equals to critical density 4. When the critical density is attained, high absorption takes place in a thin surface layer and it is further accompanied by the reflection increase. We suppose that for high fluences the rear part of the pulse can be reflected (pulse 2 The onset of a highly reflecting medium presumably arrives late in the pulse, the consequent change of the totally reflected energy normalized to the incident energy is small. 3 All the experimental curves presented in this manuscript are done for suprasil. 4 We recall here the value of critical density n cr = ω 2 Lm eε 0/e 2 (n cr = cm 3 at λ = 1025 nm).

103 Chapter 3: Analysis of energy deposition. 67 shielding) resulting in a partial arresting of energy deposition. The saturation of ablation depth is thus achieved. Figure 3.5: Ablated depth as a function of laser fluence. From these measurements, due to self-shutter behaviour, it is however difficult to conclude about the closing efficiency (that means "the exact value of the reflection coefficient of the plasma mirror") but we speculate that the plasma shielding effect is less efficient for longer pulse durations, because of less rapid and less strong saturation of ablation depth observed with respect to short pulses [114]. Fig. 3.6 and fig. 3.7 then groups the evolution of the crater diameter and volume as a function of incident fluence. We recall that we approximate the evolution of crater volume and depth by a logarithmic law. Close to the interception with the abscissa we approximate the curve of ablated volume by a linear fit. By extrapolating the linear regime to interception with zero (the ablation of null volume), we achieve the ablation threshold F th,a (fig. 3.6b). For all ablation characteristics, we also admit "linear" increase at low and moderate fluences (below 20 J/cm 2 ) followed by a partial saturation at higher fluences. In addition, we state that the absorption dynamics on the surface of dielectrics depends strongly on local intensity. The energy is still deposited radially (due to the Gaussian shape of the focused laser beam) while strong reflection of the central part of the pulse takes place yielding non-significant increase of the crater depth. On the contrary, the crater diameter and total ablated volume increase. Hence the increase of ablation volume and ablated diameter is not stopped by the plasma shielding for the same laser fluence due to the Gaussian distribution of the beam.

104 Chapter 3: Analysis of energy deposition. 68 Figure 3.6: Ablated volume as a function of laser fluence. a) The whole range of fluences follows logarithmic law. b) "Linear" regime close to V 0 determines F th,a at the crossing with zero ablated volume. Figure 3.7: Ablated crater diameter as a function of laser fluence. We note that the maximal achievable crater diameter (at the condition that the propagation of the beam is not disturbed) defined as d = πω 0 defining a diameter carrying 99 % of energy of the beam is never reached. In fig. 3.8 for illustration, we present the AFM images of crater morphology for two different fluences. One (fig. 3.8b) is close to the ablation threshold (9.7 J/cm 2 ). The crater shape is a quasi-gaussian like with the maximal depth at the hole center. The crater morphology at high fluence (71 J/cm 2 ) is "Top-hat" like and the maximal depth is achieved at the crater periphery. In the center of the crater, we see a "bump" that can be due to "non-efficient" energy deposition as very high local intensity rapidly causes high reflection and thus the stopping of effective energy

105 Chapter 3: Analysis of energy deposition. 69 deposition in the center of the laser beam. Figure 3.8: Ablated crater morphology for two incident laser fluences. a) High laser fluence corresponding to 16.2 F/F th (71 J/cm 2 ). b) Low incident laser fluence 2.2 F/F th (9.7 J/cm 2 ) and c) corresponding ablation crater profiles. The crater shape changes from nearly Gaussian at low fluence to top-hat at high fluence. In fact, the absorption curve in fig. 3.3 (as well as the ablation volume and crater diameter, fig. 3.6 and fig. 3.7) continues to slightly increase due to absorption of the incident energy at the beam edges. Quantitative analysis of ablation parameters by AFM can give such information as ablation efficiency, that we define as the ratio of the ablated volume to the incident pulse energy, V/E inc (see fig. 3.9). Figure 3.9: Ablation efficiency η eff as a function of laser fluence. F eff defines a zone where ablation efficiency exceeds 90%.

106 Chapter 3: Analysis of energy deposition. 70 Interestingly, the curve has a maximum that is attained rapidly after the threshold value followed by a saturation and after a slow decrease. For high values of incident fluences (after the maximum efficiency for F > F max,eff ), the fraction of absorbed energy decreases, and a significant part of laser photons is lost for ablation or does not participate in material ablation. The efficiency decreases, even if material removal is still present, and the ablated volume continues to grow at high fluences (see fig. 3.6). The fluence range, where the ablation is highly efficient, is determined as 90 % of F max,eff. According to that criterion, the ablation is efficient from 13 to 55 J/cm 2 (from 3 to 12.5 F/F th ). Below 13 J/cm 2, the energy is not sufficient for the "homogeneous" 5 ablation and absorption efficiency increases due to highly non-linear character of interaction and hence minimal energy should be deposited into the material to "transform" it from a transparent matter into a highly absorbing medium. The decrease of η eff curve starts from 55 J/cm 2, defining the minimal energy dose that is needed to create a highly reflecting plasma that will strongly shield the rest part of the incident pulse. But still the ablation is efficient at the periphery of the crater, that is why the slope of the decreasing efficiency curve is slow and the ablation is not completely arrested. Such behaviour of the ablation efficiency curve is then a compromise between: The minimal energy (fluence) to create an absorbing medium. Above this fluence, the ablation rapidly increases up to a maximum. And the minimal energy (fluence) to create a medium possessing highly reflecting properties (plasma shielding effect or partial plasma-mirror effect) depending on local intensity. Above this fluence, the ablation efficiency decreases Analysis In order to help in understanding the experimental results previously shown, we now confront them to the modelling described in chapter 1. The aim of the theoretical study is to precisely understand the energy balance and laser energy absorption as a function of incident laser fluence. Before presenting the results we first recall preliminary hypotheses and justify the choice of important modelling parameters Choice of the constants and input data. Influence of the effective electron background collision frequency. 1. Justification of pertinency of the Helmholtz equation as a propagation model. It is worth to note that Helmholtz equation approach is well suited for monochromatic 3 Here we mean the quality of ablation in terms of crater morphology and consider the resultant surface roughness.

107 Chapter 3: Analysis of energy deposition. 71 light. In particular, for correct comparison with the experimental results, it is important to be assured that no dispersion of the "real" beam occurs in the sample during the beam propagation. In our case, the laser bandwidth λ is narrow and equals to 3 nm and all experiments are performed on the target surface. Nevertheless, we estimate the beam dispersion induced by the propagation of the beam into the material bulk. The quasistatic length L qs defines the length superior to which two wavelengths separate. The beam dispersion is estimated according to: L qs = τ L 1/v 1 1/v 2 [115], where τ L is the laser pulse duration, v 1 and v 2 are respectively the speed of light for two extreme components of the laser pulse spectrum λ 1 = λ L + λ/2 and λ 2 = λ L λ/2 (λ L = 1025 nm). The calculation yields a quasi-static length 500 nm. Hence, it justifies the application of the Helmholtz equation for the modelling as beam dispersion is reached for depths much superior to those calculated by the program and experimentally observed depths of craters. 2. Effective electron-background collisional frequency. The effective background collision frequency includes the contribution of electron-electron and electron-phonon collisions ("solid-state modelling") and electron-neutral and electronion collisions ("plasma-state modelling") to take into account the progressive transformation of the material from solid to plasma state. All the components depend strongly on the electron density and temperature and therefore vary as a function of time and fluence as considered in our modelling. In numerous approaches [38, 116], it is shown the crucial role of this parameter for the modelling. In some works the effective collision frequency is taken equal to the plasma frequency [15, 56]. For instance, we verify that the reflection is very sensible to this parameter, while the transmission exhibits little sensitivity [77]. Here, we study the influence of the input adjustment parameters A ee and A e ph determining the magnitude of the reflection, transmission and absorption values. We initially took the values of A ee = K 2 cm 2 s and A e ph = K 1 cm 1 s from the reference data for 800 nm [83]. We tested a great number of values to adjust the input parameters for the ensemble of R, T and A in a wide range of fluences. The change of the value of the electron-electron collision parameter does not influence R, T and A, thus showing that they are low sensitive to electron-electron collision frequency. On the contrary, the electron-phonon collision parameter is responsible for important reflection and absorption change, while the transmission is in both cases little sensitive to change of the collision frequency value.

108 Chapter 3: Analysis of energy deposition. 72 We finally chose the values of A ee = K 2 cm 2 s and A e ph = K 1 cm 1 s, as they best reproduce the evolution of experimental R, T and A data. 3. Avalanche coefficient. Another input parameter, the avalanche coefficient, is studied (see fig for illustration). The avalanche coefficient strongly depends on laser wavelength and pulse duration. The choice of the tested values corresponds to the variety of values shown in literature [11, 36, 38, 68, 117]. The values are tested for different fluences to best fit the ensemble of the experimental data. In fig. 3.10, we introduce an example of calculation of R, T and A for the incident fluence of 5.3 J/cm 2. High values of avalanche ionization parameter overestimate the reflection and underestimate the transmission. Figure 3.10: Reflection, transmission and absorption as a function of avalanche coefficient. Incident fluence is 5.3 J/cm 2. We finally fix the avalanche ionization term to 2 cm 2 /J. This optimal value is better characterizing our experimental results (fig. 3.3) and is similar to values that were used for analogous conditions [36, 117]. 4. Input parameters of the modelling. In the table 3.1 we group the input parameters used in the modelling. 6 Private communication. Courtesy of B.Chimier CELIA laboratory. 7 The value of the initial density of conduction band electrons is in accordance with the impurity level of fused silica used in our study.

109 Chapter 3: Analysis of energy deposition. 73 Laser properties λ Laser radiation wavelength 1025 nm ω 0 Beam waist 6.3 µm τ Pulse duration 500 fs Properties (SiO 2 ) E gap Band gap 9 ev [33] n 0 Refractive index 1025 nm [118] N v Initial number of valence electrons cm 3 [119] ω L Photon energy for 1025 nm 1.21 ev σ 8 Multiphoton cross section 1025 nm m 13 s 1 W 8 6 C i Lattice heat capacity J K 1 g 1 [83] g 0 Material constant WK 1 cm 1 [83] α Avalanche ionization rate 2 cm 2 J 1 τ trap Recombination and trapping time 150 fs [45, 46] n e,0 Initial number of free electrons cm 3 7 n cr Critical density cm 3 ω p Plasma frequency s 1 Table 3.1: Parameters used in the modelling Comparison of theoretical and experimental curves. The theoretical model introduced in chapter 1.4 allows to compute the propagation of the electromagnetic energy, to estimate the reflected, transmitted and absorbed parts of the incident pulse and further to compare them with the experimental curves of pump depletion. All computations are performed for laser normal incidence on target surface. Numerically, the threshold fluence is described as the minimal fluence to induce the change of reflection and transmission 8. The computations yield a threshold fluence equal to 2.7 J/cm 2 (in rough accordance with the experimental value of 4.4 J/cm 2 defined according to a different criterion, see chapter 2). a) Difference of Gaussian beam distribution. In the following, we give three different cases representing three different local spatial intensities. In the theoretical model the free electron density is defined by the maximal incident energy (maximal local intensity) without consideration of the spatial Gaussian beam distribution. At the same time, the experimental reflection, transmission and absorption values are averaged radially over the Gaussian beam section. We thus take an assumption that we can use these three extreme cases (see fig. 3.11) to see the influence of the local intensity on the values of reflection, transmission and absorption and better understand the underlying phenomenas and explain the ablation crater parameters. 8 Numerically, the transmission and reflection change are simultaneous, that is why we define the threshold fluence as the change of both of them.

110 Chapter 3: Analysis of energy deposition. 74 In fig three particular cases are indicated and the computations are done for: the intensity maximum I 0, 50 % of maximum and I 0 /e 2. Figure 3.11: Theoretical distribution of intensity. Points denote three particular cases (Intensity maximum I 0, 50 % and at 1/e 2 ) for computation of reflected, transmitted and absorbed parts of the incident energy. The results of the computations of reflected, transmitted and absorbed parts of the incident energy are presented in fig From fig. 3.12a (high intensity), we can see that in the beam center the plasma shielding effect (partial plasma-mirror effect) is developed promptly (from very low fluence F > 2.7 J/cm 2 ). But, at the same time, the absorption is quite high 40 % and almost independent of the laser fluence once the threshold is overcome. The front part of the incident laser pulse creates a free electron density n cr, that, in turn, changes the behaviour of the dielectrics into a metal-like, locally yielding a high reflection (R reaches 60%). An optimum is achieved between the high absorption (F 5 J/cm 2 ) and high reflection (F 11 J/cm 2 ). This window corresponds to F 5-10 J/cm 2 where the absorption is high, but the reflection is still low and even reaches its minimum (lower than its initial value). The transmission saturates at 10%. We also notice that, even if the reflection reaches its saturation at approximately 60%, the absorption continues to increase slightly at high fluence. This could be due to: i) highly efficient absorption efficiency in the first part of the pulse when the fluence increases, ii) incomplete or partial plasma mirror effect (R < 100%). Fig. 3.12b shows that, for lower intensity (I = 50% I 0 ), the plasma shielding effect is developed less promptly in respect to the applied fluence than in the previous case (fig. 3.12a). We also observe a point of highest absorption at 14.4 J/cm 2 yielding 40% that is shifted in respect to the previous case ( 7.2 J/cm 2 at the beam center, see fig. 3.12a).

111 Chapter 3: Analysis of energy deposition. 75 Figure 3.12: Theoretical distribution of reflected, transmitted and absorbed energy as a function of incident fluence. a) Intensity corresponds to peak value I 0. b) The input intensity corresponds to 50 % of intensity maximum. c) The input intensity is taken in accordance with I 0 /e 2. We surmise that it corresponds to the best compromise between a significantly high intensity to have a high absorption of the incoming energy and a sufficiently low intensity to delay con-

112 Chapter 3: Analysis of energy deposition. 76 siderably the formation of the plasma shielding effect. This value could be compared to the experimental value of the maximal ablation efficiency, that has been discussed earlier (see also fig. 3.9). The most efficient absorption is accompanied by the increase of reflection up to 20 % which has already passed its minimum. Furthermore, the transmission decreases (depicting increased absorption) faster than the reflection reaches its maximum, contrary to the case of the peak intensity (fig. 3.12a). The transmission minimal value is 15% indicating that the dynamics and/or efficiency of absorption and plasma mirror effect are sensitive to the fluence. We see the delayed reflection increase that lasts from 10 to 20 J/cm 2 and that the level of saturation reached ( 60%) is nearly equal to the one reached at higher intensity. Again, the plasma mirror is partial and appears to not depend on the peak fluence applied, but more probably on the totally applied fluence. The saturation of R, T and A is reached later in comparison to I = I 0. For I = I 0 /e 2, the plasma shielding effect is never reached (see fig. 3.12c). The reflection passes by a minimum ( 30 J/cm 2 ) and then reaches back its initial value. The transmission and absorption change their values from 20 J/cm 2. The absorption (respectively transmission) curve progressively increases (resp. decreases) as a function of incident laser fluence. In this case A and T saturation is not achieved (for this range of fluences). The absorption reaches almost 45% and transmission equals to 50% at high fluence. At high fluence, the absorption reaches values strongly superior to I = I 0 and I = I 0 /2. The ablation is hence optimized due to the absence of plasma shielding. Differently to two previous cases, the increase (decrease) of the curves is not swift but smooth. We note that the Gaussian beam distribution modifies material in different way according to locally applied energy. That is why, for a better resulting efficiency and control (choice of ablation depth with constant diameter), it would be desirable to use a top-hat beam. Now, the highest resolution (in terms of ablation diameter, depth and volume) is better achieved with a Gaussian beam. b) Result with Gaussian beam To go further in our study and to reproduce better the experimental results in respect to the Gaussian beam distribution (in the sense of the real experimental conditions), we perform the integration over the incident beam radius according to the radial intensity distribution in the equation 1.28 in chapter The integration is done by averaging over twenty points for each fluence. The evolution of the experimental and theoretical curves for the reflection, transmission and absorption is shown in fig

113 Chapter 3: Analysis of energy deposition. 77 Figure 3.13: Reflected, transmitted and absorbed energy components as a function of incident fluence. The theoretical curves take into account the integration over the spatial intensity distribution. The modelling reproduces well the evolution of reflection and transmission for low fluences. For high fluences (> 10 J/cm 2 ), the model highly overestimates the reflection and slightly the transmission. A similar behaviour of the theoretical reflection curve can be found in reference [33]. For our pulse duration (500 fs) it can be possible that the plasma shielding is reached late in the pulse or is not reached during the pulse at all. Or maybe the free-electron shielding plasma is reached, but the free electron density is low (close to critical density) and thus the free electron plasma does not reflect strongly the rest of the pulse. Our speculations about dynamics of plasma mirror building and free electron density corresponding to it will be further investigated in our pump-probe study (see section 3.3). The discrepancy between the experimental and theoretical reflection can be due to several reasons: the experimental signal loss, theoretical overestimation of the reflection or sum of both. First explication of the higher value of reflection in theory can be due to increased scattering,

114 Chapter 3: Analysis of energy deposition. 78 resulting in experimental signal loss for high fluence. But in our experiment the collection of the signal is easy due to the large size of collecting optics and loose focusing of the incident laser beam contrary to the case of tightly focused beam. But still, we evaluate the possibility of the phase change, the influence of the expansion of the plasma and the curvature of the plasma on the measurement. The conduction band electron decays to lower energy levels with characteristic relaxation time equal to 150 fs [45]. The energy transfer from highly energetic (hot) electrons in plasmas to cold ions takes place through momentum exchange and the time of this transfer could be estimated using the following formula [59]: t ei = ( mi 2m e ) τ ei (3.2) m e is the electron mass, m i the ion mass (for fused silica, it is estimated as m i = 60 m p, where m p is the proton mass), τ ei the electron-phonon collision time (in rough approximation, we take τ ei = 1/ω p = 1 fs). That gives a value of transfer time t ei = 5.5 ps meaning that the lattice is "frozen" during the interaction. There is no significant ion motion during the laser pulse. The laser plasma plume (containing electrons, ions, atoms and molecules) is created and ejected much after the pulse end. Here presumably 9 there is no phase change during the pulse and hence we conclude that there is no scattering of the signal induced by modification of the target surface at such short time scales (< 1 ps). The second assumption is the scattering due to plasma plume expansion. If we take the speed of the plasma expansion given by Axente et al. [120] for fused silica (v = cm/s for incident fluence F = 5 J/cm 2, however measured at nanosecond timescales), one can find the distance d of the plasma expansion by the end of the laser pulse (d = 15 nm). Similar value for ion plasma (we mean oxygen) expansion speed was found by Stoian for crystalline Al 2 O 3 at femtosecond timescales [70, 71]. The speed of plasma expansion is a function of the electron temperature T e, that is why it increases with incident laser energy and more significantly with the pulse duration shortening. Gold et al. [121], in their study of prepulse suppression, considers the plasma expansion speed almost equal to the speed of sound for high intensities ( W/cm 2 ) and short pulse duration (130 fs) given by v = c s = (ZT e /m i ) 1/ cm/s = 0.1 nm/fs, where Z is the ion charge. The estimation for our pulse duration gives by the pulse end d = 50 nm which is negligible in comparison to the depth of view of the collecting optics. Moreover, we note that the maximal intensity in our experiment is W/cm 2. Similar value of plasma expansion is experimentally measured by Doumy et al. [122]. It equals to cm/s for the 9 The total acquisition time during experiment equals 1ps that is inferior to the energy transfer time t ei.

