Nonparaxial singular beams inside the focal region of a high numerical-aperture lens
|
|
- Barry Dorsey
- 8 years ago
- Views:
Transcription
1 Nonparaxial singular beas inside the focal region of a high nuerical-aperture lens Vladlen G. Shvedov Departent of hysics Taurida National V. Vernandsky University Siferopol Criea Ukraine vgs4@physics.anu.edu.au Received: Abstract. Key optical technologies including lithography data storage optical tweezers icroscopy and ultrafast laser aterials processing rely on strongly focused light beas. Such beas are often used to exploit a vectorial nature of light and so detailed knowledge of the field structure inside a tight focus becoes increasingly iportant. So far theoretical studies of intra-focal optical field coponents have been ainly concentrated on spatially hoogeneous states of light polarisation. In this work we present a new developent in the calculations of local polarisation structure of tightly focused singular beas including radially and aziuthally polarised hollow beas. Keywords: singular bea vector optical field tight focus ACS: 4.5.Ja 4.60.Jf 78.0.Bh UDC: A rapidly increasing nuber of various practical applications in the last few years have attracted significant interest to studies related to three-diensional structure of the field inside a focus of high nuerical-aperture optical systes [ 5]. xperiental intrafocal apping of the squared electric field coponents is usually indirectly achieved with near field probes [6] point scatterers [7] fluorescent olecules and beads [8 9] and the knife edge ethod [0]. Recently a new approach has been developed [] for visualising nanoscale structure of the electric field inside the focal volue of tightly focused singular beas which is based on peranent iprinting of the field in transparent edia. Fro the theoretical point of view the first coprehensive studies of tightly focused linearly and circularly polarised Laguerre-Gaussian beas have been perfored in Refs. [ 3]. In Refs. [ 4] the authors have attepted to analyse the focal spot of both radially and aziuthally polarised beas. The proble has been qualitatively solved in Ref. [4] for the case of non-apodised cylindrical vector beas hence providing basic understanding of the focal structure of real beas. The general ethod allowing one to solve such probles is based on Debye vector integrals. A coplexity of the proble for soe types of vector beas e.g. radially or aziuthally polarised beas is related to finding an integrand which would satisfy the conditions for the paraxial waves ( ( 4 i ) 0 ) and siultaneously describe the vector field coponents. In the z above expression xex ye y and u / u with ex e y being the Cartesian unit vectors and the wavelength of light. In this work we wish to show that the coplete vector function for radially or aziuthally polarised beas can be obtained by first finding solutions for linearly and circularly polarised optical vortices in which case the choice of the integrand does not pose any difficulties. We start Ukr. J. hys. Opt. 0 V 3 09
2 Vladlen G. Shvedov with finding the solutions of the Debye proble for linearly polarised optical vortices following the foralis suggested in Refs. [ ]. The coplex aplitude of a scalar Laguerre-Gaussian bea at its waist ay be written as [] p 0 0 ( r z 0) A ( r / w ) L ( r / w )exp( r / w )exp( i) () where А 0 is the characteristic aplitude at the peak of intensity r the radial distance fro the bea axis the aziuthal angle in the entrance plane (see Fig. ) L ( x ) the Laguerre polynoial with the radial index p and the aziuthal index and w 0 the bea waist. The radial coordinate can also be presented as r f sin( ) where is the angle between the optical axis and the light ray (see Fig. ). Then the ratio r/w 0 becoes r a sin sin. () w w NA sin Here NA a / f sin stands for the nuerical aperture of the focusing lens (fro now on the refractive index of the ediu in which the bea is focused is assued to be equal to unity) is the axiu angle defining the bea convergence ( ) and the ratio a / w of the entrance aperture radius a and the bea waist w represents the truncation paraeter denoting the function of the bea inside the physical aperture. It defines the fraction of the bea which goes through the lens. The lens is overfilled if and underfilled if [ ]. ax p Fig.. Representation of focal geoetry for singular beas. (x y) and (x p y p ) are the Cartesian coordinates in a plane of physical aperture and a focal plane respectively r p denotes the radial distance of point fro z axis a the physical aperture a the radius of non-transparent disk which increases efficiency of the physical aperture the nuerical aperture (NA) of an objective the angular diension of circular bea stop of radius a w the paraeter defining size of an incident bea and f the focal length. In our case which deals with an optical vortex incident on a lens the radial index p = 0. Upon taking q. () into account q. () ay be written as [4] where ( r z 0) A ( )exp( i) (3) 0 sin sin ( ) A0 exp A sin sin 0 Ukr. J. hys. Opt. 0 V 3