115 Chapter 3: Analysis of energy deposition. 79 laser fluence of 50 J/cm 2 (τ L = 60 fs), but the plasma expansion starts after a significant time t 0 (not measured), which decreases with the increase of incident laser fluence. Another important point considering experiment is that at short time delays the expansion of plasma is one dimensional [28] and not three dimensional as for long delays of laser plume expansion. That means that, if the mirror-plasma effect is created, it will be highly directional and may cause a nonsignificant signal loss compared to three dimensional expansion. This particular feature can be used for suppression of prepulse and pedestal cleaning in high intensity femtosecond laser chains [121, 122]. The last reason of such a big dispersion of the experimental and theoretical reflection evolution can be due to modelling. A set of simulations has been performed with different laser intensities to obtain intensity-dependent absorption, reflection and transmission. These values are used for integration over the incident beam radius according to the radial intensity distribution in the equation 1.28 in chapter The reflection is highly sensitive to the choice of electronphonon collision time. Now, the electron-phonon collision parameter A e ph should probably be taken variable as a function of fluence (especially at high fluence). It is also possible that the widely accepted expression of the dielectric function needs to be revised for accounting for a more complex definition of gains and losses of the electro-magnetic energy of the incident laser beam interacting with a solid target through the dielectric function. We recall that Drude model works well when the dielectric function is constant in each layer and fails when the density gradient and the spatio-temporal dielectric function change are rapid. Moreover, the modelling does not take into account the transition of a free electron plasma to an expanding plasma containing increasing number (especially at high fluence) of different species and particles and hence it does not define, completely and exactly, the material modifications. In addition, there could be some other fine physical phenomena that have not been taken into account in the modelling that could become significant. It is probably an ensemble of parameters to be taken into account to reproduce exactly the experimentally measured R, T and A Conclusion We have presented our theoretical and experimental findings such as evolution of the reflection, transmission and absorption as a function of incident fluence. At the damage threshold, the absorption equals to several percent of the incident fluence and at the ablation threshold, the absorption reaches almost 25%. The absorption saturates at 60% at high fluence. The remaining energy is divided between the part of the energy reflected by the plasma and the one that is

116 Chapter 3: Analysis of energy deposition. 80 partly transmitted. The difference in reflection increase and transmission decrease as a function of fluence puts in evidence the material modification evolving between a highly absorbing and highly reflecting material especially at high fluence. We speculate that minimal time and energy dose is needed to convert the initially transparent matter into highly absorbing opaque matter possessing metal-like properties. The study of laser energy deposition also shows that there is an optimal regime (in terms of ablated volume) followed by the decrease of the energy deposition efficiency due to the partial plasma mirror formed during the pulse. The saturation of crater depth also evokes the question about a partial mirror plasma effect. It is interesting to clarify when this plasma is effectively formed (temporal delay). In the following we thus would like to pay more attention to the temporal evolution of the reflection, transmission and absorption. The study of absorption dynamics helps to go deeper into the understanding of damaging and ablation of dielectrics. We will verify the "statement" about a good compromise between the minimal time and energy quantity for "conversion" of the initially transparent media into highly absorbing that is further followed by the increased reflection and so-called plasma shielding effect. Now, dynamics of energy deposition and the hypothesis of partial shielding of the incident pulse should be further confronted. 3.3 Temporal dynamics of energy deposition: pump-probe experiment Some relevant previous results Femtosecond laser dielectric interaction involves a complex sequence of processes that could lead to surface damage and ablation with a minimal collaterally damaged zone. This feature attracts theoreticians and experimentalists to clarify the mechanisms, but there are still open questions on damaging and ablation of dielectrics [36, 55, 58, 90, 92, 98] and on the dynamics of the ablation process [94, 117, 123]. Various works have been done for ultra-short laser pulses of duration between 20 and 200 fs and at 800 nm wavelength. Some authors are interested to measure the plasma characteristics and nonlinear self-focusing, plasma defocusing and Kerr effects in the bulk of transparent solids [33,74,94]. Some studies are devoted to the dynamics of carrier trapping and formation of self trapped excitons [43,45,124,125]. Deflection measurement by Li et al. [126] for the estimation of surface charging close to threshold fluence has been also carried out for metals and dielectrics. It puts in evidence Coulomb explosion proposed by Stoian et al. [8, 67, 68, 70, 71] for dielectrics due to strong surface charging (lasting tens of picoseconds),

117 Chapter 3: Analysis of energy deposition. 81 that is not the case for metals due to fast discharging due to high electron mobility. Sokolowski- Tinten et al. [54] investigate the transient reflectivity states of semiconductors and metals by means of time-resolved microscopy (pulse duration 120 fs and λ = 620 nm). The snapshots of the micrographs consisting of a system of concentric rings describe and analyze the plasma excitation and relaxation, ablation development and resolidication of the matter. It shows the sharp increase of the optical density over a small distance ( λ) to be the reason of these rings. The evolution of the interference patterns illustrates the relaxation of the absorbed energy and the homogeneous boiling of the material on longer time scales. After, the ionization mechanisms and influence of the polarization state on laser pulse absorption in dielectrics [94] was investigated by time-resolved interferometry. It was shown that, at oblique incidence, circular polarization yields lower multiphoton ionization than linear polarization. Time resolved measurements of probe phase shift using interference in the frequency domain [13, 46, 124, 127] allow to evaluate the evolution of laser-excited carrier density n e in the irradiated region. It states that optical breakdown depends not only upon reaching the critical density, but also on the pulse duration. The study is also targeted on the relaxation dynamics for crystalline and amorphous dielectrics. For fused silica, phase shift measurements show fast carrier decay that is attributed to rapid formation of self-trapped excitons. Puerto et al. [93,123,128] study the structural modification of crystalline and amorphous dielectrics with time-resolved microscopy (excitation by 800 nm pulse and probing by its second harmonic), and by means of time-resolved transmission measurements while irradiating the sample surface from the backside. In case of dielectric materials, only two concentric rings (compared to semiconductors and metals) were detected: one corresponding to laser ablation and the second to the affected zone. Depending on matrix structure organization (crystalline or amorphous), the final ablation craters differ. For amorphous fused silica, Gaussianlike crater walls and surface "bumps" or resolidified rim are observed while for crystalline sample (sapphire), steep crater walls and surface cracks are demonstrated. These results are attributed to the different viscosity of crystalline and amorphous dielectrics. Chowdhury incorporated collinear pump and probe reflectivity and transmissivity measurements on fused silica samples [97] and also used double wavelength measurements [89] in single shot regime for ultra-short (90 fs) laser pulses. Chowdhury shows the saturation of transmission on long delays after the end of pump pulse for 400 nm probe and relaxation to the initial level for 800 nm probe pulses. The study thus puts in evidence enhanced absorption due to defect generation. Indeed, the shorter wavelength (400 nm) excites more easily colour centers and defects due to higher photon energy in comparison to longer wavelength (800 nm). Another important point of this study is the difference in dynamics of reflection and transmission. The consequent plasma shielding

118 Chapter 3: Analysis of energy deposition. 82 of the second pulse (if both pump and probe are of equal intensity) was demonstrated when the temporal delay between two pulses increases. The reflection decays to its initial value in 10 ps, while the transmission exhibits a slow decay lasting tens of picoseconds. Similar behaviour was further shown by Puerto [93, 123, 128]. Doumy et al. [122] made a measurement of the reflectivity change and "plasma-mirror" effect for improving the temporal contrast of high power femtosecond pulses incident on quartz and antireflection coatings. The plasma-mirror effect is demonstrated to be fluence sensitive and appears earlier in the pulse when the incident fluence increases. Thus, the plasma mirror effect can be efficiently used for the application, notably for temporal "cleaning" of picosecond and nanosecond pre-pulses that could modify the target before the arrival of a femtosecond pulse. It has been also measured the plasma expansion velocity ( m/s) for high fluence. Royon et al. [129,130] investigated excitation mechanisms and transient absorption in glass bulk irradiated by multiple pulses (470 fs at 1030 nm in khz regime). It is underlined the importance of multiphoton absorption for macrostructuring of glasses and the low free electron density (two orders below critical density for fused silica) at relatively high incident intensity (up to W/cm 2 ) and high absorptivity ( 55%). Mermillod- Blondin et al. [74, 78] use phase contrast and optical transmission for time resolved microscopy investigation of microvoid formation in the material bulk. It illustrates the possibility to visualize the morphology change of the occurring void from the time of the energy transfer from electrons to ions. Gulley et al. [75] use measured spatio-temporal profiles in computer simulations and show that the beam asymmetry and the Drude dispersion operator should be taken into account when predicting the beam propagation, filamentation and damage of the material. Rosenfeld et al. [131] reported a pump-probe technique to detect the surface morphology changes for SiO 2, Al 2 O 3 and MgO by measurement of scattered light. The decrease of scattering is related to melting yielding decrease of surface roughness. Further, the increase of scattering signal is due to material ablation. To my knowledge, in single short regime, most experiments are carried out for Ti:sapphire laser at 800 nm ( [33,94,97,124]). So far we propose our study of the absorption dynamics for 500 fs laser pulses with photon energy 1.21 ev (with lower photon energy compared to 800 nm). Using a pump-probe arrangement, we thus determine the single colour material absorption at 1025 nm (irradiated by a sub-picosecond laser pulse) as a function of time delay for a wide range of incident laser fluences. Moreover, using a precise positioning in respect to the pump pulse maximum, we can estimate the effective time of energy deposition as a function of incident laser fluence. The collected experimental results and theoretical data will contribute to better understanding of the complex mechanisms of laser-matter surface interaction.

119 Chapter 3: Analysis of energy deposition Pump-probe experimental test-bench We modified the damage and ablation set-up to measure the temporal evolution of material response upon laser irradiation, in particular, the reflection and transmission (see fig. 4.1). Figure 3.14: Pump-probe reflection and transmission experimental diagnostics. M mirror; PC Pockels cell; Lift beam elevating system; BS beamsplitter; λ/2 half-waveplate; Pol Brewster polarizers; F spectral filter at 1025 nm and neutral density filters; R - retro-reflector; PD photodiode (REF reference beam; T transmitted beam; R reflected beam); L 1 = 50 mm; L 2 = 25 mm; L 5, L 6, L 5 focusing lenses; L 3, L 4 collimating lens; BD beam dump; C polarizer cube; SF spatial filter (pinhole). Note, a half-waveplate λ/2 shown with a dashed line is mainly used for the research procedure of temporal overlapping of pump and probe beams. The pump and probe beams are focused on the sample surface using f pump = 50 mm and f probe = 25 mm lenses, yielding nearly-gaussian intensity distributions with beam waists of ω 0,pump = 10.5 µm 10 and ω 0,probe = 7.5 µm 11 at 1/e 2 (measured by imaging on a CCD camera). The pump (respectively probe) is p-polarized (resp. s-polarized) in the experiment in order to avoid coherent artefacts between two signals when they are temporally overlapped. It is worth to be noted that the probe beam energy is strongly lower than the damage threshold energy (E pump,th = 10.9 µj, E probe = 50 nj; and in terms of fluence F pump,th 6.0 J/cm 2 and F probe 0.06 J/cm 2 ). 10 The telescopic system changing the focusing of the beam has been removed for this experiment. This explains the increase of the beamwaist size compared to previous one ω 0 = 6.3 µm. 11 At oblique incidence (26 ), the probe beam size (8.3 µm) is inferior to the pump beam.

120 Chapter 3: Analysis of energy deposition. 84 As before, the stability of the incident laser energy E inc (fluence) is controlled by the reference photodiode (P D ref ). The spatial superposition of the pump and probe beam is controlled by the imaging system. The angle of incidence between pump and probe is 26. It is a good compromise from the following considerations. From one hand, the angle should be sufficiently large to collect the reflected and transmitted beam with a good discrimination in respect to the pump beam. From the other hand, the angle should be minimized as much as possible to conserve or to cause the minimal increase of the pulse duration of probe beam. This parameter is critical in our experiment as all the data are the convolution of the material response and probe. Moreover, the angle between the pump and probe should be small for the efficient second harmonic generation for the temporal superposition and precise detection of "Zero" - delay. In addition, the angle of incidence of probe (26 ) is the minimal angle that is allowed by space constraints. The time Zero - delay (t = t 0 ) corresponds to the perfect temporal superposition of the maximum of pump and probe signals. It is determined by the maximum of the second harmonic generation (SHG) signal measured on the bisector between the directions of the pump and probe beams when a nonlinear negative uniaxial BBO crystal 12 conveniently oriented is mounted at the place of the sample. More detailed explanation is done in section The uncertainty on the instant t 0 is estimated to be 200 fs. For each delay case (at fixed incident laser fluence F), the results are averaged on 10 shots, each one on a fresh site of the sample. During the experiments, we consider the spectral and spatial filters for optical isolation of the signals with respect to the broadband plasma emission emitted on a wide solid angle. Afterwards, we calculate the absorption using for the dielectric: A = E abs /E inc = 1 R spec T spec = 1 E refl /E inc E trans /E inc, (3.3) where E inc, E refl and E trans are measured by photodiodes P D REF, P D R and P D T signals Sample positioning. Focusing pump and probe beams. Preliminary experiments Spatial overlapping of the laser spots on the sample surface We adjust the positions of the two nonfocused beams with respect to 4 pinholes before and after the superposition point. Then, we proceed as follows. With the visualization of the camera we look for the pump waist position by the energy and z-scan procedure. Afterwards, we superimpose probe on pump to achieve the spatial overlapping at high energy for both of them in 12 BBO of Casix: type I, phase-matching angle: θ c = 23.5, φ = 0 ; dimensions: 8mm 8mm (section) 4mm (thickness); antireflection coating for 1025 and 513 nm.

121 Chapter 3: Analysis of energy deposition. 85 single-shot regime regarding to the visualization system. We adjust the focal position of the probe to be coincident with the pump one. We decrease the probe energy to cause no structural modification of the sample (the probe beam is strongly attenuated to E probe = 50 nj). We produce a single damage with the pump and then detect on the oscilloscope the reflection and transmission signals of the probe in khz regime varying its transversal position. The minimum of the transmission probe signal corresponds to strong modification of the material induced by the pump peak and depicts the best overlapping between probe and pump. We thus finely adjust the exact spatial position of the probe and its beamwaist (see 3.15). Figure 3.15: Photodiode signal as a function of disalignment of the probe in respect to the pump position. The best superposition of the probe and pump corresponds to "zero" position. This method is very sensitive to the probe position as the disalignment of several µm in superposition of two beams gives instant increase of the transmission signal in comparison to the optimal position Second harmonic generation for superposing two laser beams temporally In our experiment we choose the second harmonic generation (SHG) as a tool to temporally superimpose pump and probe beams. As in our case the sample is irradiated by two pulses crossing with an angle of 26, a convenient technique to find the temporal zero t 0 is to generate noncollinear second harmonic emission. We utilize a BBO crystal in type I configuration (two ordinary waves produce an extraordinary one), that we put on the crossroads of the laser beam paths replacing fused silica sample (fig. 4.2).

122 Chapter 3: Analysis of energy deposition. 86 Figure 3.16: Schema of experimental SHG generation on the surface of the negative nonlinear crystal. BS beamsplitter, M mirror, Pin pinhole, L 1 pump focusing lens (f = 50 mm), L 2 probe focusing lens (f = 25 mm), PD photodiode with spectral filter at 513 nm used for the detection of non-collinear SHG between the pump and probe beams. Crystal thickness is 4 mm. For the attenuation we employ neutral density (ND) filters after the beamsplitter. Note that, during this alignment procedure and the final experiment, the same number with the same optical density of ND filters are used. The procedure of "zero" delay determination is the following. We preliminary verify that, for every beam separately, we have collinear SHG when the crystal is positioned perpendicular to the beam (see fig. 4.3a). Figure 3.17: a) Collinear SHG and b) Noncollinear SH generation If we focus the beam, strong attenuation is employed not to cause any damage of the crystal. S-polarized beam 13 is incident on the crystal surface to produce the light conversion. We find 13 For the pump beam, a half-waveplate is used to turn the polarization. During the pump-probe experiment, the half-waveplate is removed. Now taking into account the thickness of the true zero order half-waveplate by Casix as used here, the error or the determination of the time-zero is approximately 100 fs.

123 Chapter 3: Analysis of energy deposition. 87 separately the SHG for the pump (resp. probe), when the crystal is perpendicular to the pump (resp. probe) beam. We then perform an experiment without focusing pump and probe beams 14 (see fig. 4.3b). For that we turn the crystal on 90 degrees over its axis and put the crystal at the angle of phase-matching (see the estimation of the incidence angle shown in Annex B) to fulfill the non-collinear SHG condition. We change the polarization of the pump from p-state to s-state by putting on a half-waveplate. The same energy level for two arms is preferred. We also pay attention to generate the SH under condition for which both beams have an energy not sufficient to generate collinear SH by themselves. Two nonfocused beams are superimposed with the respect of 4 pinholes and with the visualization of the camera to have good overlapping on the BBO surface. We then verify the spatial superpositioning of the pump and probe beams on the surface of the crystal. The interaction zone of the unfocused beams is defined by the probe and pump beam diameters d and D, as presented in fig Figure 3.18: Interaction zone of the unfocused pump and probe beams of D and d diameters. Note, we neglect the refraction of pump and probe for this approximated calculation. We estimate the interaction zone according to the Gaussian energy distribution, considering that only the superposition of the central parts yields SHG. For both beams this criterion is taken at 0.25 from the pulse peak as marked in fig. 4.6 (A 1, A 2, B 1, B 2 ). The maximal length of the interaction is defined by b 1 b 2, with exception of two small parts outside of BBO crystal. It could be easily found from the triangle composed by A 1, A 2 and b 2. Thus we esteem A 2 b 2 taking into account the angle of superposition of two beams. The length of overlapping is 4.2 mm for 14 The idea here is to define a time window (preliminary delay line position), for which a crude temporal superposition of the probe and pump is obtained.

124 Chapter 3: Analysis of energy deposition. 88 nonfocused beams. In the case of the focused beams, the idea is the same but the interaction area is strongly reduced due to the decrease of beam sizes and focused geometry. Following the same reasoning, calculating as it is done above, we find an interaction zone of 28 µm (84 fs) for two focused beams of size ω 0,pump = 10.5 µm and ω 0,probe = 7.5 µm. It will significantly increase the confidence in the definition of t 0 delay time. The estimation of 500 fs (FWHM) laser pulse gives µm in displacement. (If all the pulse (1/e 2 ) is taken into account the length is 303 µm). That means that only during 300 µm in displacement of the translation stage the SHG could be detected for the focused beams. But, for the nonfocused beam, second harmonic could be generated along the whole crystal length. For the unfocused beam, this value equals to 4.2 mm, that means that whatever the position of the beams (just a small superposition is essential), we will have the second harmonic. We further obtain the autocorrelation signal of SHG as a function of retroreflector position (see fig. 4.4a). Figure 3.19: Second harmonic generation as a function of delay line position in non-focused (a) and focused (b) geometry. The time of interaction is taken at half maximum (FWHM) of the Gaussian beam. The total experimental length of the SHG is 1166 fs, that is in a good accordance with the theoretical one. Note, that the probe beam temporal length is 560 fs (the probe pulse is incident on the sample at the angle of 26 ). The maximum of the signal corresponds to the temporal superposition of maxima of non-focused pump and probe. This position is a reference for more precise determination of the temporal "zero" delay for focused beams. We then position the lenses (in the optical paths of pump and probe), change the polarization of the pump to p-state (for discrimination of pump and probe signals) by putting off the half-waveplate and perform the pump-probe experiment. When this experiment is done, the t 0 delay is thus defined a posteriori. For that, we replace the glass sample by the BBO crystal and look with the camera for the optimal (focused) image on the screen. We

125 Chapter 3: Analysis of energy deposition. 89 change the pump polarization to s-state. We then position the crystal at the phase-matching angle and adjust the positioning of the crystal to have the spatial overlapping of pump and probe on the crystal surface. We generate second harmonic and trace the autocollimation curve (see fig. 4.4b). The light is collimated by the lens and collected by a photodiode as the SHG signal is very weak to be detected without focusing. Spectral filtering is also used to cut the infrared component. The verification for good superpositioning of two laser beams is the SHG as the interaction zone inside is just 28 µm. If the two beams are superpositioned before the sample surface, there will not be any signal on the photodiode positioned after the crystal. If the beams are focused inside the crystal, the interaction zone will be 2 times longer ( 60 µm) 15. For the pump-probe experiment, the instant "zero delay" corresponds to the maximum of the noncollinear SHG signal and is defined with a precision of 60 fs. Now, according to other sources of error (in particular, the problem of repositioning 16, etc.), the total uncertainty is 200 fs Measurement of reflection and transmission strongly below the threshold of material modification: correct alignment of delay line We finally verify the variation of the probe while interacting with strongly attenuated pump signal (no matter modification). This curve is essential for the normalization of the experimental curves and for verifying the alignment of delay line. We show the behaviour of the experimental curves strongly below the damage threshold (fig. 4.10). Figure 3.20: The evolution of reflection and transmission as a function of short (a) and long (b) pump-probe delays for an incident fluence strongly below the damage threshold. 15 Using the energy and z-scan procedure, the probe and pump waist are positioned with a precision of a few tens of µm. The repositioning of a BBO crystal in the plane is ensured with also a precision of a few tens of microns due to high spatial resolution of SHG (see fig. 4.4b). The repositioning error is estimated to be 20 µm (60 fs). 16 According to our procedure of positioning (see chapter 2), we esteem here the error to be 10 µm yielding an uncertainty of 30 fs.

126 Chapter 3: Analysis of energy deposition. 90 The value of pump fluence is 0.8 J/cm 2 (0.13 F/F th ). The evolution of the curves characterizes the behaviour at rest of the material which is transparent to the laser irradiation and validates the alignment of delay line on a wide range of delays (up to 100 ps) Reflection, transmission and absorption during the pulse Time resolved analysis of energy deposition The ensemble of reflection and transmission curves as a function of pump-probe delay and for a wide range of incident laser fluences is presented in fig fig Each point of the experimental curves is averaged on 10 laser shots. The standard deviation is evaluated to be 1.2 % for transmission and 0.2 % for the reflection, but for the clarity of figures, the error bar is not presented. The damage threshold for this experiment is F th = 6 J/cm 2 and all experimental curves are normalized to this value. This is a little higher that is previously shown (4.4 J/cm 2 ). This change can be explained by a slight modification of the experimental test bench (removal of the telescopic system before focusing) and experimental conditions (sample, laser fluctuations, positioning, etc.). The time delay t 0 = 0 corresponds to the peak of the pump pulse. Negative delays correspond to the cases where the probe pulse arrives before the pump (exactly its peak value) and is incident on the unperturbed sample. It is important to mention, that for all the experiments, the transmission (resp. reflection) data are normalized with respect to the initial transmission (resp. reflection) of the probe at long negative delays. Note, the experimental signal is a convolution of the matter response with the probe signal ( 560 fs). The retrieved information is thus integrated on a time of 1 ps and obtained with a time increment of 200 fs at short temporal delay 17. On the contrary, the theoretical curves show instantaneous values as they are not influenced by the convolution and thus we can see the "fine" structure of energy absorption. Now, all effects really present during experiments and occurring on time scales longer compared to the pulse duration (diffusion, plasma expansion, etc...) are not taken into account. Experimentally, we "record" the non-disturbed material and then the material change and expansion of plasma of electrons and ions (the duration of plasma lifetime). Numerically, we study the material and the plasma of free electrons without taking into account the plasma expansion and evolution of its composition (static free electrons). That means, when the expansion of plasma becomes significant, more precisely, when the energy of electrons is transferred to ions ( 6 ps) and the composition of plasma evolves (electrons, ions, neutral particles), the numerical and experimental data contain different and complementary information. In the modelling, we thus pay particular attention to short temporal delays compared to pulse duration. 17 At long time delays, the time increment is 500 fs (up to 10 ps); 1 ps (up to 35 ps) and 5 ps (up to 100 ps).

127 Chapter 3: Analysis of energy deposition. 91 Figure 3.21: Evolution of transmission as a function of pump-probe delay and for different normalized fluences. The standard deviation is 1.2 %. The error bars are not represented. a) Transmission as a function of long pump-probe delays ( - 3 ps 15 ps); b) transmission as a function of pump-probe delay during the incident pump pulse ( - 1 ps 1 ps). Additionally, for more precise comparison of theory and experiment, all theoretical curves are done in accordance with the pump - probe experiment. The theoretical values shown here are the result of two calculations: first, the modification of the material by the pump signal at

128 Chapter 3: Analysis of energy deposition. 92 normal incidence and, then, the "recording" of the values seen by the probe signal in oblique incidence on the material surface. We should still mention that the thresholds for experimental and theoretical curves are depicted differently. The fluence values used in calculations cannot be directly compared to experimental ones. So we will distinguish three regions of fluences: first, 5.3 J/cm 2 that corresponds to low fluence regime: 1-2 F/F th ; second is the regime of medium fluence: J/cm 2 giving 4-5 F/F th ; and third is the high fluence regime: J/cm 2 corresponding to F/F th. Now, the theoretical curves demonstrated here are used to outline the general behaviour. Figure 3.22: Theoretical evolution of transmission as a function of pump-probe delay. Moreover, we speculate that the first minimum of the experimental transmission curve in fig. 3.21, is due to the interception of a prepulse of the pump with the probe beam that is not sufficiently filtered by the cleaning Pockels cell-based system 18. The transmission curve as a function of pump-probe delay (see fig and fig. 3.22) starts to decrease before the pulse maximum and demonstrates strong absorption of the incident pulse. The absorption effect is more pronounced for higher energies (see also fig. 3.28). The ensemble of reflection (fig and fig. 3.24) and transmission (fig and fig. 3.22) behaves differently with in particular different dynamics and slope (see delays from 1 to 5 ps) to return back to their initial values at rest. 18 Note, the curves are also superimposed considering this instant.

129 Chapter 3: Analysis of energy deposition. 93 Figure 3.23: Evolution of reflection as a function of pump-probe delay and for fluences normalized to the damage threshold. The standard deviation is 0.2 %. a) Reflection as a function of long pump-probe delays ( - 3 ps 10 ps); b) reflection as a function of pump-probe delay during the incident pump pulse ( - 1 ps 1 ps). The difference in dynamics of reflection and transmission has been already shown by Chowdhury et al. [89, 97]. It is worth to be noted that the reflection behaviour in oblique incidence depends strongly on the polarization state of the incident beam, as it was already shown by

130 Chapter 3: Analysis of energy deposition. 94 Sokolowski-Tinten et al. [132]. In the experimental curves, we can only see the tendencies due to high pulse duration of the probe and we thus analyze the theoretical curves for more profound comprehension of the physical phenomena at short time scales ( < 1 ps). The maximal increase of 7% in the experimental curve can be considered as small taking into account the establishment of a reflecting plasma (plasma mirror) and theoretical calculation (R max 0.9 reached promptly). Now one should recall that experimentally we do not dispose of a Dirac probe that could yield the value of the instantaneous reflection. Moreover, experimentally, we normalize our curves to the incident energy "recorded" during the totality of the pulse duration. In addition, we already evoked (see section ) number of reasons explaining this discrepancy. At low fluence (5.3 J/cm 2 ), the transmission curve (see fig. 3.22) drops swiftly from its initial value to 30% from the time delay t = fs before the pulse maximum. At the same time the reflection is still very low (see fig. 3.24) reaching only 10 % for this fluence. It means that the incident energy can be absorbed during all the pulse. With the incident fluence increase from 10.6 J/cm 2, the transmission reaches its minima ( 0) for all applied fluences. The reflection in its turn, reaches a maximum ( 90%) that is followed by a slow decrease. The dynamics of reflection and transmission evolution is different in the same range of fluences. The reflection increases swiftly and relaxes slowly after reaching its maximum. The transmission drops smoothly during 50 fs and upon reaching its minimum stays constant up to the rear part of the incident pulse. Figure 3.24: Theoretical evolution of reflection as a function of pump-probe delay. This defines efficient absorption (increasing with temporal delay) from the moment when the maximum of the reflection is overcome. We corroborate that the front part of the pulse is transmitted and the rest of the pulse is partly absorbed and partly reflected [12, 13]. It validates

131 Chapter 3: Analysis of energy deposition. 95 our hypothesis about a minimal time to create an absorbing and further reflecting medium and thus defining a temporal "window" of efficient energy deposition (see also fig. 3.29). Considering fig. 3.24, the reflection reaches its maximum instantaneously (once the plasma mirror effect is triggered) and then starts to decrease slowly. That means that the energy absorption is instantly stopped temporarily, but not arrested completely for the remaining part of the pulse. It is now interesting to consider the free electron density evolution during the pulse (fig. 3.25). For low fluence (5.3 J/cm 2 ), the critical electron density is never reached, the value of the free electron density being strongly below n cr. When the fluence increases two times, the free electron density overcomes the critical density and nearly corresponds to the ionization of the totality of valence electrons (in our model we consider a single ionization only). We note the inflection point at high fluences ( J/cm 2 ) where the free electron density increases dramatically above n cr. This moment coincides with the abrupt instantaneous reflection increase up to its maximum and partial "closing" of the energy deposition. The time delay to create a highly reflecting material is shown to be highly nonlinear and inversely proportional to the applied fluence. For laser fluences between 10.6 and 21.3 J/cm 2, the swift increase of the free electron population is also present, but it is less pronounced than for higher fluences. When the critical density is attained, high absorption is turned on in a thin surface layer and is accompanied by reflection increase. We note from our theory and experience that it is possible to reach relatively high transmission and absorption of laser energy even when the critical density is not reached (see the case of 5.3 J/cm 2, fig and fig. 3.29). Figure 3.25: Theoretical evolution of free electron density n e as a function of pump-probe delay. Number of atoms for fused silica is at/cm 3. Inset shows free electron density as a function of pump-probe delay for incident laser fluence of 5.3 J/cm 2. Further if the energy (fluence) is still deposited, the electron plasma density evolves from lowsubcritical (n < n cr ) to high-overcritical (n > n cr ). When the overdense plasma is created, it

132 Chapter 3: Analysis of energy deposition. 96 starts to strongly reflect for a short time the incoming pulse (plasma shielding effect). The energy deposition is not completely stopped as the free electron population starts to decrease due to recombination and the late part of the pulse is absorbed. The energy deposition here illustrated by the behaviour of the free electron population is thus a good compromise between competing increased reflection and decreased transmission. In addition we study the behaviour of collision frequency during the pulse (see fig. 3.26). The evolution of reflection defined by the real part of the dielectric function (see equation1.5) is highly sensitive to the change of free electron density and electron-background frequency. By examining the theoretical curves we presume that reflection increases almost instantaneously when the free electron density achieves critical density and the electron-background collision frequency reaches its minima. This instant will define the change of material properties meaning the transition from solid state which is defined by electron-phonon and electron-electron collisions to plasma state described by electron-neutral and electron-ion collisions. To be more precise, it is needed to integrate (in respect to depth) the value of collision frequency. The pictures given here can give an idea of the material transformation during the pulse. We are further interested to investigate the practical consequences of the effect of "plasma mirror" development during the pulse (see fig. 3.23). We remark that, for reflection values from 1.2 F/F th to 1.4 F/F th, there is no reflection change neither during the pulse nor at its end. The value of 1.3 F/F th (laser intensity 2x10 13 W/cm 2 ) roughly corresponds to the ablation threshold for fused silica in accordance with [97, 117]. The maximal level of reflection increases from 1.4 F/F th and further saturates from 3.4 F/F th (laser intensity 4x10 13 W/cm 2 ) at approximately 7 %. We then esteem the time of onset of reflection change taking as a criterion an increase of 10 % with respect to the initial value (see fig. 4.8a). The evolution of the reflection increase onset describes the minimal time to create a reflecting medium as a function of fluence. There is no significant reflection change before 1.7 F/F th. For laser fluences lower than 2.0 F/F th, a partial plasma-mirror establishes at the falling edge of the incident pulse ( 200 fs after the pulse maximum). Upon laser fluence increase, the reflection change starts earlier and from 2.5 F/F th, it is attained during the front part of the incident pulse. We then evaluate the instant of building of plasma shielding. As criterion, we take the increase of 1.5 times from the initial value of the reflection (fig. 4.8b). We clearly see that, for F/F th 3.4, the "plasma mirror" effect is established during the front part of the pulse ( 100 fs before the pulse maximum). Meanwhile, for low fluence close to the threshold (< 2.5 F/F th ), a significant increase of the reflection is never reached. For the fluence of 2.5 F/F th, the building

133 Chapter 3: Analysis of energy deposition. 97 Figure 3.26: a)theoretical evolution of free electron density n e as a function of time in the surface layer of material. b)temporal evolution of reflection during the pump pulse. c)theoretical evolution of electron-background collision frequency ν col as a function of pump-probe delay in the surface layer of material.

134 Chapter 3: Analysis of energy deposition. 98 of the partial plasma mirror is accomplished by 600 fs from the maximum of the incident pulse or after the laser pump pulse end. Figure 3.27: a) Estimation of the instant of plasma mirror onset. Negative values corresponds to the front side of the pump pulse. b) Time of building of "plasma-mirror" effect. The criterion taken is the reflection increase of 1.5 times with respect to the initial value. Note, the value of the plasma mirror onset that starts before the pump pulse (t onset fs at 5.5 F/F th ), as we suppose, is due to the prepulse artefact. The plasma mirror onset should be considered saturating close to fs. We thus conclude that for low fluences (up to 2.5 F/F th ) there is no significant plasma mirror during the pulse. We also notice that from 2.5 F/F th the time for building the plasma shielding effect significantly and swiftly decreases, passing from a formation at the pulse end to the front edge of the pulse with the saturation at 150 fs before the maximum of the pump pulse. These results also confirm the evolution of reflection during pump-pump experiment (see fig. 3.3). We suppose that in our experiment the exact instant cannot be determined, because of the probe duration. Nevertheless, we can confidently conclude, that for low fluences plasma shielding is never attained or eventually attained at the rear part of the pump pulse and at high fluences it is formed at the front part of the pulse. The study of Puerto et al. [123] confirms our results. The reflection maximum is delayed in respect to the maximum of the pump pulse and is dependent on the local fluence. Now, considering ionization mechanisms, we presumably think that avalanche (impact) ionization prevails over multiphoton (optical field) ionization as observed in other works [122]. Indeed, especially at low fluence, the plasma shielding requires a significant time to be established (see fig. 4.8). Second, the avalanche ionization shows lower sensitivity to the variation of the incident electro-magnetic field and does not require instantaneous multiple photon absorption (see the smooth variation of electron density in time for "long delays", i.e. second half of the pulse, fig. 3.25). Third, the character of avalanche ionization is that it is more effective when the free electron density in the conduction band is high enough.

135 Chapter 3: Analysis of energy deposition Timing of absorption process We present the curve of the dielectric absorption experimentally measured (fig. 3.28) and theoretically calculated (fig. 3.29). From those two curves we compare the dynamics of the absorption during the pump pulse and estimate the beginning, end and effective time of absorption duration. The absorption (fig. 3.28) increases from 5% at 8.3 J/cm 2 (1.4 F/F th ) up to 50% at at 32.7 J/cm 2 (5.5 F/F th ). The relaxation of the absorption to the initial value is achieved for fluences up to 15.1 J/cm 2. The "residual" absorption present at high fluences can be the result of: i) structural modifications of the material (temperature increase, melting, material decomposition); ii) interaction of the probe pulse with an expanding plasma; iii) the combination of two. This point will be further discussed in section Concerning small delays ( ps), we note that the dynamics of the absorption is fluence sensitive. Figure 3.28: Evolution of absorption as a function of pump-probe delay. The absorption initiation moves towards the pulse beginning with fluence increase, which is confirmed by the modelling (fig. 3.29). As explained before, the theoretical curve reveals the "fine" structure of absorption. The evolution of the theoretical absorption curve confirms the hypothesis of minimal time and energy to transform the initially transparent dielectric in a metallic-like highly absorbing material. The increase of absorption of the probe beam at the rear part of the incident pulse cannot be explained by multiphoton ionization as the local electric field decreases. However, we think that the front part of the pulse is mainly absorbed due to the multiphoton ionization. Indeed, high free electron density is swiftly attained (see fig. 3.25), and further trig-

136 Chapter 3: Analysis of energy deposition. 100 gers plasma shielding effect. Figure 3.29: Theoretical evolution of absorption as a function of pump-probe delay for a wide range of incident fluences. The quantity of absorbed energy (here we consider only the front part of the pulse) appears to be almost independent on incident fluence (see the first maximum of absorption, fig. 3.29). With the fluence increase, the beginning of absorption moves towards the beginning of the pulse but the plasma mirror too (temporary arresting the energy deposition during a window nearly corresponding to central energetic part of the pulse at high fluence, see also fig. 3.24) further followed by a partial "reopening" of the energy deposition for the late part of the pulse. The free electron density is high that favours the avalanche ionization inducing "residual absorption" that lasts approximately 600 fs near the end of the pulse (1/e 2 ). On our opinion, the late part of the pulse is absorbed due to avalanche ionization. The behaviour of curves is similar whatever fluence and seems not to depend much on the applied fluence in accordance with the experiments showing the saturation of absorption at high fluence (see fig. 3.3). The theoretical evolution of the beginning and end of absorption is shown in fig The negative delays in the graph correspond to the front part of the pulse. In this figure for increasing fluences the beginning of the absorption moves towards the front of the pump pulse. In addition, the end of absorption finishes later with fluence increase. But the onset of absorption seems to saturate at 450 fs before the pulse maximum (minimum energy and time for material "transformation"). Actually, at very high fluence, the time τ init is nearly reduced to zero (result of calculation) that means an absorbing medium is created immediately (multiphoton ionization) at the beginning of the pulse (defined at 1/e 2 ). The numerical fit of τ init illustrates that, when incident fluence is high, the time delay to create an absorbing medium equals to 50 fs corre-

137 Chapter 3: Analysis of energy deposition. 101 sponding in our conditions to 10 % of the FWHM pulse duration. Figure 3.30: Initiation τ init and end τ end of absorption as a function of the incident laser fluence. The instants τ init and τ end are defined at 1/e 2 from the maximal value of absorption for each fluence. The fits for τ init and τ end are exponential in the form t = t 0 + Aexp(bF ). For τ init t 0 = , A = 0.504, b = ; and for τ end t 0 = 0.825, A = , b = The absorption continues to slightly increase after the end of the pulse demonstrating the predominance of avalanche ionization. However, we do not see this "fine" structure in our experimental curves. It can possibly be due to the convolution of the pump with the probe or be hidden by free electron plasma evolution and expansion. Afterwards, we evaluate the effective time of energy deposition for each given fluence and compare to experiment (see fig. 3.32). For the experimental curves, a "residual" absorption of the probe is present after the pump pulse end. We take an approximation that each curve decreases to 0 with the same slope defining the end of the absorption of the pump pulse (see fig. 3.31). We extrapolate 19 the experimental curves with the same slope at high fluences based on the following. The behaviour of experimental curves at low fluence does not exhibit brutal slope change for all time delays corresponding to the rear part of the incident pulse. Moreover, theoretical curves show similar behaviour of the slope of absorption curves. The behaviour of the rear part 19 One should be attentive here. Theoretical curves demonstrate the pulse absorption, while experimental curves show the laser pulse absorption and plasma absorption. Based on pump-pump experiment, we could define the instant of the end of absorption by integrating the area under the absorption curve and comparing it to pumppump value. Mathematically speaking: A tot = +τ imp A(t)dt. However, the probe pulse is not a Dirac function, τ imp it is thus impossible to use this approach.