3 Nonparaxial singular describes the aplitude function of a colliated optical vortex. According to the focusing geoetry shown in Fig. the field distribution in the focal region is given by 0 (4) ( r z) ( ia/ ) A ( ) ( ) A ( )exp( i) expikr sin cos( ) exp ikz cos sin dd where А is a coefficient that depends on the optical paraeters of the syste [6] the light wavelength the ter ( ) defines the polarisation distribution [4] at the entrance pupil and A gives the apodising function which is equal to cos for aplanatic lenses [5]. The polarisation distribution of the incident bea in the entrance pupil plane ay be presented as [4 ] ( ) b (cos cos sin sin cos ) b (cos sin cos ) b sin cos b sin sin where b and b denote the strengths of the x- and y-linearly polarised incident beas respectively. Then q. (4) can be reduced to a single integral by using the identity exp( i)exp( ikr sin cos( )) d i J( kr sin )exp( i ) (6) 0 where J ( kr sin ) is the Bessel function of the first kind and the th order. Taking into consideration the above arguents one can write the electric field coponents in the focal region of the x-polarised vortex bea as [] x y exp( ( ) ) exp( ( ) ) i exp( i ) I i exp( i( ) ) I i exp( i( ) ) I i i i I i i i I z i exp( i( ) ) I i exp( i( ) ) I. For coparison when the incident vortex is y-polarised the coponents of its electric field in the focal region are given by Here x exp( ( ) ) exp( ( ) ) y i i i I i i i I i exp( i ) I i exp( i( ) ) I i exp( i( ) ) I z i i exp( i( ) ) I i i exp( i( ) ) I. I ( r z) ( ia/ ) A ( ) cos ( cos ) J ( kr sin )exp ikz cossin d I ( r z) ( ia/ ) A ( ) cos J ( kr sin )exp ikz cos sin d I( r z) ( ia/ ) A ( ) cos ( cos ) J( kr sin )exp ikz cossind. The analysis of the above expressions shows that all of the three electric field coponents are present in the focal region of the optical vortex and the light intensity is generally nonzero at the optical axis: (5) (7) (8) Ukr. J. hys. Opt. 0 V 3
4 Vladlen G. Shvedov x ( ) y ( ) z ( ) I r z r z r z. The solutions found above also allow one to exaine focusing of elliptically polarised optical vortices with the coplex field aplitude in the entrance pupil plane given by: i ( ) A ( )exp( i) e (9) where x and y stand for the x and y vector field coponents and is the phase shift between the. (Notice that the bold type indicates a vector variable). A circularly polarised vortex is produced when x y and /. The following sign convention for the circularly polarised beas is adopted hereafter: the circular polarisation is referred to as right-handed if / and left-handed if / i.e. i σ. Here σ ( xi y )/ denotes the unit vector of circular polarisation x y and x y the unit Cartesian vectors. Using the sign convention introduced we can add the field coponents in qs. (7) and (8) taking into account the phase shift given by q. (9). Then the Cartesian coponents of the righthanded field in the vicinity of the focus take the following fors: x exp( ) exp( ( ) ) y exp( ) exp( ( ) ) i i I i i I i i i I i i i I z 4 exp( ( ) ) i i I. Siilarly for the left-handed light field we obtain x i exp( i ) I i exp( i( ) ) I y exp( ) exp( ( ) ) i i i I i i i I z 4 exp( ( ) ) i i I. Using the sae notations we get i expi I i expi I x y i i exp( i ) I i exp( i( ) ) I 4i expi I. z for the both vortices. These relations allow one to deduce the salient features of the electric field in the focal region. For instance the fundaental Gaussian bea at the focal point (z = 0 r = 0) always retains the initial state of polarisation []. At the sae tie the optical vortices with the topological charges = have in general nonzero electric fields at this point due to contribution fro the longitudinal coponents of the field. When the topological charge is greater than three (i.e. 3 ) the focal intensity is always zero at the centre of the bea [ 6]. Of particular interest is the case of circularly polarised vortices with. According to qs. (0) the vortex preserves zero intensity along the whole optical axis when the sign of the topological charge coincides with that of the handedness ( ). When the charge and the polarisation have the opposite signs ( ) an intensity axiu appears at the focus owing to the longitudinal coponent of the electric field z (see Fig. a). A detailed analysis of the properties of circularly polarised and ore coplex singular odes is easier to perfor using the polar basic vectors of the circular cylindrical coordinates (see q. (9)): x y (0) Ukr. J. hys. Opt. 0 V 3
5 Nonparaxial singular e x cos y sin r e y cos x sin where e r and e are the unit vectors along the radial and aziuthal directions. The field coponents in q. (9) transfor to the new coordinate syste as follows: r exp( ( ) ) exp( ( ) ) i i I i i I i i exp( i( ) ) I i exp( i( ) ) I z 4 i exp( i( ) ) I. After siplification they can be rewritten as r i I I expi ii I I expi 4i expi I. z In order to obtain solutions for the radial and aziuthal odes at the focus we use the following reasoning. Radial and aziuthal beas with coinciding waists and the sae divergences acquired while propagating along the optical axis z of a focusing syste can be presented as TM r / w0 G e r / 0 where G A0 exp r / w0 Ukr. J. hys. Opt. 0 V 3 3 () () T r w G e (3) describes the fundaental Gaussian bea given by q. (). The circularly polarised optical vortices with a zero orbital angular oentu ( ; ) ay be presented as a superposition of the two odes given by qs. (3) [7 8]: TM T 0 i r / w Gσ exp( i) (4) where σ ( er i e )exp( i ) is the unit vector of circular polarisation in the cylindrical coordinates. Hence by knowing the focal field distribution of the circularly polarised vortices () it is possible to reconstruct with the aid of q. (4) the field of the corresponding radial and aziuthal odes. Indeed fro the syste of equations we find where TM i T TM i T TM. (5) T i In this case the fields given by qs. () ay be expressed as r r i I I i I I i I I i I I z 4 0 z 4 0 I I (6)
6 Vladlen G. Shvedov I ( r z) ( ia/ ) A ( ) cos ( cos ) J ( kr sin )exp ikz cossin d I ( r z) ( ia/ ) A ( ) cos ( cos ) J ( kr sin )exp ikz cos sin d I ( r z) ( ia/ ) A ( ) cos J ( kr sin )exp ikz cossin d 0 0 I ( r z) ( ia/ ) A ( ) cos ( cos ) J ( kr sin )exp ikz cossin d I ( r z) ( ia/ ) A ( ) cos ( cos ) J ( kr sin )exp ikz cossin d. By applying the well-known identity J( x) J( x) to the above integrals for the circularly polarised single-charged vortices one can reduce qs. (6) to the following: where r ii 4 ii z I0 r 4 r z ii r 4 ii 4 I I ( ia/ ) A ( ) cos J ( kr sin )exp ikz cossin d r I ( ia/ ) A ( ) cos J ( kr sin )exp ikz cossin d I ( ia/ ) A ( ) cos J ( kr sin )exp ikz cossin d. 0 0 Substituting qs. (7) into qs. (5) we find the electric field coponents of the focused radial and aziuthal odes: 4 ii 0 8 I 0 8 ii 0. r( TM ) r ( TM ) z( TM ) 0 r( T) ( T) z( T) In the vector representation the focal field coponents of the radial and aziuthal odes becoe as follows: TM 4 iir er I0ez. (9) T 8iI e One can easily see fro these expressions that the aziuthal ode preserves both its polarisation and zero intensity along the whole optical axis even in the regie of tight focusing whereas the intensity and the polarisation structure of the radial ode undergo significant transforations (see Fig. ). This difference in the behaviours of the two odes inside the tight focus can be exploited when solving various practical probles. For instance conservation of the zero intensity in the aziuthal ode facilitates significantly optical iplosion of aterials. This novel phenoenon has recently been deonstrated in the experients on copressing fused silica with double-charge fetosecond vortex laser pulses [9 0]. On the other hand the longitudinal coponent of the electric field is also crucial for soe iportant applications [5]. Radially polarised beas focused with high nuerical-aperture optics are now routinely used in icroscopy [] second-haronic generation [ 3] Raan spectroscopy [4] and particle trapping or anipulation [5]. (7) (8) 4 Ukr. J. hys. Opt. 0 V 3
7 Nonparaxial singular Fig.. Siulated intensity distributions in the focal plane for an optical vortex ; ((a) and (d)) and aziuthally ((b) and (e)) or radially ((c) and (f)) polarised beas. Solid lines in (d) (f) show total intensity distribution dotted lines correspond to intensity distributions in the transferred polarisation state and dashed lines give intensity distributions for the longitudinal polarisation state inside the beas. The paraeters of the optical syste and the beas are as follows: NA = 0.9 = 780 n a =. and a =. Acknowledgeent I thank Dr. Cyril Hnatovsky and rof. Alexander Volyar for useful discussions. References. Wang H Shi L Lukyanchuk B Sheppard C and Chong C 008. Creation of a needle of longitudinally polarized light in vacuu using binary optics. Nature hotonics. : Hnatovsky C Shvedov V Krolikowski W and Rode A 0. Revealing local field structure of focused ultrashort pulses. hys. Rev. Lett. 06: Wang Z Guo W Li L Luk'yanchuk B Khan A Liu Z Chen Z and Hong Z 0. Optical virtual iaging at 50 n lateral resolution with a white-light nanoscope. Nature Coun. : Helseth L 006. Sallest focal hole Opt. Co. 57: Zhan Q 009. Cylindrical vector beas: fro atheatical concepts to applications. Adv. Opt. hotonics. : Rhodes S Nugent K and Roberts A 00. recision easureent of the electroagnetic fields in the focal region of a high-nuerical-aperture lens using a tapered fiber probe. J. Opt. Soc. Aer. A. 9: Wilson T Juškaitis R and Higdon 997. The iaging of dielectric point scatterers in conventional and confocal polarisation icroscopes. Opt. Coun. 4: Novotny L Beversluis M Youngworth K and Brown T 00. Longitudinal field odes probed by single olecules. hys. Rev. Lett. 86: Bokor N Iketaki Y Watanabe T and Fujii M 005. Investigation of polarization effects for high-nuerical-aperture first-order Laguerre-Gaussian beas by D scanning with a single fluorescent icrobead. Opt. xpress. 3: Ukr. J. hys. Opt. 0 V 3 5