138 Chapter 3: Analysis of energy deposition. 102 of absorption curves is almost homothetic and constant for all fluence cases. Figure 3.31: Absorption as a function of pump-probe delay. a) Low laser fluence case is without extrapolation. b) High fluence case is with extrapolation. The slope of curves for high fluence is approximated with respect to the experimental evolution shown in fig. 3.31(a). We thus suppose that it justifies the extrapolation. Considering fig. 3.32, it should be noted that the shown results of the pump-probe experiment are convoluted, thus giving longer absorption duration in comparison to the theoretical results. Together with pump-pump experiment, this information gives the ensemble of the phenomenas and quantify the absorbed, reflected and transmitted energy during the pulse. For both cases (experiment and theory) the absorption duration and dynamics depend on applied fluence (but finally not much on the total integrated absorption) and absorption starts earlier for high fluence (reduced time for material ionization). Both theoretical and experimental curves qualitatively follow similar dynamics (see fig. 3.32).

139 Chapter 3: Analysis of energy deposition. 103 Figure 3.32: Duration of absorption as a function of incident laser fluence. For low fluences, strong absorption starts at the second half of the pulse. For high fluence, the absorption duration lasts almost the length of the pulse. Note also, that for the optimal fluence window yielding efficient absorption and ablation defined with the pump-pump experiment, the duration of absorption also corresponds to almost the total pulse duration. In other words, a very large part of the incoming energy (up to 60%) can be used when working with a long femtosecond laser. We will see in the following (see also chapter 5) if this energy is finally efficiently used for high quality micromachining Reflection, transmission and absorption on long temporal delays We now analyze the experimental curves on long temporal delays (1-100 ps) starting from the end of the pump pulse (see fig and fig. 3.34). The reflection shows a rapid rise at the front or at the rear part of the pulse depending on applied fluence. After the pump pulse end, the reflection stays constant for about 2-3 ps and then drops slowly but within the first 10 picoseconds returns to approximately its initial value, especially for low fluence. Note that, for high fluence, after reflection curves decay, their values do not inevitably reach the initial value of non-perturbed medium. The free electron plasma decays yielding reflection decrease. The successive saturation from 3.4 F/F th at the level R and fast decay at picosecond delays (< 10 ps) are attributed to plasma relaxation and expansion. The energy of the electron population is transferred to ions within 6 picoseconds (see section ). We note, that Penano

140 Chapter 3: Analysis of energy deposition. 104 et al. [32] show theoretically that the reflection as a function of fluence is higher for shorter pulses (50 fs) and absorption reaches higher values for longer (400 fs) laser pulses for the same range of laser fluences. The fast (150 fs) electron relaxation and self-trapping in fused silica leads to the efficient energy transfer to the lattice. For short pump-probe delays, the material is in highly nonequilibrium conditions (T e T i ). The electron relaxation yields a decrease in the reflection (see fig and fig. 3.33). But in reflection curves, we see different slopes for low and high incident laser fluences. For low and medium fluence the electron relaxation is slow and is accomplished by 10 picoseconds, a value comparable to those reported earlier and comparable to the decrease of the total energy (n e, T e ) contained in the free electron gas formed [97, 123]. Figure 3.33: Evolution of reflection from negative to 100 ps pump-probe delay for different incident laser fluences. For high fluence the value of reflection reaches a value different than the initial one R 0 within a few picoseconds. R 0 is the reflection value of non-perturbed matter. The dynamics of this decrease is faster at high than at low and medium fluence. The transmission drops sharply from 1.2 F/F th at instant around zero delay then followed by a fast increase reproducing the Gaussian shape of the laser pulse (see fig. 3.34). After the end of pump pulse, the transmission gets back quickly to its initial value for 1.2 F/F th to 1.4 F/F th. This is due to fast electron-phonon coupling and relaxation at low incident energy. The relaxation is related to the creation of self-trapped excitons (STE) and colour centers taking place in order of 150 fs. Note, the created absorption bands at 4.2 ev and 5.2 ev for the self-trapped excitons [43, 89] and at the colour centers, notably on defects at 2.0 ev for the non-bridging

141 Chapter 3: Analysis of energy deposition. 105 oxygen hole center (NBOHC) and the E-center of silicon at 5.6 ev [89, 133] can absorb incident probe pulse at long delays (> 1 ps). This absorption can last for a long time due to relaxation of STE and colour centers (up to 400 ps [45]). Figure 3.34: Evolution of transmission as a function of pump-probe delay and for different incident laser fluences. This effect is more pronounced at high incident pulse energy due to higher electron densities, thus increasing the total residual absorption (decreasing transmission correspondingly). For high fluence, from 2.5 F/F th after the pump pulse end (> 10 ps), the transmission saturates at a value considerably below the initial value of the non-perturbed dielectric (from the delay > 1 ps). This saturation lasts more than 100 picoseconds whatever fluence (see fig. 3.34). With increase of the incident laser fluence the level of the "residual" absorption increases. As we suppose, it demonstrates more and more significant material modifications with respect to incident fluence. The laser fluences from 2.5 F/F th cause strong ablation of the dielectric. As the time of energy transfer from electrons to lattice is rapid ( T ei 6 ps ), the transmission and reflection saturation at levels different that the initial ones can be the result of surface ablation or from a more general point of view, of structural modification of the surface (phase transition). We already explained that a part (at least) of the residual absorption can be attributed to the formation of STE at the dielectric surface. In addition, we presumably think that those structural modification are accompanied by the plasma evolution and expansion. We thus verify if the dynamics of matter ejection can be extremely rapid and the surface modifications could influence the measurement of transmission or not. In order to estimate the pertinence of different hypothesis, we made several calculations and experiments. First, we would

142 Chapter 3: Analysis of energy deposition. 106 like to verify if the structural modifications of the matter can be "read" by the pump-probe setup. Indeed, we know that at very long delay a structural modification (ablation) has occurred representing the final material modification. We thus measure the probe transmission at very long delay ( delay, fig. 3.35). The material is first modified by the pump pulse without any measurement by the probe (the probe signal is mechanically blocked). After this modification, the pump beam is blocked and the probe signal coming from the modified region is collected. The transmission change as a function of fluence is shown in fig for two delay cases. From fig. 3.35, it appears that the structural modifications of the material can be distinguished. For t = 100 ps, the change of T is small at low fluence and significantly increases at high fluence. For low fluence (< 15 J/cm 2 ), the difference between time delay of t = 100 ps and t = is significant. On the contrary, when the incident laser fluence increases, the difference between the values of transmission at t = 100 ps and t = is less pronounced. It probably means that the structural modifications are produced on longer timescales for low fluences. For high fluences, for t = 100 ps, we "test" the evolution of more opaque plasma containing particles resulting from structural change of the material. Moreover, there is no significant difference between the level of transmission at 10 and 100 picoseconds for high fluences (see fig. 3.34). We speculate that the delay of 10 ps approximately corresponds to the time for ejecting a significant number of particles, after the transfer of deposited energy from electronic to ionic subsystems. Figure 3.35: Transmission as a function of incident laser fluence for long temporal delay. t = 100 picoseconds correspond to a delay when the material exercises structural modifications. For t = 1 second temporal delay, we measure the probe signal long after the pump end. This delay demonstrates the resulting modification of the target and can be understood as material at time delay t =.

143 Chapter 3: Analysis of energy deposition. 107 In addition, we also test the hypothesis of increasing surface scattering at long delay ( 10 ps) that could be the reason of reflection decrease at high fluence on long time scales. Indeed, the signal can be scattered due to increased surface roughness and high diffuse reflection, meanwhile the measurement is assumed only for specularly reflected light. As reported by Rosenfeld [131], the increase of scattering for SiO 2 starts at 2-3 ps and is attributed to surface ablation. We verify this hypothesis using the values of resultant surface roughness in the bottom of ablation crater with the help of the following formula [80] 20 : R r R i exp( (4πδ σ /λ) 2 ) (3.4) where R r is the reflection for a rough surface, R i the reflection of the initial smooth surface, δ σ the surface roughness in the bottom of ablation crater. This approximation is valid only for δ σ /λ 1. According to the calculations (δ σ is measured in the range nm with AFM), the change of surface roughness causes the change of reflection superior to 20 % 21 that is somewhat similar to values in fig and can explain the change of reflection on long time scales. It hence confirms the previous assumption that structural modification of matter and particle ejection is significantly initiated at relatively short delays ( 10 ps). Now let us discuss the dynamics of the ablation induced by thermo-mechanical effects. The electron temperature relaxation is due to the electron-phonon collisions. The total equilibrium of ionic and electronic temperatures (T e = T i ) is achieved within T ei 6 ps. After this energy transfer to the lattice, a rapidly expanding high pressure hot material phase (thermal melting) establishes and the so-called phase explosion (explosive boiling) is declared [67]. The target experiences a rapid transition from the state of superheated liquid to a mixture of vapor and liquid droplets [90]. A partially opaque plasma containing ions, neutrals, clusters, etc... is thus formed and expands in front of the probe pulse yielding significant signal attenuation for a wide range of delays. At longer time delays (> 10 ps) the signal passing through the heated material could explain the saturation of the transmission below the initial transmission level. A shock wave accompanied by the rarefaction wave propagating in opposite directions compensate this swift temperature rise and cause the pressure relaxation. 20 The calculations are done considering the "top-hat" crater shape. It is thus unlikely that the change of reflection is induced by the diffusion from the crater walls. 21 The crater diameter is always inferior to the total beam diameter d = πω 0 and reaches 60 %d, that is why the total reflection is less sensitive to the surface roughness in the bottom of ablation crater and consists of the reflection of non-modified and modified matter.

144 Chapter 3: Analysis of energy deposition. 108 Here we try to find the explanation of the different slopes for low and high fluences on short temporal delays (1-10 ps). We assume that at high fluences the reason is very fast ablation and thus plasma expansion on short temporal delays. If the electromagnetic field is high enough, the electronic effects so-called Coulomb explosion mechanism proposed by Stoian [67 71] or the effect of electrostatic acceleration of ions proposed by Gamaly et al. [15] 22 can be produced. We think here that it is almost the same process (at least the cases are both related to electronic effects) seen by two different views: "the electron view" where the electrons pull out the ions meaning "electrostatic ablation" and "the ion view" where the ions separated from their electrons repulse each other and are ejected to allow the material to return rapidly to neutrality ("Coulomb explosion"). When the incident electromagnetic field overcomes a certain threshold value and causes surface charging, the high free electron density created during irradiation process can generate a strong electrostatic field that breaks atomic bonds and disintegrates the material. The material from the surface is thus ejected in a short time scale ( 1 ps) due to the electro-static phenomena. Ultra fast phase change on a short time period have been already demonstrated for covalently bonded materials [134, 135]). Rethfeld [26] has done an analytical estimation that proves the possibility of the impact of high-density electron-hole plasma on the destruction of lattice stability, that, in turn, could provoke fast material ablation. The threshold electromagnetic field is expressed [69]: E EMf,th = 2 H sub n 0 ε gω ɛ 0, (3.5) where E EMf,th is the local electromagnetic field, H sub the latent heat of sublimation, n 0 the total atomic density, ɛ 0 the vacuum permittivity. For fused silica H sub = 21.4 kj/cm 3, we thus find E EMf,th = V/m. We further calculate the values of ablated depth ejected due to the electron phenomena as the depth where the condition of E laser (z) E EMf,th is satisfied (see fig 3.36). The theoretical depth considering the condition of electrostatic ablation does not exceed 30 nm in the studied fluence range. The minimal depth found close to threshold equals to 5 nm and represents approximately the ablation of several percents of the totally ablated material (see fig. 3.5). The calculated values are strongly inferior to the ones achieved experimentally. Such small values of the ablation depth are 10 % of the total ablation depth in accordance with ref. [70]. The final crater depth is formed during the following phases taking place on larger time scales (up to µs) and is the result of explosive boiling, hydrodynamic motion and resolidification. 22 This effect, when the ions exercise strong electrostatic field generated by free electrons, is possible during the laser pulse. But the authors does not precise the duration of this strong electrostatic field, thus due to ion inertia and electron plasma expansion the effect can be less probable.

145 Chapter 3: Analysis of energy deposition. 109 Figure 3.36: Evolution of ablation depth due to the electrostatic effects as a function of incident laser fluence. Now, the existence of fast ablation can be possibly the reason of the specific behaviour of reflection and transmission curves for high fluence at short temporal delays (fig and fig. 3.34). Indeed, we recall that when the laser fluences are in order 4.2 F/F th to 5.5 F/F th the reflection decay is faster than for lower fluences. It is possibly due to the expansion of the material ablated by electronic effects that become important at high fluence and we thus collect less the reflection signal. Note, that the reflection signal interacts with small quantity of matter contrary to the transmission signal. That is why the resultant change is more important for the transmission curves. To conclude, the change of slopes of reflection and transmission on short temporal delays ( ps) at high fluence suggests that the electronic mechanism of ablation (Coulomb explosion or electrostatic ablation) is produced. It is presumably not the dominant mechanism of ablation, but its appearence is "read" by transmission and reflection signals. The major part of plasma plume is produced by the "classical" thermo-mechanical mechanism (heating and evaporation of the material) taking place at longer time delays (> 10 ps). Material ablation is a gradual sequence of phenomenas which are produced at short and long time delays and the saturation of transmission is probably due to the plasma expansion and material heating and transitional material modifications (see fig. 3.35).

146 Chapter 3: Analysis of energy deposition Energetic considerations After the determination of the precise balance and dynamics of relaxation of the energy deposited into the material, we would like to consider again the main processes yielding material ablation. Previously we have shown that the laser ablation is a combination of an electronic ablation (occurring on short time scales following the end of the pulse) and thermo-mechanical ablation mechanisms. We now test the pertinence of the following energetic criteria to correlate the energy absorbed by the material with the final ablation craters experimentally characterized by an AFM system. The energetic consideration to reproduce the crater depths measured with an AFM considers that the energy deposited into the material should be superior to fusion/sublimation enthalpy 23. The energy necessary to melt or respectively evaporate one cm 3 is given by H m = ρc p (T m T 0 ) 24, where ρ is the density of the material, C p 25 the heat capacity, T 0 the initial temperature, T m the melting (sublimation) point 26. As the time of interaction is short enough in comparison to carrier and heat diffusion, any process of energy loss can be neglected. For fused silica, the value of fusion enthalpy equals to 0.28 kj/cm 3 and sublimation enthalpy is 21.4 kj/cm 3. If the energy deposited into the system Q (calculated using equation 1.23, chapter 1) exceeds H m, the corresponding volume will be melted or ablated. The spatial profile of the energy absorbed per cm 3 is shown in fig Fusion and sublimation enthalpies and bonding energy 27 ( E = 54 kj/cm 3, in the literature this value is sometimes used as an ablation criteria [60]) are also shown in fig The relative evolution of the ablated depth is reproduced, but the quantitative evolution is underestimated (fig. 3.38). Indeed, when only considering total decomposition of matter (as supposed by the criteria based on bonding energy), we fail to recover the experimental depths by a large factor. The comparison of experimental measurements with the theoretical calculations demonstrates that to retrieve the evolution of the experimental ablated depth, it is needed to melt and further evaporate the material. 23 Sublimation is the process of endothermic phase transition of a matter (in its phase diagram) from the solid state to the gas phase without passing through a liquid phase. 24 Fusion or sublimation enthalpy given here is taken into consideration under equilibrium or nearly-equilibrium conditions. 25 Heat capacity in used temperature range is the same for fusion and sublimation and equals to C p = 1450 J kg 1 K The melting (fusion) point of fused silica is 1873 K and the sublimation point is 2503 K. 27 Sublimation enthalpy considers material evaporation, while the bonding energy is energy required to mechanically disintegrate an atom into free electrons and a nucleus (the process includes the breaking of chemical bonds). 28 For low fluence 5.3 J/cm 2, the subsurface variation of the absorbed energy is just an artefact of the modelling. For this fluence case, there is no subsurface melting or any other important subsurface alteration.

147 Chapter 3: Analysis of energy deposition. 111 Figure 3.37: Theoretical distribution of absorbed energy at the end of the femtosecond laser pulse (1/e 2 ). Fusion and sublimation enthalpies and bonding energy are presented as horizontal lines. Figure 3.38: Theoretical estimation of the ablated depth. The absorbed energy is compared to the fusion and sublimation enthalpy and bond energy. Now, it is also seen that thermal effects play an increasing role at high fluence (compare for instance the data at F = 10 J/cm 2 and 50 J/cm 2 ). Moreover, according to the modelling, the melted region is 500 nm (see fig. 3.37). So the zone surrounding the ablated region is melted and resolidified as confirmed by fig In the study of Ben-Yakar et al. [28] this zone is characterized to have a constant value whatever fluence. Nevertheless, it is worth to recall that up to 30 nm at high fluence can be "gently" ablated by the electronic effects (see fig 3.36

148 Chapter 3: Analysis of energy deposition. 112 in section 3.3.5). Figure 3.39: A characteristic ablation picture taken with an optical microscope for two different fluences. According to the discussion above, the fusion and sublimation enthalpies are much inferior to the energy absorbed per cm 3 by target up to depth of 100 nm for a large range of fluences. In the superficial layers, it reaches almost 500 times the enthalpy of sublimation. We thus speculate that the ablation plume includes electrons, ions (both with high kinetic energy) and other ablation products containing the "excess" of absorbed energy due to highly non-equilibrium absorption process [12, 28, 70]. Now, we verify whether the ablated plume could contain high energy particles (electrons and ions) based on: i) the estimation of the electron and lattice temperatures at the end of the laser pulse (theoretical study) and ii) the estimation of the fraction of the sublimation energy ( H=24 kj/cm 3 ) in the absorbed energy measured experimentally. The spatial profiles of electron and ion temperatures at the end of the incident laser pulse ( 400 fs after the pulse maximum) are shown in fig and fig They correspond to maximal temperatures achieved at the pulse end (T e = 700 kk in fig and T i is almost 30 times lower as presented in fig. 3.41). This high difference in temperatures is due to high inertia of the lattice (ion mass for fused silica is estimated as m i = 60 m p ). We recall that the transfer of the deposited energy to the lattice via low energetic carrier-phonon scattering is accomplished within 6 picoseconds (see calculations in section ) [15]. But, for the fast electronic effects, the energy from the electronic system will not be totally transferred to matter ions or/and atom, hence confirming the idea that the ablation plume contains highly energetic particles.