8 Vladlen G. Shvedov 0. Dorn R Quabis S and Leuchs G 003. Sharper focus for a radially polarized light bea. hys. Rev. Lett. 9: Torok and Munro 004. The use of Gauss-Laguerre vector beas in STD icroscopy. Opt. xpress. : Singh R Senthilkuaran and Singh K 008. ffect of priary spherical aberration on highnuerical aperture of a Laguerre-Gaussian bea. J. Opt. Soc. Aer. A. 5: Volyar A Shvedov V and Fadeyeva T 00. The structure of a nonparaxial Gaussian bea near the focus: II. Optical vortices. Opt. Spectrosc. 90 (): Youngworth K and Brown T 000. Focusing of high nuerical aperture cylindrical vector beas. Opt. xpress. 7: Richards B and Wolf 959. lectroagnetic diffraction in the optical systes.. Structure of the iage field in an aplanatic syste. roc. Roy. Soc. London Ser. A. 53: Izdebskaya Y Shvedov V and Volyar A 005. Focusing of wedge-generated higher-order optical vortices. Opt. Lett. 30: Fadeyeva T Shvedov V Izdebskaya Y Volyar A Brasselet Neshev D Desyatnikov A Krolikowski W and Kivshar Y 00. Spatially engineered polarization states and optical vortices in uniaxial crystals. Opt. xpress. 30: Fadeyeva T Shvedov V Shostka N Alexeyev C and Volyar A 00. Natural shaping of the cylindrically polarized beas. Opt. Lett. 35: Shvedov V Hnatovsky C Krolikowski W and Rode A 00. fficient bea converter for the generation of high-power fetosecond vortices. Opt. Lett. 35: Hnatovsky C Shvedov V Krolikowski W and Rode A 00. Materials processing with a tightly focused fetosecond laser vortex pulse. Opt. Lett. 35: Watanabe K Horiguchi N and Kano H 007. Optiized easureent probe of the localized surface plason icroscope by using radially polarized illuination. Appl. Opt. 46: Biss D and Brown T 003. olarization-vortex-driven second-haronic generation. Opt. Lett. 8: Yew and Sheppard C 007. Second haronic generation polarization icroscopy with tightly focused linearly and radially polarized beas. Opt. Coun. 75: Hayazawa N Saito Y and Kawata S 004. Detection and characterization of longitudinal field for tip-enhanced Raan spectroscopy. Appl. hys. Lett. 85: Zhan Q 004. Trapping etallic Rayleigh particles with radial polarization. Opt. xpress. : V.G. Shvedov 0. Nonparaxial singular beas inside the focal region of a high nuericalaperture lens Ukr.J.hys.Opt. : Анотація Основні оптичні технології зокрема такі як літографія запис даних використання оптичних пінцетів мікроскопія та надшвидка обробка лазерних матеріалів базуються на сильному фокусуванні світлових променів. Використання цих променів здебільшого базується на векторній природі світла тому детальна інформація про структуру поля всередині фокуса є особливо важливою. Однак теоретичне дослідження внутрішньо фокусних оптичних компонент поля досі переважно концентрувалося на просторово однорідних станах поляризації світла. У даній роботі представлено нові результати розрахунку структури локальної поляризації сильно сфокусованого сингулярного променя включаючи випадки радіально та азимутально поляризованого пустотілого променя. 6 Ukr. J. hys. Opt. 0 V 3
Multiple Focal Segment Generation of Tightly Focused Non-Diffracting Transversely Polarized Beam with Diffractive Optical Element
J. Environ. Nanotechnol. Volume 3, No.4 pp. 73-77 ISSN (Print): 2279-0748 ISSN (Online): 2319-5541 doi: 10.13074/jent.2014.12.144114 Multiple Focal Segment Generation of Tightly Focused Non-Diffracting
More informationPhase singularities of the longitudinal field components in the focal region of a high-aperture optical system
D. W. Diehl and T. D. Visser Vol. 21, No. 11/November 2004/J. Opt. Soc. Am. A 2103 Phase singularities of the longitudinal field components in the focal region of a high-aperture optical system Damon W.
More informationTight focus of a radially polarized and amplitudemodulated annular multi-gaussian beam
Tight focus of a radially polarized and amplitudemodulated annular multi-gaussian beam Chen Jian-Nong( ) a), Xu Qin-Feng( ) a), and Wang Gang( ) b) a) School of Physics, Ludong University, Yantai 26425,
More information2005 Optical Society of America (OSA) Reprinted with permission.
Klas Lindfors, Tero Setälä, Matti Kaivola, and Ari T. Friberg. 2005. Degree of polarization in tightly focused optical fields. Journal of the Optical Society of America A, volume 22, number 3, pages 561
More informationMonochromatic electromagnetic fields with maximum focal energy density
Moore et al. Vol. 4, No. 10 /October 007 /J. Opt. Soc. Am. A 3115 Monochromatic electromagnetic fields with maximum focal energy density Nicole J. Moore, 1, * Miguel A. Alonso, 1 and Colin J. R. Sheppard,3
More informationLecture L26-3D Rigid Body Dynamics: The Inertia Tensor
J. Peraire, S. Widnall 16.07 Dynaics Fall 008 Lecture L6-3D Rigid Body Dynaics: The Inertia Tensor Version.1 In this lecture, we will derive an expression for the angular oentu of a 3D rigid body. We shall
More informationDOING PHYSICS WITH MATLAB COMPUTATIONAL OPTICS RAYLEIGH-SOMMERFELD DIFFRACTION INTEGRAL OF THE FIRST KIND
DOING PHYSICS WITH MATLAB COMPUTATIONAL OPTICS RAYLEIGH-SOMMERFELD DIFFRACTION INTEGRAL OF THE FIRST KIND THE THREE-DIMENSIONAL DISTRIBUTION OF THE RADIANT FLUX DENSITY AT THE FOCUS OF A CONVERGENCE BEAM
More informationLecture L9 - Linear Impulse and Momentum. Collisions
J. Peraire, S. Widnall 16.07 Dynaics Fall 009 Version.0 Lecture L9 - Linear Ipulse and Moentu. Collisions In this lecture, we will consider the equations that result fro integrating Newton s second law,
More informationNear-field scanning optical microscopy (SNOM)
Adviser: dr. Maja Remškar Institut Jožef Stefan January 2010 1 2 3 4 5 6 Fluorescence Raman and surface enhanced Raman 7 Conventional optical microscopy-limited resolution Two broad classes of techniques
More informationPhysics 211: Lab Oscillations. Simple Harmonic Motion.
Physics 11: Lab Oscillations. Siple Haronic Motion. Reading Assignent: Chapter 15 Introduction: As we learned in class, physical systes will undergo an oscillatory otion, when displaced fro a stable equilibriu.
More informationPure Bending Determination of Stress-Strain Curves for an Aluminum Alloy
Proceedings of the World Congress on Engineering 0 Vol III WCE 0, July 6-8, 0, London, U.K. Pure Bending Deterination of Stress-Strain Curves for an Aluinu Alloy D. Torres-Franco, G. Urriolagoitia-Sosa,
More informationAxial intensity distribution of lens axicon illuminated by Gaussian-Schell model beam
46 1, 018003 January 2007 Axial intensity distribution of lens axicon illuminated by Gaussian-Schell model beam Yuan Chen Jixiong Pu Xiaoyun Liu Huaqiao University Department of Electronic Science and
More informationExperiment 2 Index of refraction of an unknown liquid --- Abbe Refractometer
Experient Index of refraction of an unknown liquid --- Abbe Refractoeter Principle: The value n ay be written in the for sin ( δ +θ ) n =. θ sin This relation provides us with one or the standard ethods
More informationA CHAOS MODEL OF SUBHARMONIC OSCILLATIONS IN CURRENT MODE PWM BOOST CONVERTERS
A CHAOS MODEL OF SUBHARMONIC OSCILLATIONS IN CURRENT MODE PWM BOOST CONVERTERS Isaac Zafrany and Sa BenYaakov Departent of Electrical and Coputer Engineering BenGurion University of the Negev P. O. Box
More informationThe Velocities of Gas Molecules
he Velocities of Gas Molecules by Flick Colean Departent of Cheistry Wellesley College Wellesley MA 8 Copyright Flick Colean 996 All rights reserved You are welcoe to use this docuent in your own classes
More informationHomework 8. problems: 10.40, 10.73, 11.55, 12.43
Hoework 8 probles: 0.0, 0.7,.55,. Proble 0.0 A block of ass kg an a block of ass 6 kg are connecte by a assless strint over a pulley in the shape of a soli isk having raius R0.5 an ass M0 kg. These blocks
More informationRevision problem. Chapter 18 problem 37 page 612. Suppose you point a pinhole camera at a 15m tall tree that is 75m away.
Revision problem Chapter 18 problem 37 page 612 Suppose you point a pinhole camera at a 15m tall tree that is 75m away. 1 Optical Instruments Thin lens equation Refractive power Cameras The human eye Combining
More informationSubwavelength focusing of azimuthally polarized beams with vortical phase in dielectrics by using an ultra-thin lens
Subwavelength focusing of azimuthally polarized beams with vortical phase in dielectrics by using an ultra-thin lens Kun Huang, 1 Huapeng Ye, 1 Hong Liu, 2 Jinghua Teng, 2 Swee Ping Yeo, 1 and Cheng-Wei
More informationEigenfunction expansion of the electric fields in the focal region of a high numerical aperture focusing system
Eigenfunction expansion of the electric fields in the focal region of a high numerical aperture focusing system Sherif S. Sherif, Matthew R. Foreman, and Peter Török Optics Group, Institute for Microstructural
More informationFar-field mapping of the longitudinal magnetic and electric optical fields
Far-field mapping of the longitudinal magnetic and electric optical fields Clément Ecoffey, Thierry Grosjean To cite this version: Clément Ecoffey, Thierry Grosjean. Far-field mapping of the longitudinal
More informationFURTHER VECTORS (MEI)
Mathematics Revision Guides Further Vectors (MEI) (column notation) Page of MK HOME TUITION Mathematics Revision Guides Level: AS / A Level - MEI OCR MEI: C FURTHER VECTORS (MEI) Version : Date: -9-7 Mathematics
More informationOptical Microscopy Beyond the Diffraction Limit: Imaging Guided and Propagating Fields
Optical Microscopy Beyond the Diffraction Limit: Imaging Guided and Propagating Fields M. Selim Ünlü, Bennett B. Goldberg, and Stephen B. Ippolito Boston University Department of Electrical and Computer
More informationA magnetic Rotor to convert vacuum-energy into mechanical energy
A agnetic Rotor to convert vacuu-energy into echanical energy Claus W. Turtur, University of Applied Sciences Braunschweig-Wolfenbüttel Abstract Wolfenbüttel, Mai 21 2008 In previous work it was deonstrated,
More informationUse of extrapolation to forecast the working capital in the mechanical engineering companies
ECONTECHMOD. AN INTERNATIONAL QUARTERLY JOURNAL 2014. Vol. 1. No. 1. 23 28 Use of extrapolation to forecast the working capital in the echanical engineering copanies A. Cherep, Y. Shvets Departent of finance
More informationHW 2. Q v. kt Step 1: Calculate N using one of two equivalent methods. Problem 4.2. a. To Find:
HW 2 Proble 4.2 a. To Find: Nuber of vacancies per cubic eter at a given teperature. b. Given: T 850 degrees C 1123 K Q v 1.08 ev/ato Density of Fe ( ρ ) 7.65 g/cc Fe toic weight of iron ( c. ssuptions:
More informationA Guide to Acousto-Optic Modulators