149 Chapter 3: Analysis of energy deposition. 113 Figure 3.40: Electron temperature in the depth of the material at the end of the incident pulse. Figure 3.41: Ion/lattice temperature as a function of material depth at the end of the incident pulse. T melt = 1873 K and T subl = 2503 K. From the experimental point view we verify the possibility that the ablated plume could contain high energy particles (electrons and ions) by estimating the fraction of the sublimation energy ( H=24 kj/cm 3 ) in the absorbed energy measured experimentally. Actually, we would like to estimate the part of the beam total energy that is deposited locally in volume to yield material sublimation and compare it to the sublimation energy. Indeed, the laser pulse incident on material surface yields material ablation in the central part and material melting in surrounding zone. We thus calculate the local energy contained in the central part of the beam and corresponding to the volume of the ejected material. The integration is done with respect

150 Chapter 3: Analysis of energy deposition. 114 to the ablated volume (dark zone) according to the equation 1.29 (see fig. 3.42). Figure 3.42: Schematic presentation of the estimation of absorbed energy by the volume of material to be ejected. Depending on incident laser fluence, the considered diameter of the laser beam is taken equal to the AFM measurement of the ablation diameter (the interaction here is considered fully deterministic). The diameter is varied in the range from 2r to the beamwaist size 2ω 0. The results of this calculation are presented in fig Figure 3.43: Absorbed energy normalized to the energy of sublimation as a function of incident laser fluence. Close to threshold, it appears that it is necessary to deposit a lot of energy to transform the initially transparent material into highly absorbing ( 5 times the sublimation energy). In fact, this observation could be related to the fact that the absorption of the energy in femtosecond regime is a highly non-equilibrium process (see fig and fig. 3.41). The fraction of the energy of sublimation in the energy absorbed by the material increases with laser fluence. It reaches

151 Chapter 3: Analysis of energy deposition. 115 almost 75 times at high fluence! This calculations thus confirm our theoretical findings and demonstrate that the ablation plume may contain high energy particles. The experimental measurement of the energy of positively charged ions within the ablation plasma in dielectrics by Stoian [70] also shows that, the high portion of deposited energy is contained in the ablation plume. 3.5 Conclusion In this chapter we have presented experimental results of the measurement of laser reflection, transmission and absorption for a wide range of incident energies. The study has been accompanied by a computer simulation based on the propagation of the laser pulse in dielectric medium and rate equation for laser ionization. There have been important findings such as: Theoretical and experimental findings such as the evolution of the reflection and transmission allows to conclude that there is a minimal time needed and a minimal energy to be deposited to create a highly absorbing medium from initially transparent fused silica. At the damage threshold, absorption equals to 2% defining the minimal energy to be deposited for dielectric transformation into an absorbing medium. At the ablation threshold (1.3 F/F th ), the absorbed energy roughly amounts to 25 % of the incident energy defining the energy to create a highly absorbing medium. With increase of the incident laser fluence, the minimal time to create highly absorbing medium decreases up to 50 fs ( 5% of the total pulse duration (1 ps)). The increase of the laser fluence above the minimal fluence to create a highly absorbing medium rapidly yields a maximum of the ablation efficiency (in terms of material removal µm 3 /µj). There is a minimal time and energy needed to establish a medium possessing highly reflecting metal-like properties (the plasma shielding effect or the partial plasma-mirror effect) depending on the local intensity. This phase corresponds to the decrease of the ablation efficiency. The time delay to create a highly absorbing and reflecting material is sensitive to the applied fluence. The time delay to create a reflecting medium follows inversely proportional dependence with respect to the fluence. The time delay to create a highly absorbing material has an exponential form (t = t 0 + Aexp(bF )).

152 Chapter 3: Analysis of energy deposition. 116 The optimal regime of ablation efficiency is situated between 13 and 55 J/cm 2 (from 3 F/F th to 12.5 F/F th ). The efficiency below 13 J/cm 2 is low for micromachining due to highly non-linear nature of absorption and the energy deposition at the laser fluence higher than 55 J/cm 2 is affected by the plasma shielding effect formed during the pulse. The free electron density is responsible for the partial plasma mirror effect. Upon reaching critical density the reflection significantly increases and instantaneously temporarily arrests the absorption. In the optimal fluence window defining efficient absorption, the duration of absorption almost equals the total pulse duration. Ablation of dielectrics by a subpicosecond laser pulse is the result of two phenomena. The electronic effects, the so-called Coulomb explosion or electrostatic ablation, are responsible for ablation of several nanometers (up to 30 nm at high fluence). This effect occurs rapidly after the end (defined at 1/e 2 ) of the pulse. Thermo-mechanical effects are the reason of femtosecond ablation on longer time scales and explain the ablation depth up to 300 nm. The best energetic consideration for the prediction of the ablation depths is the comparison of the sublimation enthalpy and the energy absorbed per cm 3 by the material. Theoretical calculations and data treatement put in evidence the highly non-equilibrium process of the energy deposition. energetic particles. At high laser fluence ablation plume contains highly A subpicosecond laser is a unique tool for dielectric material micromachining. The plasma mirror effect is not strong and delayed with respect to the effective absorption. The incident energy is efficiently absorbed (up to 60%) during all the pulse. We suppose that the mostly effective temporal shape of the pulse for most efficient micromachining consists of a short ( 50 fs or below) and strong (high fluence) prepulse to create a highly absorbing medium and followed by a long lasting plateau for efficient energy absorption and optimal drilling characteristics (see fig. 3.44). In the following chapter we show some applications of the femtosecond laser in micromachining and medicine.

153 Chapter 3: Analysis of energy deposition. 117 Figure 3.44: Temporal shape of the pulse for most efficient micromachining.

154 Chapter 3: Analysis of energy deposition. 118

155 Chapter 4 Applications: micromachining of dielectrics and biological tissues Contents 4.1 Introduction Pump-probe experimental test-bench Sample positioning. Focusing pump and probe beams Spatial overlapping of the laser spots on the sample surface Generation of the second harmonic of the laser for superposition two laser beams temporarily Reflection, transmission and absorption as functions of time in theory and experiment Energy balance. Distinction between damage and ablation thresholds Moment of the beginning and end of absorption. Absorption duration Comparison of the theoretical and experimental time scales for energy deposition Efficiency of the 500 fs laser, optimal F Conclusion

156 "Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world." Albert Einstein

157 Chapter 4: Applications: micromachining of dielectrics and biological tissues Introduction In the previous chapter we studied the reflection, transmission and absorption dependence on energy and time. We have demonstrated that the dynamics of absorption and plasma shielding processes are energy (fluence) dependent. In particular, we have defined an optimal fluence window yielding high efficiency of energy deposition. It is now interesting to estimate the quality of micromachining (especially in this fluence range) to validate this process of surface direct laser-writing. In the following we discuss the morphology of ablation craters and also the interest to use, in terms of ablation selectivity, a 500 fs laser for dielectric material treatment. The last part of this chapter is devoted to the study of a medical application of subpicosecond lasers. We develop a parametric study to optimize the laser parameters for reproductible corneal grafting. This study aims to find and to fix the ensemble of laser parameters to benefit from the special feature of a femtosecond laser such as the precision of the energy deposition and the minimal energy dose for minimizing postoperative complications and facilitating tissue healing. 4.2 Application of femtosecond lasers for drilling Concerning the applicative aspect of the present work, let us consider the selectivity of laser ablation in the wide range of fluences explored. We present the ablation characteristics (ablated diameter, volume and depth) in fig 5.1 and the topology of the ablation craters in fig 5.2 and in fig All data are normalized with respect to the damage threshold (4.4 J/cm 2 ). From fig. 5.1a, we see that the ablated diameter never achieves the total diameter size defined as d = πω 0. From 2 F/F th there is a linear increase of the ablation diameter up to 6 F/F th. Moreover, the crater diameter does not depend on intensity but only on normalized fluence F/F th as it is shown in ref. [114]. Hence using a small increment in fluence opens the possibility to control with a one micron precision the transversal size of the ablated holes by thoroughly choosing applied fluence. Note however that subpicosecond laser pulses having more pronounced thermo-mechanical effects compared to ultrashort laser pulses (electronic effects) could have a depressed rim surrounding ablation crater [28]. The quality of ablation at low fluence is characterized by a higher level of debris and loss of regularity, but with fluence increase the crater walls and bottom becomes free of debris (see fig 5.2 and in fig. 5.3) that are probably ejected far from the target. The fluence range where the ablation is efficient is determined as 90 % of F 1 max,eff (see fig. 3.9 in section ). According to that criterion, the ablation is 1 In terms of ablated volume to incident energy expressed in µm 3 /µj.

158 Chapter 4: Applications: micromachining of dielectrics and biological tissues 122 efficient from 3 F/F th to 12.5 F/F th (in terms of laser fluence from 13 to 55 J/cm 2 ). Figure 4.1: Ablation characteristics as a function of normalized laser fluence. a) Ablated crater diameter vs F/F th. b) Ablated crater volume vs F/F th. c) Ablated crater depth vs F/F th. Error bars correspond to the standard deviation of the data (mean value of 3 measurements).

159 Chapter 4: Applications: micromachining of dielectrics and biological tissues 123 Figure 4.2: Three dimensional AFM snapshots (left) and one dimensional profiles (right) for three laser fluences. The laser fluences 1.7 F/F th and 2.8 F/F th are below and 5.2 F/F th is in the range of optimal fluences for micromachining as it is defined from fig. 3.9 in section The total beam diameter d = πω 0 = 19.8 µm.

160 Chapter 4: Applications: micromachining of dielectrics and biological tissues 124 Figure 4.3: Three dimensional AFM snapshots (left) and 1D profiles (right) for two fluences. The laser fluences 8.8 F/F th is in the range of optimal fluences for micromachining and 16.2 F/F th is above this range. The total beam diameter d = πω 0 = 19.8 µm. The fluence range (from 1.7 F/F th to 16.2 F/F th ) analyzed here starts from values below the optimal fluence and finishes when the ablation becomes again non-efficient. The shape and morphology of ablated crater is irregular for 1.7 F/F th (see fig. 5.2) close to ablation threshold (1.3 F/F th ). The crater shape is Gaussian-like with high roughness of the crater walls and bottom. The maximal depth achieved for this fluence is in order of 65 nm and the crater diameter is 4.5 µm. When the incident fluence increases, the crater depth and diameters increases, but for low fluence (2.8 F/F th, see fig. 5.2) high irregularity is still present. The crater shape is also Gaussian-like similar to the previous case. We now examine the laser fluence that is in the range of optimal micromachining regime. In the range of optimal laser fluences all ablation characteristics increase with the normalized fluence. Ablated depth increases swiftly up to 3 F/F th, where the control in depth increment

161 Chapter 4: Applications: micromachining of dielectrics and biological tissues 125 becomes comparable with 20 nm. The maximal depth achieved at 12.5 F/F th equals to 300 nm. By varying incident laser fluence and considering the focusing used here (NA = 0.09), one can reach different depths from 50 to 300 nm (up to 0.003z r ) and diameters from 4 to 13 µm (up to 2.06ω 0 ) using a subpicosecond laser. Indeed, femtosecond laser possesses highly deterministic and precise nature. Note that it could be even possible to have a better resolution (ablation selectivity) with a more stable laser system (in our case 5% rms pulse to pulse energy fluctuations). For the laser fluence in the range of optimal ablation efficiency (5.2 F/F th, see fig. 5.2), the crater depth increases further, but the difference with two lower fluences consists in smoother bottom surface and crater walls. There is no influence of the plasma shielding and the laser pulse absorption is more efficient in the center of the beam where the local intensity is higher yielding Gaussian-like crater shape. With further fluence increase, the depth saturation causes a transition from Gaussian-like to "Top-hat" shape of the resulting ablation crater (8.8 F/F th, see fig. 5.3). The progressive change of the crater shape in the range of optimal ablation efficiency hence allows to access to particular shape, i.e. Gaussian-like or "Top-hat" only be adjusting the incident laser fluence. For high fluence cases (8.8 F/F th and 16.2 F/F th ), the crater depth saturates to 250 nm, but the crater diameter still increases. We therefore conclude that the axial resolution (crater depth) depends more on local fluence 2 and the crater diameter depends on total fluence. The quality of the crater walls is high, they are steep and smooth. For 8.8 F/F th, a small bump appears in the crater bottom. It is probably related to the plasma mirror effect that is reached in the region of the highest local intensity. This bump becomes more pronounced at fluence 16.2 F/F th and causes the degradation of the quality of laser ablation. It is thus important to work in the optimal fluence window range, since here the maximal absorption is attained and the energy deposition is not significantly disturbed by the plasma shielding effect. A subpicosecond laser therefore has one important advantage over ultra short laser pulses, the working window is wider than for ultra short pulses [114]. 4.3 Experimental study of the femtosecond laser interaction with the corneal tissue One of the important applications of femtosecond laser is medicine and especially laser surgery [30, ]. In ophthalmology femtosecond laser is a good tool for precise dissection of healthy and pathologic tissue such as retina [142], lens [143,144] and cornea [ ]. A part of ophthalmological operations aims to: i) produce initial corneal incisions, capsulotomy, and also fragment 2 In the related study [114], we additionally show that changing the pulse duration allows to tune the axial resolution (crater depth). The axial resolution is indeed dependent on local intensity.

162 Chapter 4: Applications: micromachining of dielectrics and biological tissues 126 the crystalline lens of patients suffering from cataracts; ii) vision correction by reshaping the cornea and iii) corneal grafting to treat some corneal diseases. A more detailed description of the eye and corneal structure is given in Annex C Corneal diseases Alterations in corneal shape, transparency or/and refractive power resulting from congenital malformations, infections, trauma or metabolic disorders give rise to changing degrees of visual function that may be treated with drugs. In other more complex cases, surgical intervention is required using corneal grafts in order to recover transparency or refractive power and, respectively, vision. The most common diseases or pathologies demanding surgery to recover vision are grouped in table 5.1. Pathology Dysfunction of endothelial cells tiple Dystrophy Infection Graft rejection (mul- surgeries) Patients 35 to 50 % 10 to 20 % 10 to 20 % 5 to 10 % Table 4.1: List of the most frequent pathologies requiring corneal graft. It corresponds to an alteration of the function of endothelial cells most often related to ageing. Moreover, as the endothelial cells does not regenerate and diminish with age, this increases the risk of surgical intervention. The term dystrophy describes an inherited disorder affecting single cells, tissues, or organs or their combination. Corneal dystrophies concern primary corneal disorders that are not associated with inflammation, trauma, underlying systemic diseases or environmental factors. They progress slowly without any symptoms and they appear usually during the second decade of life. Dystrophies affect vision by two mechanisms: a) increase of light diffraction from corneal debris or corneal oedema; b)irregular corneal surface and stromal disarrangements resulting in image blurring. Dystrophies could be divided by the level of corneal pathology involved, which separates them into epithelial and subepithelial, Bowman layer, stromal, Descemet s membrane, and endothelial dystrophies. Corneal infection includes such pathologies as epithelial keratitis, neurotrophic keratopathy, necrotizing stromal keratitis, immunological stromal keratitis, and endothelitis. The complications or severe forms of these infections are usually treated by corneal grafting. The Herpes Simplex Virus types 1 and 2 can for instance be a cause of corneal infection. Sometimes a small trauma of the conjunctiva playing the dominant role in the protection of the cornea by the tear film against bacteria could create an epithelial perforation through which bacteria may enter the eye. For some people, the operation can be advised in the context of chronic ocular pain, eye irritation, tearing, foreign-body sensation that could be caused by keratitis of viral origin. There are some risks attached to any operation. The most important risk of corneal graft is graft rejection. The cornea due to its avascular structure and low cell content is an immunologically privileged tissue. But nevertheless there is a risk that the graft becomes opaque as a result of immune response when the body recognizes the tissue as foreign. Usually it occurs after penetrating surgeries (4 to 6%), but it is rare with lamellar corneal grafts. If rejection is found, it is

163 Chapter 4: Applications: micromachining of dielectrics and biological tissues 127 treated with steroid drops. After the treatment, most corneal grafts recover from the rejection, but there are still some patients from the "high rejection risk group" who may be advised to receive a "tissue matched" graft. This risk is higher when accompanied by the inflammation due to infection or chronic decompensation. Another reason of graft rejection is that too many endothelial cells are lost during or after grafting History of treatment of corneal disease and interest of laser-based process Since the first successful graft (in 1887 by Von Hippel [152]), surgery process has been continuously improved. Today laser surgery procedures attains about operations (including LASIK and corneal graft) per year worldwide [ ]. The oldest technique of corneal graft is the penetrating keratoplasty or the graft of the entire corneal thickness. It consists in replacement of the whole depth of the cornea by the graft coming from a donor. This type of procedure has a lot of post-operative complications (astigmatism, infections, etc.) rejection. and increase the risk of an immune response that can yield finally to graft During the last ten years, lamellar graft has been used more often than full depth keratoplasty. It consists in replacement only of the pathologic part of cornea without any intervention on the healthy part. The procedure allows to decrease the immune risk and keep the original ensemble of the eyeball. By now, most of graft interventions are assisted by a mechanical device called microkeratome and are performed manually. Once dissected with a circular trepan or lamellar scalpel, the graft is stitched with a nylon sew. The success of the transplantation is related to the quality of the cut and surface regularity which can induce post-operative aberrations and possibility of graft rejection. This procedure is particularly tricky when dealing with a mechanical microkeratome. The procedure of vision correction called LASIK or LAser InSitu Keratomileusis appeared in 1989 (see fig. 5.4). The corneal flap is dissected with a microkeratome at low depth (< 200 µm) and pulled off opening the stroma. Afterwards, with the help of an excimer laser, the central corneal curvature is modified or reshaped to restore the visual power. Then the hinge is repositioned back and is fitted by the adhesion forces without sewing stitches. Nowadays, this procedure evolved to femtosecond LASIK, where the microkeratome is replaced by a femtosecond laser. By depositing energy locally in volume, without alteration of the outermost layers and of the adjacent tissues (little or absence of collateral effects), a femtosecond laser yields better precision, control and reproducibility than manual microkeratome.