A Guide to Acousto-Optic Modulators D. J. McCarron December 7, 2007 1 Introduction Acousto-optic modulators (AOMs) are useful devices which allow the frequency, intensity and direction of a laser beam
More informationStructure Factors 59-553 78
78 Structure Factors Until now, we have only typically considered reflections arising from planes in a hypothetical lattice containing one atom in the asymmetric unit. In practice we will generally deal
More informationImaging techniques with refractive beam shaping optics
Imaging techniques with refractive beam shaping optics Alexander Laskin, Vadim Laskin AdlOptica GmbH, Rudower Chaussee 29, 12489 Berlin, Germany ABSTRACT Applying of the refractive beam shapers in real
More informationarxiv:0805.1434v1 [math.pr] 9 May 2008
Degree-distribution stability of scale-free networs Zhenting Hou, Xiangxing Kong, Dinghua Shi,2, and Guanrong Chen 3 School of Matheatics, Central South University, Changsha 40083, China 2 Departent of
More informationNEAR FIELD OPTICAL MICROSCOPY AND SPECTROSCOPY WITH STM AND AFM PROBES
Vol. 93 (1997) A CTA PHYSICA POLONICA A No. 2 Proceedings of the 1st International Symposium on Scanning Probe Spectroscopy and Related Methods, Poznań 1997 NEAR FIELD OPTICAL MICROSCOPY AND SPECTROSCOPY
More informationOptical Storage Technology. Optical Disc Storage
Optical Storage Technology Optical Disc Storage Introduction Since the early 1940s, magnetic recording has been the mainstay of electronic information storage worldwide. Magnetic tape has been used extensively
More informationReliability Constrained Packet-sizing for Linear Multi-hop Wireless Networks
Reliability Constrained acket-sizing for inear Multi-hop Wireless Networks Ning Wen, and Randall A. Berry Departent of Electrical Engineering and Coputer Science Northwestern University, Evanston, Illinois
More information5. Scanning Near-Field Optical Microscopy 5.1. Resolution of conventional optical microscopy
5. Scanning Near-Field Optical Microscopy 5.1. Resolution of conventional optical microscopy Resolution of optical microscope is limited by diffraction. Light going through an aperture makes diffraction
More informationMeadowlark Optics LCPM-3000 Liquid Crystal Polarimeter Application Note: Determination of Retardance by Polarimetry Tommy Drouillard
Meadowlark Optics LCPM- Liquid Crystal Polarieter Application Note: Deterination of Retardance by Polarietry Toy Drouillard 5 Meadowlark Optics, Inc.. Introduction: The iediate purpose of a polarieter
More informationThe Virtual Spring Mass System
The Virtual Spring Mass Syste J. S. Freudenberg EECS 6 Ebedded Control Systes Huan Coputer Interaction A force feedbac syste, such as the haptic heel used in the EECS 6 lab, is capable of exhibiting a
More informationLesson 44: Acceleration, Velocity, and Period in SHM
Lesson 44: Acceleration, Velocity, and Period in SHM Since there is a restoring force acting on objects in SHM it akes sense that the object will accelerate. In Physics 20 you are only required to explain
More informationLongwave IR focal-plane binary optics
Longwave IR focal-plane binary optics Z. Sikorski, H. Polakowski Institute of Optoelectronics, Military University of Technology, 2 Kaliskiego Str., -98 Warsaw, e-mail: zsikorsk@wat.waw.pl Abstract In
More informationExercise 4 INVESTIGATION OF THE ONE-DEGREE-OF-FREEDOM SYSTEM
Eercise 4 IVESTIGATIO OF THE OE-DEGREE-OF-FREEDOM SYSTEM 1. Ai of the eercise Identification of paraeters of the euation describing a one-degree-of- freedo (1 DOF) atheatical odel of the real vibrating
More informationView of ΣIGMA TM (Ref. 1)
Overview of the FESEM system 1. Electron optical column 2. Specimen chamber 3. EDS detector [Electron Dispersive Spectroscopy] 4. Monitors 5. BSD (Back scatter detector) 6. Personal Computer 7. ON/STANDBY/OFF
More informationNOVEL FOCUSING OPTICS FOR IR LASERS Paper 1504
NOVEL FOCUSING OPTICS FOR IR LASERS Paper 1504 Gary Herrit 1, Alan Hedges 1, Herman Reedy 1 1 II-VI Incorporated, 375 Saxonburg Blvd., Saxonburg, PA, 16056, USA Abstract Traditional focusing optics for
More informationEvaluating Inventory Management Performance: a Preliminary Desk-Simulation Study Based on IOC Model
Evaluating Inventory Manageent Perforance: a Preliinary Desk-Siulation Study Based on IOC Model Flora Bernardel, Roberto Panizzolo, and Davide Martinazzo Abstract The focus of this study is on preliinary
More informationApplying Multiple Neural Networks on Large Scale Data
0 International Conference on Inforation and Electronics Engineering IPCSIT vol6 (0) (0) IACSIT Press, Singapore Applying Multiple Neural Networks on Large Scale Data Kritsanatt Boonkiatpong and Sukree
More informationChapter 5. Principles of Unsteady - State Heat Transfer
Suppleental Material for ransport Process and Separation Process Principles hapter 5 Principles of Unsteady - State Heat ransfer In this chapter, we will study cheical processes where heat transfer is
More informationA quantum secret ballot. Abstract
A quantu secret ballot Shahar Dolev and Itaar Pitowsky The Edelstein Center, Levi Building, The Hebrerw University, Givat Ra, Jerusale, Israel Boaz Tair arxiv:quant-ph/060087v 8 Mar 006 Departent of Philosophy
More informationJUST THE MATHS UNIT NUMBER 8.5. VECTORS 5 (Vector equations of straight lines) A.J.Hobson
JUST THE MATHS UNIT NUMBER 8.5 VECTORS 5 (Vector equations of straight lines) by A.J.Hobson 8.5.1 Introduction 8.5. The straight line passing through a given point and parallel to a given vector 8.5.3
More informationBeam shaping to generate uniform Laser Light Sheet and Linear Laser Spots
Beam shaping to generate uniform Laser Light Sheet and Linear Laser Spots Alexander Laskin, Vadim Laskin AdlOptica GmbH, Rudower Chaussee 29, 12489 Berlin, Germany ABSTRACT Generation of Laser Light Sheet
More informationCLOSED-LOOP SUPPLY CHAIN NETWORK OPTIMIZATION FOR HONG KONG CARTRIDGE RECYCLING INDUSTRY
CLOSED-LOOP SUPPLY CHAIN NETWORK OPTIMIZATION FOR HONG KONG CARTRIDGE RECYCLING INDUSTRY Y. T. Chen Departent of Industrial and Systes Engineering Hong Kong Polytechnic University, Hong Kong yongtong.chen@connect.polyu.hk
More informationPREDICTION OF MILKLINE FILL AND TRANSITION FROM STRATIFIED TO SLUG FLOW
PREDICTION OF MILKLINE FILL AND TRANSITION FROM STRATIFIED TO SLUG FLOW ABSTRACT: by Douglas J. Reineann, Ph.D. Assistant Professor of Agricultural Engineering and Graee A. Mein, Ph.D. Visiting Professor
More informationAudio Engineering Society Convention Paper 5788 Presented at the 114th Convention 2003 March 22 25 Amsterdam, The Netherlands
Audio Engineering Society Convention Paper 5788 Presented at the 4th Convention 2003 March 22 25 Asterda, The etherlands This convention paper has been reproduced fro the author's advance anuscript, without
More informationAnswer, Key Homework 7 David McIntyre 45123 Mar 25, 2004 1
Answer, Key Hoework 7 David McIntyre 453 Mar 5, 004 This print-out should have 4 questions. Multiple-choice questions ay continue on the next colun or page find all choices before aking your selection.
More informationCalculation Method for evaluating Solar Assisted Heat Pump Systems in SAP 2009. 15 July 2013
Calculation Method for evaluating Solar Assisted Heat Pup Systes in SAP 2009 15 July 2013 Page 1 of 17 1 Introduction This docuent describes how Solar Assisted Heat Pup Systes are recognised in the National
More informationExploiting Hardware Heterogeneity within the Same Instance Type of Amazon EC2
Exploiting Hardware Heterogeneity within the Sae Instance Type of Aazon EC2 Zhonghong Ou, Hao Zhuang, Jukka K. Nurinen, Antti Ylä-Jääski, Pan Hui Aalto University, Finland; Deutsch Teleko Laboratories,
More informationChapter 1 High-Resolution Optical and Confocal Microscopy
Chapter 1 High-Resolution Optical and Confocal Microscopy Olaf Hollricher and Wolfram Ibach Abstract In this chapter, the theory of optical image formation in an optical microscope is described, and the
More informationELECTROMAGNETIC ANALYSIS AND COLD TEST OF A DISTRIBUTED WINDOW FOR A HIGH POWER GYROTRON
ELECTROMAGNETIC ANALYSIS AND COLD TEST OF A DISTRIBUTED WINDOW FOR A HIGH POWER GYROTRON M.A.Shapiro, C.P.Moeller, and R.J.Temkin Plasma Science and Fusion Ceer, Massachusetts Institute of Technology,
More informationFraunhofer Diffraction
Physics 334 Spring 1 Purpose Fraunhofer Diffraction The experiment will test the theory of Fraunhofer diffraction at a single slit by comparing a careful measurement of the angular dependence of intensity
More informationIntroduction to Optics
Second Edition Introduction to Optics FRANK L. PEDROTTI, S.J. Marquette University Milwaukee, Wisconsin Vatican Radio, Rome LENO S. PEDROTTI Center for Occupational Research and Development Waco, Texas
More informationComputations of the Directivity of Spherical Microphone Arrays
paper ID: 132 /p.1 Coputations of the Directivity of Spherical Microphone Arrays C.F. Cardoso, P.A. Nelson Institute of Sound and Vibration Research, University of Southapton, University Road, Highfield,
More information11.1. Objectives. Component Form of a Vector. Component Form of a Vector. Component Form of a Vector. Vectors and the Geometry of Space
11 Vectors and the Geometry of Space 11.1 Vectors in the Plane Copyright Cengage Learning. All rights reserved. Copyright Cengage Learning. All rights reserved. 2 Objectives! Write the component form of
More informationAudio Engineering Society. Convention Paper. Presented at the 119th Convention 2005 October 7 10 New York, New York USA