164 Chapter 4: Applications: micromachining of dielectrics and biological tissues 128 Figure 4.4: Schematic drawing of LASIK procedure: dissecting the cornea; opening, pulling of the flap; reshaping the corneal stroma; and redeposition of the flap. Source: World Wide Web. Photodisruption is the mechanism used here for laser tissue dissection [138]. The physical phenomenas associated with photodisruption of ocular tissue are plasma formation, shock wave generation, cavitation and jet formation. When corneal tissue is irradiated by a femtosecond laser, the plasma is formed in a spatially confined volume. The spatial localization of the energy deposition and the expansion of the plasma yields a shock wave that expanses out of the focal region and finally becomes an acoustic wave. The cavitation bubble is formed during the shock wave propagation. It oscillates (expansion and contraction) several times before collapsing. The collapse of the bubble causes the formation of a second shock wave due to the pressure increase during collapse inside the bubble. During photodisruption, the tissue is split by mechanical forces. In addition, the confinement and the use of a low level of laser energy is essential for laser cut. Indeed, heating higher 40 C is mortal for the cells. Laser systems of picosecond and nanosecond duration have significant heat propagation and higher amount of deposited energy. Moreover, even small tissue alterations near the incision can induce undesired post-operative results. As we have previously shown on fused silica for a subpicosecond laser, electronic effects are small and ablation is a result of thermo-mechanical effects. Thus subpicosecond laser dissection can give good (or nearly optimal) quality of laser cut both for LASIK or more deep procedures. LASIK is the most convenient procedure giving good reproducibility and is well adapted for correcting optical distortions caused by myopia, hyperopia and astigmatism. Based on the success of LASIK procedure, the application of femtosecond lasers recently entered into the full depth and deep lamellar keratoplasty (corneal graft) to replace the mechanical or semimechanical techniques. Compared to LASIK the dissection technique must be performed in

165 Chapter 4: Applications: micromachining of dielectrics and biological tissues 129 deep corneal layers (> 200 µm). The comparison of femtosecond laser dissection and mechanical microkeratome for corneal flaps demonstrates similar value for successful corneal grafting. The probability of successful grafting is very high (more then 90 %) due to immunological privilege, new techniques of graft preservation and surgery techniques, advanced pre- and post- operative care. But for laser methods of cornea dissection, decrease of surface roughness, faster healing after laser intervention and better patient comfort can be achieved [ ]. Thus, the necessity of the optimization and a rigorous choice of irradiation dose for defining an "optimal working regime" is a necessity for laser graft surgery. Using the defined earlier protocol, we first study the surface modifications 3 of different corneal layers. This study aims to examine the action of a wide range of fluence and identify a "working window" that will provide the minimal laser irradiation dose for maximal cutting efficiency of ocular tissue and consequently minimal collateral effects. In addition, the study gives the information of the maximal dose of irradiation not to damage upper (notably surface) layers of the cornea, when using laser for deep lamellar keratoplasty. The second part of the study consists in investigating laser dissection of deep corneal layers with a femtosecond laser. The technique demands a depth > 200 µm and now with commercial laser systems could allow for different cut shapes (mushroom, z-shape, top-hat) that may facilitate tissue healing and decrease graft rejection. The research is based on using a commercially available clinical laser system with similar characteristics as in our laboratory (1040 nm, 600 fs) with some adjustable parameters (number of laser passes and depth of cutting). We look for the minimal pulling off force (the force to pull off the corneal flap from the corneal bed) and minimal final surface roughness for the laser dissected corneas. The lamellar keratoplasty assisted by a femtosecond laser is considered successful if high regularity (minimization of number of tissue bridges and low residual roughness) of the laser-machined flap surface for both recipient bed and donor hinge is achieved that causes fast tissue healing, lower aberrations and post-operative complications and recovered vision Measurement of laser induced modifications of biological tissue Damage threshold measurement is not a trivial issue for inanimate objects and even more complicated for living or biological matter such as cornea (possessing specific characteristics as heterogeneity, surface irregularity, specific chemical composition). Even the definition of the threshold is arduous. For biological tissue, one can propose the following classification directly inspired from the classification we used for dielectrics (see chapter 2): 3 Further we will not distinguish damage or/and ablation for surface modifications causing tissue dissection as it has been previously defined for hole drilling in fused silica.

166 Chapter 4: Applications: micromachining of dielectrics and biological tissues At low fluence, the material properties can be modified without any significant morphology change of the surface, e.g. permanent traces arising from chemical effects [30, 47], requiring advanced in-situ (second harmonic generation or two-photon fluorescence, see fig. 5.5) or ex-situ microscopy tools to be characterized. The modifications can be highly localized and extremely small in comparison to the laser spot size. Using a high number of laser pulses during a long time (up to several seconds), laser cut can be achieved. But this technique is little adapted for corneal grafting, because of time consuming and low quality of dissection on a large scale. Figure 4.5: Second harmonic generation and two-photon fluorescence providing information about locally laser induced non-thermal and non-ablative modifications of single collagen fiber structure. This photo-modification is similar to the one produced by collagen thermal denaturation at 60 C. Red and green represent SHG and two-photon fluorescence respectively [161]. 2. At higher fluence, large and irreversible changes of tissue morphology appear. They are accompanied by material removal, and in the case of biological objects, we speak about photodisruption (more than ablation). It is usually associated with ablation plume expansion (fig. 5.6) which has a mushroom-like shape with a ring vortex at the top. This ablation could also be put in evidence by using volume measurement tools like AFM, as we did for amorphous materials, but in the case of soft and irregular biological tissue, it is a knotty problem. The final crater comes with collateral damage of the adjacent tissue that can be easily detected using an optical microscope. Indeed, during photodisruption, one can achieve simple tearing away of the tissue, its burning or even irregular crater or carbonized surface surrounded by damaged tissue, etc. Moreover, the surface roughness could be much more important in comparison to an inanimate object making difficult the use of an AFM. Thus the evolution of the ablated volume is not physically and technically adapted for the characterization of living matter.

167 Chapter 4: Applications: micromachining of dielectrics and biological tissues 131 Figure 4.6: Laser plume expansion for PMMA (used as a phantom of cornea) and cornea after ArF excimer laser irradiation (λ = 193 nm, fluence 120 mj/cm 2 ). The ablated area diameter is 7 mm [47] Study of laser fluence yielding tissue modification Determination of ablation threshold is a key issue for the technical development of laser surgery. If one wants to preserve the tissue integrity, the knowledge of the threshold of tissue modification is essential. Working with a fluence close to photodisruption threshold provides good dissection results, as it avoids high temperature rise and minimizes the collateral effects in adjacent tissues. We concentrate here on the accurate determination of the damage (or "tissue modification") threshold of epithelial and Bowman s layers of human corneal tissue in single-shot regime giving the "working window" in terms of energy (fluence) dose of tissue irradiation to protect the surface layers of the cornea, when focusing the laser in the corneal depth to perform penetrating or deep lamellar keratoplasty. For that, we implement the methodology described in chapter 2 and rely upon using statistical approach of laser-matter interaction (see section ). For realizing the measurements, we slightly modify the experimental set-up introduced in chapter 2 (see fig. 5.7) in order to accommodate specific samples like biological tissue. In particular, to provide conditions suitable for studying living or biological material, important parameters related to handling and preservation of the sample during the entire experiment are carefully addressed (see hereafter). All experiments are done with human corneas coming from the French Eye Bank (La Banque Des Yeux; EFS: Etablissement français du sang, Marseille, France).

168 Chapter 4: Applications: micromachining of dielectrics and biological tissues 132 Figure 4.7: Schematic drawing of the test bench for laser damaging of the cornea [162]. M mirror; PC Pockels cell; Lift beam elevating system; λ/2 half-waveplate; Pol Brewster polarizers; L telescopic system; Camera visualization system; PD REF reference photodiode; L mm focusing lens (beam waist at 1/e 2 and Rayleigh length w 0 = 10.7 µm, z r = 350 µm); L 1 alignment lens (25 mm); OD optical density filters set in for obtaining low fluence values; BD beam dump. A HeNe laser is used for rapid alignment (centering) of the sample position. The corneas are samples rejected for transplantation 4 due to the nonconformity to standard operating protocols specified by the European Eye Bank Association. But they remain representative of corneal samples used for surgery. Among them, we specifically study non-pathological corneas. The eyes are obtained within 36 hours after death and stored in Optisol-GS at room temperature. The liquid solution Optisol-GS allows for the conservation of corneal tissue without alteration of the cells or swelling [164]. The storage in Optisol-GS does not exceed ten days. After removal of the sample from this solution and during the preparation of the tissue, the hydration is maintained by instillation of the Balanced Salt Solution (BSS) from the posterior part. BSS is injected through the liquid feed duct to pump the cornea and keep it under constant pressure, providing suitable biological conditions. Nevertheless, BSS is never used on the surface during laser experiments to avoid any excess of liquid and thus alteration of the experimental measurements. For measurements on the anterior stroma (Bowman s membrane), the 60 µm 4 For the clinical transplantation the conditions of conformity [163] should be accomplished: endothelial cells density > 2000 cells/mm 2 ; percentage of the dead cells is less then 2 %; regularity of the mosaic structure of the endothelial cells; no diffuse stromal opacification.

169 Chapter 4: Applications: micromachining of dielectrics and biological tissues 133 thick epithelium is previously removed by a surgical sponge (Microsponge, Alcon laboratories, Fort Worth, TX, USA). The total time of the sample preparation does not exceed 10 minutes. Corneal samples are positioned on a Barron artificial anterior chamber (fig. 5.8, Katena Products, Dennville, NJ, USA) mounted on a three-axis manually-controlled translation stage. Figure 4.8: Barron artificial anterior chamber by Katena ( used for positioning and maintaining biological conditions (hydration and pressure) of corneal samples during experiment. Minimization of the experiment duration is crucial due to fast dehydration of the corneal samples [165]. So we implement a particular and rapid procedure for positioning the sample in the beam focal plane. We first precisely locate the beam waist position with the focusing lens (L 2, f = 100 mm) using a standard energy-scan and z-scan procedure on the surface of a "reference target" (microscope slide), thus defining a reference position. We then remove this lens, positioned on a magnetic base (to keep memory of this position), and with the use of a short focal lens (L 1, f = 25mm) we locate this reference position with high accuracy 5 by examining the sharpness of the image captured by a CCD camera coupled to an objective. Afterwards, we place the corneal sample at this reference position. L 1 is then removed and replaced by the L 2 lens used during experiment. This procedure allows dramatically shortening the experiment time as the z-scan procedure (the beam waist positioning) is avoided for the corneal sample (automatically avoiding the dehydration of the studied sample), and also limiting the problem of correct and often time consuming (re)location of the target. In addition, this kind of manipulation is free off chromatic aberrations (and thus error) as the reference position is determined by the femtosecond laser beam. A low power He-Ne laser is also aligned collinear to the incident laser beam to materialize the optical axis and facilitate and accelerate the positioning of the corneal sample. The experimental area is a flat zone, typically a square of 1 mm 2, and roughly accounts for 100 shots. The total duration of the experiment is approximately 15 minutes. This limited 5 the Rayleigh range associated to the long focusing lens L 2 used for the experiments.

170 Chapter 4: Applications: micromachining of dielectrics and biological tissues 134 time of experiment is found to be a good compromise with respect to the dynamics of dehydration of the corneal sample [165]. Afterwards, we determine the damage threshold (as it was shown before in chapter 2.2) with the help of optical microscopy and using a statistical approach Damage threshold measurement and interpretation The general view of an experiment is shown in fig Each line presents different fluence levels. We choose the statistical approach for determination of the threshold due to the specific behaviour of surface topology of the corneal samples. Near the threshold, large morphology fluctuations could be observed, thus making confusing the measurement of crater diameters or ablated volume (illustrated in fig. 5.9 and fig. 5.10). Indeed, one can hardly distinguish some craters. Now, some difference in damage appears for low and high fluence. They emerge from Figure 4.9: General view of an experiment on Bowman s layer. There is a reference mark prior to the horizontal experimental line consisting of a serie of 10 impacts at a fixed fluence in singleshot regime. A set of data consists typically of 10 different fluences, resulting in a 10x10 matrix. Continuous lines determine the border of the experimental area. almost undistinguished points at low fluence (lines 1-4 from the bottom in fig. 5.9) to explosive character of damages at high fluence (lines 1-5 from the top in fig. 5.9). Even at the same fluence, the damages appear differently: from small and regular craters to star-like shapes. This is mainly due to the heterogeneity of living corneal tissue, or for instance the change of its chemical composition induced by laser irradiation, irregularity of surface state, etc.

171 Chapter 4: Applications: micromachining of dielectrics and biological tissues 135 Figure 4.10: Microscopy pictures of typical damages obtained on epithelium for a fluence: (a) close to the threshold (F = 5 J/cm 2 ) and (b) much higher than the threshold (F = 8.2 J/cm 2 ). In addition, corneal tissues are neither as rigid nor flat as inert dielectric materials (like fused silica), making more difficult their handling and their correct positioning at the beam focus. The surface roughness is also much more significant ( µm nm). Thus, it is evident that the standard damage or/and ablation threshold measurements applying damage diameter or ablation volume regression techniques are very tricky and fails in this case. The use of the statistical approach with the counting of the number of damages thus appears to be a convenient solution for treating this particular case and estimate the threshold of material change with a good confidence. As can be seen in fig. 5.11, experiments for different corneas exhibit reasonable reproducibility given the unavoidable differences between samples when working with living materials. Figure 4.11: Damage probability for epithelium and Bowman s membrane for 3 different corneal samples. Error bars are not shown [162]. From those plots we deduce two important fluence values. The first value defines the maximum fluence (F th,low ) under which a damage (or tissue modification) is never detected (damage probability equals to 0). It can be referenced as a "safety level" to ensure eye-security. The second value determines the minimum fluence (F th,high ) above which a damage is systematically

172 Chapter 4: Applications: micromachining of dielectrics and biological tissues 136 detected (damage probability equals to 1). It indicates the lowest fluence level required for controlled processing with minimal irradiation dose and thus minimum unwanted collateral effects. These two thresholds therefore provide essential information for the technical development of the cutting surgery process. Their values are summarized in Table 5.2. Measurement Epithelium Bowman s membrane (Mean ± Std deviation) (Mean ± Std deviation) F th,low, J/cm ± ± 0.1 F th,high, J/cm ± ± 1.1 F th, J/cm ± ± 1.1 Table 4.2: Results of the statistical method for the damage threshold measurement for the anterior corneal layers. The given values are averaged on three different samples for each layer. We calculate maximal fluence in the form: F=2E/πω 2 0 with ω 0 measured at the level 1/e 2. The damage threshold of the epithelial layer is F th,low = 2.7 ± 0.1 J/cm 2 that is significantly inferior to the Bowman s layer one (F th,low = 3.4 ± 0.1 J/cm 2 ) averaged over three samples. Olivié et al. [166] investigated the surface ablation threshold of corneal stroma as a function of wavelength and determined slightly lower values for porcine eyes at the same wavelength (1025 nm). Giguère et al. [167] has also measured damage threshold for epithelium and stroma for different pulse durations. His results are somewhat lower than ours but also exhibit the same tendency in difference of threshold fluence for stroma and epithelium. The difference in absolute fluence values given in literature can partly come from the definition of threshold fluence (peak or mean value), if the definition is given. One of the possible explications in this difference of thresholds for the epithelium and Bowman s membrane can arise from the surface state, preparation and conditioning of the sample. Indeed, the epithelial surface may be highly irregular and degraded due to the direct contact of this layer with the storage medium during all conservation period (from 5 to 10 days in our case). At the same time, the Bowman s layer is prepared just before the experiment thus minimizing the time of undesired contact with the ambiance and reducing eventual contamination or manipulation errors. We also suppose that the difference in damage thresholds arises from different physical and biochemical composition of anterior corneal layers. It is widely known that cellular organization and composition of epithelium and Bowman s membrane have unique characteristics that are attributed to physiological functions of each corneal layer (see Annex C). First, the epithelium ( 50 µm thick) is the most outer corneal layer that stays in contact with the tear film. It consists of some cube-shaped cell layers that flatten at the surface. Second, the Bowman s membrane is an acellular structure of 10 µm composited of randomly organized collagen fibers and special proteins - proteoglycans of small diameter. Hydration differences [168]

173 Chapter 4: Applications: micromachining of dielectrics and biological tissues 137 and electrolyte gradients [ ] among the different layers of cornea have also been measured. Hydration decreases from the Bowman s layer to epithelium. Lower levels of sodium and chloride ions are also found in epithelium (those ions are markers of extracellular matrix) and potassium and phosphorus content is higher in epithelial layer. Langefeld et al. [171] measured sulphur concentration in human cornea. The sulphur-containing molecules in the cornea are known to be collagen and proteoglycans responsible for the collagen maintenance. Those electrolytes can behave as centers of absorption thus yielding difference in thresholds for epithelium and Bowman s membrane. We thus suppose that the structural composition of epithelium and Bowman s membrane defines the difference in threshold values. Then, it is followed by the hydration and biochemical composition of corneal layers. But there is no scientific data of the influence of those chemical elements for specific absorption in the near infrared region. We note that the damage threshold for the epithelium is lower than the one for the Bowman s membrane. Any damage of epithelium is undesired during laser dissection of deep corneal layers (lamellar keratoplasty). As a consequence, the focusing strength (numerical aperture) has to be carefully adjusted to reach a sufficient fluence in the stroma and in the same time to keep off from damaging the superficial layer while performing subepithelial laser incision (LASIK). In addition, even small epithelial traumas could cause serious complications such as epithelial ingrowths thus decreasing visual perception. Moreover, the precise knowledge of low and high damage thresholds allows minimizing the laser irradiation doses in the chosen layer. Indeed, the high damage threshold (F th,high ) roughly corresponds to the minimal laser fluence that defines the optimal operating condition. At the same time, for controlled and reproducible surgery process, the fluence transition ( F = F th,high - F th,low ) has to be avoided Study of the clinical corneal graft process The procedure of profound laser dissection required for corneal graft is much more complicated due to the organization of collagen and moisture level in the depth of the corneal tissue. Human cornea is a tissue possessing scattering properties (a turbid media), thus the delivery of exact dose of laser irradiation in the depth becomes complex. Moreover, the physical and biochemical composition varies strongly on the surface or subsurface and in posterior layers. Anterior stroma is composed of interwoven collagen and less hydrated, while posterior stroma has collagen fibers organized in one direction and high hydration due to the close presence of Descemet s membrane acting as an ionic pump. It is still an area of active scientific research to find the optimal parameters and techniques for precise and reproducible incision and optimal removal of donor and recipient corneal grafts. In particular, the precision of the cut (equality in the lateral size

174 Chapter 4: Applications: micromachining of dielectrics and biological tissues 138 of donor flap and recipient bed) and the minimization of surface roughness of donor flap and recipient bed are mandatory for fast tissue healing and good clinical results. In the context of our study, we are intended to improve the functional result of the existing femtosecond surgery. In the frame of this research we proceed in exactly the same manner as during femtosecond laser assisted corneal grafting. The optimization of "free" parameters of the used commercial laser systems is the objective of the study. Some of parameters that could improve the process cannot be accessible or modified. For example, they are the laser wavelength, spatio-temporal pulse distribution, focusing, etc... In our study, we investigate the dissection of cornea while fixing parameters (see table 5.3) and changing the dissection depth and number of laser passages. Those two parameters allow to indirectly define the minimal dose to be used for each particular depth. The aim is to optimize the experimental protocol for successful deep lamellar keratoplasty (> 200 µm) assisted by femtosecond laser. The principal requirement is to get minimal collateral damage and high regularity (minimization of the number of tissue bridges) of the flap surface for both recipient and donor. In our study, the experimental protocol is separated between three laboratories 6. The corneas are first cut with the commercial clinical laser system of the hospital CHU La Timone and in conditions representative of the clinical transplantations. The experiments on the traction force measurement are performed at LP3 Laboratory. This experiment consists in measurement of the force to be used for separation of the corneal flap from the corneal bed. It also represents the gesture of the surgeon during grafting surgery. The surface roughness measurement yielding the estimation of resultant surface quality are carried out at Fresnel Institute. All specimens are obtained from the French Eye Bank (La Banque Des Yeux; EFS: Etablissement français du sang, Marseille, France) following the same procedure as before (see section ). The conservation in the preservation liquid Corneamax never exceeded 15 days Corneal dissection (CHU La Timone) The corneal dissections are realized with a subpicosecond laser system of Technolas company. This laser-based medical device allows an automatic control of the procedure, the parameters being chosen by the surgeon depending on the pathology level. The laser (see fig. 5.12) is operated at 80 KHz and at the wavelength of 1040 nm. 6 These works are developed in the frame of the regional project "DCOUP" implying CHU La Timone, Fresnel Institute and LP3. We would like to thank the hospital and Fresnel Institute for supplying laser dissection and surface roughness measurements

175 Chapter 4: Applications: micromachining of dielectrics and biological tissues 139 Figure 4.12: Medical laser system "Technolas" of CHU La Timone for corneal graft operation. The cornea is placed on an artificial anterior chamber (fig. 5.13a) to preserve the curvature, moisture and integrity of the tissue at physiological conditions and normal corneal pressure. A snake-like pattern of laser spots shown in fig. 5.13b is used in our experimental study. The ensemble of those spots in the corneal stroma produce the "cleavage plan" and consequent easiness while pulling off the corneal flap. The quality of the "cleavage plan" is a central element of our study. Figure 4.13: a) Barron artificial anterior chamber used during the laser dissection; b) Schematic drawing of spatial positioning of the laser spots during the laser cut procedure (snake-like pattern). For our study, the laser cut is done with the following constant laser parameters (see table 5.3). The variable parameters are the depth (200, 400, 600 µm) and number of laser passes (one or two). Lamellar keratoplasty is used to replace just pathologic tissue and to keep the integrity of the cornea that reduces risks of graft rejection. Thus those three different depths represent

176 Chapter 4: Applications: micromachining of dielectrics and biological tissues 140 various demands for corneal transplantation of different pathology degrees. The number of laser passes gives indirectly the access to the delivery of optimal energy dose for good post-operative results and vision recuperation. Parameter Energy, nj Value Stromal bed 1000 Border 1300 Spacement (A-C/A-B) Stromal bed 6.5/6.5 Border 3.0/6.0 Diameter, µm 8500 Rim angle Table 4.3: Set of parameters kept constant for the parametric study of cornea dissection. After the experiment, the measurement of the corneal total depth and control of the laser dissection depth can be performed by means of an OCT. The final operation consists in thread attachment for the traction test. Fig demonstrates how two threads of 5.0 ethilon polyamide are positioned at the border of the corneal flap. They are separated by the distance of 2 mm. Figure 4.14: Schematic drawing of thread attachment. Two threads separated by a distance of 2 mm are attached at the border of the corneal graft previously dissected with the laser. The choice of the thread positioning is done to reproduce the movement of the surgeon during the delicate procedure consisting in pulling out the flap from one side of the cornea with a quick gesture Traction measurement: laser parameter optimization for corneal graft surgery (LP3) Here, we measure the easiness of removal of the corneal transplant that reflects the impact on roughness and healing after the surgery. The measurement of the pull off force is done at LP3 laboratory using the traction testing machine (fig. 5.15a).

177 Chapter 4: Applications: micromachining of dielectrics and biological tissues 141 Figure 4.15: a) Test bench for the pull off force measurement (by Lloyd Instruments, LFPlus); b) - c) Description of a test. The cornea is positioned in the same manner on the artificial anterior chamber as for the laser dissection (fig. 5.15b). The traction speed is kept constant (22 mm/min) during all experiments. The precision of the measurement is 0.01 % for the 10 N sensor. Fig finally shows a sequence of photos describing the pulling off the corneal flap from the corneal bed. Figure 4.16: Illustration of the pulling off force measurement. At the end of an experiment, we obtain the curve of pull off force vs the elongation (fig. 5.17). The maximal force in our opinion presents more realistically the pull off force as almost the totality of the corneal flap is pulled off (mostly all tissue bridges are included). The rupture force is representative of the final step for the pull out of the flap from the corneal bed. From this type of curve we are also able to evaluate the pulling off energy (J = N m) that is calculated from the integration of the surface below the curve of the force. This energy describes (qualitative estimation) the minimal energy leading to the tearing away of the dissected corneal flap (see hereafter).

178 Chapter 4: Applications: micromachining of dielectrics and biological tissues 142 Figure 4.17: Typical curve obtained during experiment Measurement of the resultant surface roughness (Fresnel Institute) Another important information consists in measuring the surface roughness of the corneal bed. Indeed, it will answer to the question of the quality of laser dissection and pulling off the corneal flap. High quality of cut defined by low resultant surface roughness ensures success of corneal transplantation resulting in vision correction. Measurement with optical profilometry (fig. 5.18a), that is based on the observation of the topography of the corneal stroma roughness, aims to characterize the surface state. Figure 4.18: a) Commercial optical profilometre; b) Schematic drawing of profilometry working principle: BS beamsplitter, L lens or microscope objective, M piezoelectric mirror; c) Image treatment with the program Talysurf, surface of 900x900 µm, microscope objective 20x. The principle of the measurement is shown in fig. 5.18b and consists of the interferometric scanning of surface topography. Measurements are done in the central part of the corneal bed. The analysis of interference fringes gives the cartography of the surface state (fig. 5.18c) with a

179 Chapter 4: Applications: micromachining of dielectrics and biological tissues 143 maximum lateral resolution of 500 nm and vertical resolution inferior to 1 nm Results and discussion We performed 15 experiments 7. This number is relatively small to define the conditions for the surgery process. The dispersion of experimental values is still high but there are already some tendencies and important remarks to underline 8. The work will be continued using the defined protocol. In table 5.4, the mean values and error bars of maximal and rupture forces, the slope of the curve of force as a function of elongation and the resultant surface roughness for dissection depth of 200, 250, 400 and 600 µm are grouped. Depth, µm Maximal force (N) Rupture force (N) Slope Roughness (nm) Single pass : ± ± ± ± ± ± ± ± ± ± ± 432 Double pass : ± ± ± ± ± ± ± ± ± ± Table 4.4: Mean values and error bars of pull off force, rupture force, slope of the curve of force vs elongation and surface roughness for one and two laser passes. only one experimental value is acquired during the experimental series. In fig the maximal force as a function of photodisruption depth for single and double passes is shown. The curve examination uncovers the decrease of the pull off force for all the depths with increase of the number of passes 9. This behaviour is logic, the increase of number of laser passes increases the totally deposited energy due to cumulative effects, thus simplifying the separation of the graft from the corneal bed. For important depths (more than 400 µm), increasing the number of laser passes seems not significantly change the tendency, that could be due to the structural change of the corneal tissue, in fact the change of the density and size of fibril and its organization with increase of the depth (difference in the anterior and posterior 7 In fact, more experiment ( 30) have been performed but some of them fail for various reasons (low sample quality or the problem of the positioning of a sample on the anterior chamber (too small size of the sample), removal of the thread, too long conservation time,...) 8 A second series of experiments that is currently in progress confirms those tendencies. 9 We consider the difference between 400 et 600 µm non significative (but it should be confirmed by multiplication of the number of experimental results). From the graph it may be supposed the non validity of our hypothesis with the final increase of the pull off force for 600 µm and two laser passes. This result is obtained with low number of experimental points and the work for the verification of tendencies is currently in progress.

180 Chapter 4: Applications: micromachining of dielectrics and biological tissues 144 stroma, between 200 and 600 µm). Figure 4.19: Maximal force for pulling off the corneal flap. In addition, the structural difference explains the decrease of the pull off force with increase of depth. Indeed, the diffusion and energy loss by scattering 10 induced by the collagen fibers and corneal structural elements are probably compensated by the lower organization of the collagen fibers in the posterior stroma, that in turn demands less energy to disrupt the corneal tissue. This is the more probable explication of the decrease of pull off force at high depth (see fig. 5.20). The evolution of the pulling off energy (see fig. 5.20) with number of passes and dissection depth certifies previous results and conclusions. In particular, it is illustrated by the decrease of the minimal energy for flap separation. Moreover, the surface roughness significantly decreases with increase of number of laser passes (see fig. 5.21). The additional energy absorbed by the corneal tissue during the second laser pass leads to smoother tissue surface and to a more perfect procedure of laser dissection. It corroborates with the previous results defining better surgical result, in particular, in terms of surface roughness. Note that the difference in the resultant surface roughness is not significant whatever depth and depends only on number of passes. 10 It was predicted for humans, that according to the differential density of the collagen fibres for any given wavelength light scattering per unit depth will be approximately twice higher in the anterior corneal segment of the stroma than in the posterior [172]. Patel et al. [173] also measured the refractive index of the cornea showing it decrease from at the epithelium to at the endothelium via intermediate value in the corneal stroma (1.380).

181 Chapter 4: Applications: micromachining of dielectrics and biological tissues 145 Figure 4.20: Pulling off energy as a function of cutting depth and number of laser passes. Figure 4.21: Surface roughness for single and double laser passes. Now let us discuss in more details the difference (pull off force) observed between shallow ( 200 µm) and deep ( 400 µm) laser dissection. It is now generally accepted that the organization of the corneal lamellar in the central and periphery parts of the cornea is responsible for its transparency. It is also widely known that corneal stroma is highly inhomogeneous [169,171, ]. The corneal stroma consists of 200 collagenous lamellae layers in the center and 500 layers at the periphery [175]. Some authors measured the density of the lamellae and their density was more than 50% greater in the anterior region of the stroma than in the posterior stroma [175, 177]. According to Meek at al. [175] the mean lamellae values are 57 ± 12 units per 100 µm for

182 Chapter 4: Applications: micromachining of dielectrics and biological tissues 146 the anterior segments vs. 38 ± 5 units per 100 µm for the posterior segments of the stroma. In the anterior stroma, the collagen lamellae are thin (about µm thick and µm wide) [176], undulating and interwoven [178, 179]. In the mid and posterior stroma, collagen lamellae are arranged parallel to the surface and are thicker ( µm thick and µm wide) [176]. Moreover, concerning the mechanical property, the elasticity modulus is found to be different for the anterior and posterior stroma [180]. The maximal value of bulk modulus can vary between 200 kpa and 20 MPa and depends on testing method and orientation of the corneal fibers with respect to the applied stress. To our opinion, those structural differences are the key parameter defining the difference in pull off force and its decrease with depth. Moreover, the posterior stroma is highly hydrated compared to anterior [168, 174, 178, 179, 181]. Anterior stroma maintains the correct shape of the cornea due to specific lamellar interweaving of the anterior stroma and insertions into Bowman s layer thus preventing it from swelling. On the contrary, in posterior part of cornea, collagen-free regions or lakes exist [182]. Their appearance may be caused by the replacement by water of regions previously occupied by cells (for example, keratocytes) [178]. In the infrared region, there is important water absorption present [183], thus the moisture level will strongly participate in increase of efficiency of energy deposition in posterior corneal layers. As a consequence, the easiness in pulling off the graft is achieved. From the bio-chemical point of view, there are also differences between anterior and posterior part of cornea. Electrolyte concentration measured for different corneal layers (from epithelium to endothelium) shows highly inhomogeneous structural composition and, thus physiological functions. For example, the phosphorus has higher concentration in Descemet s membrane and lower value for subepithelial layer with minimal value in the middle stroma. For Chloride and Sodium (the extracellular matrix markers), the highest concentrations are found in middle stroma and Descemet s membrane while lower values are found in subepithelial and posterior stroma [169]. A high level of phosphorus is found in cellular cornea layers [170, 171] and in a lower concentration with keratocytes in stroma. The total sulfur content does not change with age, nevertheless the collagen responsible for elasticity and proteoglycan structures does. Electrolytes can be seen as impurities similar to ones in amorphous dielectrics. Those centers of absorption thus can be the reason of difference in thresholds for photodisruption in subepithelial and posterior layers and decrease of the pull off force and energy with depth. By now, there is no a profound study of their influence on laser dissection process. We suppose that it will be interesting to continue the research on the absorption of those cornea components in infrared region in order to evaluate the importance of their concentration in corneal layers on laser cut. We can not avoid to say that there are some difficult points or parameters during measurement

183 Chapter 4: Applications: micromachining of dielectrics and biological tissues 147 that can make difficult the parametric study. Indeed, the age, sex, and differences in corneal thickness could impact the measurement. It is known that the cornea stiffens and Descemet s membrane thickens with age [180, 184]. It can be also due to different compositions, functions (see Annex C) and renewal. 4.4 Conclusion In this chapter we have presented experimental results concerning practical applications of a femtosecond laser. In micromachining a supbicosecond laser can give high selectivity in terms of ablated depth ( 20 nm) and ablated diameter ( 1 µm), if one selects carefully the applied fluence (for a given pulse duration). In our operating conditions, the maximal values achieved are: ablated depth 300 nm ( 0.003z r ) and ablated diameter 13 µm ( 2ω 0 ). The axial resolution (crater depth) principally depends on local fluence and the transversal resolution depends on total fluence. The quality of ablation is low (debris and high irregularity) at low fluence, but in the range of the optimal removal efficiency the crater walls are steep and smooth and the crater bottom is regular. The evolution of crater shape can also be controlled by the thorough choice of the incident fluence (Gaussian-like or "Top-hat"). During the medical aspect on this work we have studied laser dissection of anterior ( 200 µm) and posterior (> 400 µm) corneal layers without alteration of the surface and subsurface layers. The research was aimed to optimize the corneal dissection (minimizing of pull off force and surface roughness) by a subpicosecond laser (a commercially available clinical laser system with similar characteristics as in our laboratory) hence increasing patient comfort and security. It has been affirmed that the increase of laser passes gives smoother tissue surface thus facilitating healing, vision recuperation and decreasing post-operative complications. The increase of the number of laser passes increases the totally deposited energy (cumulative effects) thus simplifying the separation of the graft from the corneal bed. It has been also demonstrated the decrease of the pull off force (reproducing the gesture of the surgeon during surgery) and energy at profound corneal depth. We suppose that it is due to the structural difference of the anterior and posterior corneal layers. In addition, higher hydration level in posterior stroma may increase laser absorption and thus causes simpler pulling off the corneal flap from the corneal bed.

184 Chapter 4: Applications: micromachining of dielectrics and biological tissues 148

185 Conclusion The aim of the present study has been to deeply study and shed light on mechanisms of laser energy deposition into a dielectric and laser ablation. The study of material ablation demands a systematic approach concerning different aspects of the process: energy deposition and dissipation, material ejection and finally the characterization of structures. The precise methodology and diverse experiments during this study have allowed to obtain and compare different results concerning the process of laser ablation of a transparent medium. In particular, the comprehension of the phenomena of energy deposition as evidenced in this work uncovers various applications of a subpicosecond laser both for micromachining and medicine. To our knowledge, there has been done just a few studies of different aspects of interaction on the same material (fused silica) through different (pump-pump and pump-probe) experiments accompanied by a modelling. The main results that have been obtained during the study are now listed below. Laser ablation mechanisms Femtosecond laser regime allows to access to nonlinear absorption of an initially transparent material (dielectric) via multiphoton ionization followed by electronic avalanche. The building up of high free electron density in the conduction band is necessary to initialize laser damage or ablation of wide bandgap materials. By means of transmission and reflection measurements, we have observed the dependence of laser absorption on incident energy and the dynamics of absorption. Minimal time and energy (fluence) are needed to be deposited to create a highly absorbing metal-like medium (transformation of an initially transparent dielectric in absorbing matter). High absorption has a competing mechanism during energy deposition, it is reflection. The reflection being strongly dependent on the real part of dielectric function increases upon reaching the critical density and temporarily arrests the energy deposition. But the controlled increase of free electron density over the critical value then allows to find a compromise between high laser absorption and increased reflection. We thus show that for subpicosecond laser pulses energy deposition lasts during all the pulse duration for moderate and high fluences. The minimal time to create an absorbing medium 149

186 Conclusion 150 moves towards the beginning of the pulse with the increase of incident fluence. Further the laser energy deposited to the electron subsystem followed by the energy transfer to ions, that finishes after the pulse end, causes material modifications. In the case of "long" femtosecond laser pulses ( 500 fs), the ablation consists of a harmonious composition of electronic (Coulomb explosion or electrostatic ablation) effects taking place during or just after the pulse end and thermo-mechanical effects taking place on time scales longer compared to the pulse duration. These effects are strongly localized in a micrometric volume. It thus gives access to precise micromachining and laser dissection of biological tissues with low collateral effects. Femtosecond laser application for micromachining For numerous applications of femtosecond lasers, the key points are control of the procedure, micrometrical resolution and reproducibility. We have demonstrated that a subpicosecond laser is a precise tool for localized ablation. The main mechanism of laser ablation is thermal (thermomechanical), but a thin surface layer can be ablated due to electronic effects. The quality of ablation depends strongly on applied laser fluence both in terms of efficiency of ablation (expressed in µm 3 /µj ) and the quality of final ablation crater (smooth walls and crater bottom). With a highly stable laser system it is possible to achieve high repeatability for the chosen characteristics. The high selectivity of ablation is defined by the strongly deterministic character of interaction and is achieved by thoroughly adjusting incident laser fluence. In our case the resolution in transversal and axial directions is respectively 1 µm and 20 nm. The analysis of the experimental and theoretical data provides an important tool for the spatio-temporal beam shaping and thus to optimize laser energy deposition and utilization. Femtosecond laser application for corneal graft Laser dissection or photodisruption is based on thermo-mechanical effect induced by the laser. That is why subpicosecond lasers can be well adapted to all kinds of tissue dissection. Femtosecond laser have been used for laser surgery, like so-called LASIK since 1989 for vision correction (small propagation depth). Nowadays this procedure is well adapted to surgery demands and reproducible. Based on LASIK procedure, femtosecond laser possess a good potential for deep lamellar surgery that is used in case of corneal grafting. In our study we were intended to improve the existing laser dissection quality of a commercial clinical laser system hence satisfying the demands of ophthalmological society for minimizing the energy dose for faster post-operative vision recovery and better comfort of patient. Our results demonstrated the improvement of laser dissection in the corneal depth without increase of the laser irradiation dose and more regular

187 Conclusion 151 and smooth surface with increase of the number of laser passes. Perspectives In the perspective of this study is the research and comprehension of the mechanisms of interaction of an ultra short femtosecond laser with a dielectric. For the moment ultra short lasers are the area of active scientific research and the laser system of 10 fs pulse duration may open the possibilities to even higher axial and transversal resolution for material ablation and microstructuring. The energy deposition mechanisms and the relaxation mechanisms such as electron-electron coupling and electron-phonon coupling could be easily accessible and studied with an ultra short femtosecond laser. This study may shed light on applicability of the existing theoretical models. We also note that widely accepted theoretical approach based on Drude model should be refined or reviewed according to the findings concerning dependence of electron collision frequency on electron concentration and electron temperature and finally due to the difference of the initial conditions during laser interaction with metal or dielectric. The definition of the behaviour of the dielectric function of a transparent material under intense irradiation is an interesting field of theoretical study. Concerning the study of the femtosecond laser surgery process, it is necessary to have more data of absorption of such chemical elements as sodium, potassium, sulphur in near infrared region in order to better understand laser absorption of transparent biological tissues (such as cornea). The influence of tissue elasticity on laser dissection and water concentration will be instructive for perfectioning laser photodisruption process. Afterwards, it should be important to carry out further clinical studies in order to determine the exact level of the best operating energy (in terms of efficiency of the cut and post-operative surface regularity). This study would aim to increase reliability, comfort of the patient, homogeneity of the clinical results and rapidity of healing with respect to minimization of the collateral effects for the corneal surgery process. Moreover, if we take into account the advantages of a femtosecond laser especially in the biology domain, the comprehension of mechanisms of interaction with animate matter and the deposition of the minimal dose of laser irradiation allows to access to non-thermal and non-destructive DNA study (quantitative analysis of RNA), laser printing of biomaterials, and biodevice fabrication.

188 Conclusion 152

189 Annex A: Structural characteristics of fused silica Instead of having discrete energies as in the case of free atoms, the electronic structure of dielectric materials consists of available energy states for electrons, which form bands. In dielectric materials, the electrons in the valence band (the last completely filled band) are separated by a large gap (band gap with energy states forbidden for electrons) from the conduction band (the first non-occupied band). The most common insulating material used for industry is silicon dioxide, which is not a form of ionic crystal 1, as for a example sapphire Al 2 O 3 crystal. In the silicon-dioxide structure silicon atoms are surrounded by four oxygen atoms, forming a regular tetrahedron, and each oxygen atom is bonded to two silicon atoms as it is shown schematically in fig. i. Each oxygen atom is positioned equidistantly from its two silicon neighbors and Figure i: Schematic diagram of silicon dioxide. The white circles are the silicon atoms, each connected to four neighboring silicon atoms by a bent oxygen-atom bridge (dark circles) [185]. forms a bent bond, or a bridge, between the two silicons. The simplest crystal lattice of SiO 2 is arranged as in the elemental silicon structure but with the silicon-silicon bonds replaced by oxygen bridges. The directions between two neighbors oxygen and silicons make an angle of about 144. The oxygen bridges can be rotated allowing the bond lengths and angles to preserve their values near the ideal ones. In order to understand the electronic structure further, the two silicon 1 An ionic crystal consists of ions bound together by their electrostatic attraction [84]. 153

190 Chapter : Annex A: Structural characteristics of fused silica 154 hybrids directed toward an oxygen atom are shown (fig. ii). The angle of 18 characterizing the bend in the oxygen bridge is half the difference between the bond angle, 144, and 180. A bonding unit for a solid must be stochiometric; that means that the unit must have the same ratio of constituent atoms as the compound. Only in this case it is possible to construct a crystal out of such units. This criterion is fulfilled for the oxygen atom on fig. ii. A silicon atom with four oxygen neighbors is not allowed as a bonding unit. As long as the entire crystal also includes impurities and inclusions, it should be taken into account that there are more than one set of bonding units in some structures. In our study we take the classical value of the bonding units for electronic states in terms of the total number of the orbitals of oxygen and silicon. Figure ii: Si and O hybrids. If we do so, we shall obtain the energy-level diagram of the formation of Si-0 bonds in SiO 2 (shown in fig. iii). Figure iii: Theoretical band structure of SiO 2. All the bonding and antibonding orbitals are formed from the silicon and oxygen hybrids.

191 Chapter : Annex A: Structural characteristics of fused silica 155 The valence bands are formed by the bond (ε b ), lone-pair (ε lp ), and π-states (ε π ) where there are enough electrons to fill them; the antibonding (ε a ) orbitals form the conduction bands. There are two basic ways of making quartz / silica glass: By melting silica grains either by gas or electrical heating (the type of heating affects some optical properties). For some applications the material can be transparent or opaque. By synthesizing the glass from chemicals. This synthetic material, normally referred to as synthetic fused silica, has better optical properties and is somewhat more expensive than the other type. Fused silica has outstanding physical characteristics such as thermal properties (thermally shock resistant, low coefficient of thermal expansion) with excellent optical transmission properties from the deep UV to the infrared wavelength range, with good electrical and corrosion performance. In the table 5, we group the main properties of fused silica. Property Value Units General Chemical Formula SiO 2 Mechanical Density 2.2 g/cm 3 Hardness 570 Knoop Tensile Strength 50 MPa Young s modulus 72 GPa Compressive Strength 1100 MPa Poisson s Ratio 0.17 Fracture Toughness 1.2 MPa m 1/2 Electrical Dielectric 20 C kv/mm Dielectric Constant 1 MHz Volume Resistivity 7 x 10 9 ohm-cm Thermal Coefficient of Thermal Expansion C Thermal 20 C 1.4 W/mK Specific C 964 J/kg K Maximum Working Temperature C Optical Index of Refraction (1.06 µm) Transmission Band λ, µm Band gap 9 ev Table 5: Physical properties of SiO 2 [186, 187]. In our study we mainly use synthetic SiO 2 material SUPRASIL produced by Heraeus. This high purity fused silica is manufactured by flame hydrolysis of SiCl 4. This material has controlled index of homogeneity ( n) that is specified either in one direction (functional direction) or in all three functional directions. This synthetic fused silica is practically free from bubbles and inclusions (total bubble cross section within the volume 0.015mm 2 /100 cm 3, OH-group is

192 Chapter : Annex A: Structural characteristics of fused silica 156 present). A second type of fused silica used in the experiment is HOQ 310 also by Heraeus. HOQ material is manufactured by fusion of natural quartz crystals, that has bubble class 3 (total bubble cross section within the volume 0.5mm 2 /100 cm 3 ) and low impurity content such as Al, Ca, Fe, OH-group, Li, Mg and some others (Au, As, Cu, Cr, K, Na, Sb) that are not significant. Optical transmission properties of silicon dioxide are presented in fig. iv. This material has low linear absorption from 190 to 2000 nm. That is essential for femtosecond laser treatment of fused silica as the interaction is nonlinear for a wide range of laser wavelengths. Figure iv: Transmission spectrum of fused silica [188]. We made a spectroscopic analysis of the plasma plume obtained during laser-matter interaction experiment (see fig. v). The spectroscopic analysis was done in ambient air with fast sample displacement and with an acquisition time of 1 s for every curve. The experimental curves are the result of the averaging of 7 measurements, performed in single shot regime (fig. v). Discrete spectral lines on the spectrum obtained with the microscope slide are present and intense, confirming high content of impurities such as K, Ca, Na, H,... Suprasil and HOQ 310 do not show these impurity lines and yield similar emission spectrum. They present only traces of some chemical impurities (potassium, Na). We can conclude that both HOQ 310 and suprasil samples are high purity glasses with similar composition.

193 Chapter : Annex A: Structural characteristics of fused silica 157 Figure v: Emission spectrum of fused silica of different quality. High purity SiO 2 : suprasil and HOQ 310 and low purity: microscope slide. The spectral line at 1025 nm corresponds to laser light irradiation. For discriminating the three curves, a different offset is applied to each glass sample.

194 Chapter : Annex A: Structural characteristics of fused silica 158

195 Annex B: Estimation of phase matching angle for non-collinear SHG The beams are incident on the nonlinear crystal surface as shown in fig. vi. Figure vi: Noncollinear second harmonic generation. Estimation of phase matching angle. The incidence and refraction angles for probe (resp. pump) are i probe = 2, i pump = 28, r probe = 1.2, r pump = 16.5, γ = r pump r probe = 15.3, γ/2 = The phase matching angle is given by the intersection: sin 2 θ c = X2 (n2ω (n ω = e ) 2 0 )2 (n 2ω (n 2ω 0 ) 2 (n ω 0 )2 (n ω 0 )2 0 )2 (n 2ω e ) 2, (1) where the refractive index of the ordinary are n ω 0, n2ω 0 and the extraordinary beam n ω e, n 2ω e. The ordinary surface of the ω is a circle: X 2 + Z 2 = (n ω 0 ) 2 (2) 159

196 Chapter : Annex B: Estimation of phase matching angle for non-collinear SHG 160 The extraordinary surface of the second harmonic beam(2ω) is an ellipse: X 2 (n 2ω e ) 2 + Z2 (n 2ω = 1 (3) )2 The substitution of eq. 2 in eq. 3 gives: sin 2 θ c = and θ c = The phase matching yields the vectorial condition: 0 k ω + k ω = k 2ω (4) In space, we have (x, z ) (x, z), but the difference consists only in rotation θ between them. The projection on axis x gives: n ω e ω(1 + cos(γ)) = n 2ω e (θ)2ω cos(γ/2) (5) The projection on axis z yields: n ω e ω sin(γ) = n 2ω e (θ)2ω sin(γ/2) (6) Multiplying the eq. 5 by eq. 6 gives: (n ω e ) 2 (1 + cos(γ)) sin(γ) = 4(n 2ω e (θ)) 2 cos(γ/2) sin(γ/2), (7) then, thus, (n ω e ) 2 (1 + cos(γ)) sin(γ) = 2(n 2ω e (θ)) 2 sin(γ), (8) (n ω e ) 2 (1 + cos(γ)) = 2(n 2ω e (θ)) 2 (9) Considering: 1 + cos(γ) 2 = cos 2 (γ/2), (10) we finally find: n 2ω e (θ) = n ω e cos 2 (γ/2) (11) So now, while taking fixed value of γ, we can find n 2ω e (θ) (n 2ω e (θ) = ) and respectively θ, that is the direction of the second harmonic wave vector k 2ω. The value of n 2ω e (θ) is found from

197 Chapter : Annex B: Estimation of phase matching angle for non-collinear SHG 161 the equation of ellipse (eq. 3) in space (x,z) in form: Thus with n ω 0 n 2ω e 1 (θ) = cos2 (θ) (n 2ω + sin2 (θ) 0 )2 (n 2ω e ) 2 = cos2 (θ)[ 1 (n 2ω (n 2ω 0 )2 1 (n 2ω e ) 2 ] + 1 = ; n2ω 0 = ; n ω e = , we find θ = e ) 2 (12) From θ c = 23.5, θ = 31.5 and γ = 15.3, we retrieve r 1 = θ - θ c - γ/2 = 0.4 giving the angle of incidence for the probe i probe = 0.65 and r 2 = θ - θ c + γ/2 = giving the angle of incidence for the pump i pump = That is in a good accordance with the experimentally found values.

198 Chapter : Annex B: Estimation of phase matching angle for non-collinear SHG 162

199 Annex C: Human eye General discription Vision is an essential human sense giving information about our environment. The eye is a very complex organ, realizing the important function of light detection and visual sense. The eyeball is an organ of small volume (6.5 cm 3 ) and weights approximately 7 grammes. Its size is 2.85 cm wide and deep, and 2.3 cm tall. Figure vii: Anatomy of the human eye. The anatomy of the human eye is shown in fig. vii. The shape of the eye is maintained by the outer layers: cornea and sclera. Sclera is typically white and cornea is a transparent tissue. Light enters the eye through the cornea which refracts the incoming light onto the crystalline lens. The iris is on the light path to the crystalline and acts as a diaphragm. Finally focused light arrives on the retina, a layer of light sensing cells lining the back of the eye that converts light into neuronal signals or impulses transferred to the brain by the optic nerve. The cornea is responsible for most of the visual power of the eye and the crystalline lens guided by the ciliary muscles only finely tunes the focus. The lens separates the eye into two fluid-filled sections: the cornea, the iris, and a clear, watery substance called aqueous humor composing the anterior 163

200 Chapter : Annex C: Human eye 164 segment; and the posterior segment consisting of a clear, gel-like material called the vitreous humor, the retina, and the optic nerve. The different components with their parameters are presented in table 6 in the order from the outermost to inner eye structure. Parameter Index of refraction Value Cornea Aqueous humor Lens Vitreous body Radius of curvature (mm) Cornea (ant. surface) 7.7 Cornea (post. surface) 6.8 Lens (ant. surface) 10.0 Lens (post. surface) -6.0 Optical power (diopters) Cornea Lens Eye (total) Table 6: Optical parameters of the unaccommodated human eye, provided by Gullstrand [138]. Corneal structure and functions The cornea is the eye outermost layer. It is a clear, avascular, dome-shaped surface covering the front of the eyeball. The cornea consists of a highly organized group of cells and proteins and receives its nourishment from tears and aqueous humor filling the chamber just behind it. It does not contain any pigment cells. Considering cornea in terms of optics and refractive power, the curvature radius of its external central part is 7.7 mm. The cornea is steeper at the center than at the periphery and its anterior surface is like an ellipse. The internal or posterior surface has a radius of 6.8 mm. Due to its unique properties, absence of blood vessels and transparency, the cornea is responsible for % of eye visual power. Corneal thickness is less at the center (530 µm) than at the periphery (700 µm) and corneal thickness could reach up to 1 mm in pathological conditions. The average diameter of the cornea horizontally is 11 to 12.0 mm and vertically 9 to 10 mm. The cornea must remain transparent and durable to perfectly perform its functions: 1) To refract the light onto the retina as the outer lens of the eye. 2) To protect the eye from germs, dust, and other harmful substances. It shares this function with eyelids, tears, and sclera.

201 Chapter : Annex C: Human eye 165 3) To protect the crystalline lens and the retina from the harmful ultraviolet irradiation coming from the sunlight. To perform well its functions, cornea consists of 5 layers (fig. viii): epithelium, Bowman s membrane, stroma, Descemet s membrane and endothelium [189]. Figure viii: Schematic drawing of the full depth corneal structure, including two membranes and the basic corneal component - stroma. Source: World Wide Web. The mucous layer is an hydrophilic submicron sized (4 to 10 µm) coating of superficial epithelial cells. It moistures and protects from the bacteria the rest of the cornea. Aqueous tear film rests on the mucous surface in normal eyes. Epithelium is the outer corneal layer that stays in contact with the tear film. It consists of five to seven cube-shaped cell layers 2 that flatten at the surface. The thickness of the corneal epithelium is 50 to 52 µm. Its role is to protect against the penetration of harmful substances and prevent liquid losses. In combination with tear fluid, epithelium provides a smooth surface of the cornea 3 and it also absorbs oxygen and cell nutrients from tears, which are furhter distributed to the rest of the cornea. Epithelial cells are quickly renewed by mitosis in the period of 5 to 7 days. The superficial corneal epithelial cells have hydrophilic properties due to presence of extracellular matrix of glycoproteins-glycocalix (responsible for spreading the tears). Deeper layer cells are less hydrophilic, due to the lack of network of microvilli and glycocalix [190]. The inner surface of the epithelium so-called the basement membrane, where the epithelial cells are organized, connects epithelium to the fist corneal membrane. Bowman s membrane is situated just below the epithelium and is a unique feature of primates, 1 Cells with an exceptional density of nerve endings are estimated to be 300 or 400 times greater than in the skin epidermis for fast response on external impact. 2 The alteration of the roughness of the corneal surface can cause the blurry and unfocused imaging on the retina.

202 Chapter : Annex C: Human eye 166 including humans, but nonexistent in many mammals. It is an acellular structure of 8-12 µm composed of randomly organized collagen fibers of types I and III and special proteins called proteoglycans of small diameter. The comprehension of the functions of this membrane is still not clear, but it is believed to play a protective role (as it is very hard to cut or pull off) as well as to contribute to the smoothness of the corneal surface. If Bowman s layer is injured, a scar can be formed while healing. Stroma includes about 90 % of the corneal thickness (500 µm). It consists primarily of water (78 %), collagen of type I, V, VI and XII (16 %), proteoglycans, glycosaminoglycans, and other proteins, which can absorb an amount of water 1000 times larger than their volume. It does not contain any blood vessels. The principal components of corneal stroma are attached to an extracellular matrix giving the cornea its strength, elasticity, and form. The organization of the collagen fibrils (fig. ix) is stacked one on another producing a network that is parallel to the corneal curvature. Figure ix: Schematic drawing of the spatial organization of collagen.a triple-helix structure of tropocollagen consisting of glycine and amino acids. (modified from [47]). These fibrils are constituted from basic units of tropocollagen (TC) molecule of size 1.5 nm in diameter and 300 nm long. This molecule has a form of spiral composed of 3 polypeptide chains (a triple-helix structure with a periodicity of 86 Å shown in fig. ix). The maintenance of the relative position of the fibrils is helped by the proteoglycans and they also restrict the growth of fibrils. These molecules composed of a core protein joined to one or more polysaccharide chains are called glycosaminoglycans. The cellular components of the extracellular matrix called the keratocytes (elongated cells) are responsible for the stability of the corneal shape and regularity of its organization. Descemet s membrane is an acellular membrane situated between the stroma and the endothe-

203 Chapter : Annex C: Human eye 167 lium and plays a role of protective barrier. It is 10 to 12 µm thick and composed of heterogene molecules: fibronectin, laminin, proteoglycan and collagen of types IV,VII. Endothelium is the last innermost layer of the cornea. It is in direct contact with the aqueous humor, providing the passage of nutrients inside the cornea and controlling hydration. It is composed of a single layer of hexagonal cells distributed with an average of cells per mm 2. The size of the endothelial cells is 4-6 µm. With age, the number of endothelial cells diminishes (approximate decrease rate is 0.33 % per year). They are not replaced and once damaged or in case of disease, these cells will not regenerate. The only mechanism is cell enlargement and extension. In a healthy eye, the fluid moves slowly from inside the eye into the stroma. The physiological function of the endothelium is to pump the liquid out of the stroma and keeps cornea clear. If this balance is broken, cornea swells with water, became hazy and opaque causing corneal edema and even blindness.

204 Chapter : Annex C: Human eye 168

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218 Interaction laser femtoseconde - diélectrique à intensité modérée: analyse du dépôt d énergie et application à l ablation de la silice fondue et de la cornée Résumé De nombreux processus fondamentaux ont lieu sur des échelles de temps femtosecondes à plusieurs centaines de picosecondes. En outre, les demandes continues d augmentation de résolution et de précision dans l industrie du micro-usinage de pointe exigent la compréhension fine des mécanismes physiques d ablation et l identification précise des conditions optimales de mise en œuvre des systèmes laser femtosecondes. Ces systèmes doivent ainsi permettre la production de structures de taille micrométrique de manière contrôlée et étalonnée. Dans ce travail de thèse, nous étudions l interaction d un laser femtoseconde (500 fs, λ = 1025 nm) avec une cible diélectrique en utilisant un banc d essai spécifique. La première partie de cet ouvrage décrit les aspects fondamentaux du dépôt d énergie laser dans les diélectriques (SiO 2 ) et de dissipation au sein du réseau ainsi que le processus d ablation de la matière, au moyen de techniques pompepompe et pompe-sonde résolues en temps. L étude expérimentale est accompagnée d une modélisation prenant en compte la propagation du faisceau dans la matière (équation de Helmholtz monodimensionnelle), le processus de dépôt d énergie en régime hors équilibre (modèle à deux températures) et l ionisation du matériau (équation de population de la densité d électrons libres). Enfin, nous mettons en évidence l intérêt des lasers femtosecondes pour la modification de la matière (notamment pour l endommagement en surface et l ablation) et les applications, notamment dans le domaine du micro-usinage et de la chirurgie de la cornée par laser. Mots-clefs: laser, endommagement, ablation, diélectrique, pompe-sonde, modélisation, microusinage, chirurgie laser oculaire. Femtosecond laser - dielectric interaction at mid intensities: analysis of energy deposition and application to the ablation of fused silica an cornea Abstract Numerous fundamental processes take place on time scales from several femtoseconds to hundreds of picoseconds. Moreover, the continuous demands of downscaling and increase of precision in the cutting-edge micromachining industry require the comprehension of the physical mechanisms and the identification of key laser parameters for an optimized use of femtosecond laser systems. Those systems shall allow production of controlled and calibrated micrometer-size structures with high spatial selectivity. In this PhD work, we study the interaction of a femtosecond laser (500 fs, λ = 1025 nm) with a dielectric target using a dedicated test-bench. The first part of this work describes the fundamental aspects of laser energy deposition in dielectrics (SiO 2 ), its redistribution to the lattice and the process of laser ablation by means of pump-pump and timeresolved pump-probe experiments. The experimental study is accompanied by a computational modeling taking into account the beam propagation (one-dimensional Helmholtz equation), the non-equilibrium process of the energy deposition (two-temperature model) and the matter ionisation (rate equation describing the free electron density change). Finally, we put in evidence the interest of femtosecond lasers for material modification (notably for surface damage and ablation) which high specific benefit in such applications as micromachining and laser corneal surgery. Keywords: laser, damage, ablation, dielectrics, pump-probe, modeling, micromachining, laser eye surgery