Audio Engineering Society Convention Paper Presented at the 119th Convention 2005 October 7 10 New York, New York USA This convention paper has been reproduced fro the authors advance anuscript, without
More informationImage restoration for a rectangular poor-pixels detector
Iage restoration for a rectangular poor-pixels detector Pengcheng Wen 1, Xiangjun Wang 1, Hong Wei 2 1 State Key Laboratory of Precision Measuring Technology and Instruents, Tianjin University, China 2
More informationMachine Learning Applications in Grid Computing
Machine Learning Applications in Grid Coputing George Cybenko, Guofei Jiang and Daniel Bilar Thayer School of Engineering Dartouth College Hanover, NH 03755, USA gvc@dartouth.edu, guofei.jiang@dartouth.edu
More informationL 2 : x = s + 1, y = s, z = 4s + 4. 3. Suppose that C has coordinates (x, y, z). Then from the vector equality AC = BD, one has
The line L through the points A and B is parallel to the vector AB = 3, 2, and has parametric equations x = 3t + 2, y = 2t +, z = t Therefore, the intersection point of the line with the plane should satisfy:
More informationAn Integrated Approach for Monitoring Service Level Parameters of Software-Defined Networking
International Journal of Future Generation Counication and Networking Vol. 8, No. 6 (15), pp. 197-4 http://d.doi.org/1.1457/ijfgcn.15.8.6.19 An Integrated Approach for Monitoring Service Level Paraeters
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More informationAC VOLTAGE CONTROLLER CIRCUITS (RMS VOLTAGE CONTROLLERS)
AC TAGE CNTRER CRCUT (RM TAGE CNTRER) AC voltage controllers (ac line voltage controllers) are eployed to vary the RM value of the alternating voltage applied to a load circuit by introducing Thyristors
More information2. FINDING A SOLUTION
The 7 th Balan Conference on Operational Research BACOR 5 Constanta, May 5, Roania OPTIMAL TIME AND SPACE COMPLEXITY ALGORITHM FOR CONSTRUCTION OF ALL BINARY TREES FROM PRE-ORDER AND POST-ORDER TRAVERSALS
More informationChapter 4. Electrostatic Fields in Matter
Chapter 4. Electrostatic Fields in Matter 4.1. Polarization A neutral atom, placed in an external electric field, will experience no net force. However, even though the atom as a whole is neutral, the
More informationConfocal profiling of grooves and ridges with circular section using the divided aperture technique
INVESTIGACIÓN REVISTA MEXICANA DE FÍSICA 51 (4) 420 425 AGOSTO 2005 Confocal profiling of grooves and ridges with circular section using the divided aperture technique J.F. Aguilar Instituto Nacional de
More informationGeneral tolerances for Iinearand angular dimensions and geometrical=.tolerances
oa / - UDC 21 753 1 : 21 7 : 21 9 : 744 43 DEUTSCHE NORM April 1991 General tolerances for Iinearand angular diensions and geoetrical= tolerances (not to be used for new destgns) '-j' ;,, DIN 718 Allgeeintoleranzen
More informationManaging Complex Network Operation with Predictive Analytics
Managing Coplex Network Operation with Predictive Analytics Zhenyu Huang, Pak Chung Wong, Patrick Mackey, Yousu Chen, Jian Ma, Kevin Schneider, and Frank L. Greitzer Pacific Northwest National Laboratory
More informationChapter 22: Electric Flux and Gauss s Law
22.1 ntroduction We have seen in chapter 21 that determining the electric field of a continuous charge distribution can become very complicated for some charge distributions. t would be desirable if we
More informationAngular Spectrum Representation
Chapter 7 Angular Spectrum Representation The angular spectrum representation is a mathematical technique to describe optical fields in homogeneous media. Optical fields are described as a superposition
More informationVECTORIAL ELECTRIC FIELD MONTE CARO SIMULA- TIONS FOR FOCUSED LASER BEAMS (800 nm 2220 nm) IN A BIOLOGICAL SAMPLE
Progress In Electromagnetics Research, Vol. 142, 667 681, 2013 VECTORIAL ELECTRIC FIELD MONTE CARO SIMULA- TIONS FOR FOCUSED LASER BEAMS (800 nm 2220 nm) IN A BIOLOGICAL SAMPLE Fuhong Cai 1, Jiaxin Yu
More informationPolarization of Light
Polarization of Light References Halliday/Resnick/Walker Fundamentals of Physics, Chapter 33, 7 th ed. Wiley 005 PASCO EX997A and EX999 guide sheets (written by Ann Hanks) weight Exercises and weights
More informationAnalyzing Spatiotemporal Characteristics of Education Network Traffic with Flexible Multiscale Entropy
Vol. 9, No. 5 (2016), pp.303-312 http://dx.doi.org/10.14257/ijgdc.2016.9.5.26 Analyzing Spatioteporal Characteristics of Education Network Traffic with Flexible Multiscale Entropy Chen Yang, Renjie Zhou
More informationDoppler effect, moving sources/receivers
Goals: Lecture 29 Chapter 20 Work with a ew iportant characteristics o sound waves. (e.g., Doppler eect) Chapter 21 Recognize standing waves are the superposition o two traveling waves o sae requency Study
More information1 Basic Optics (1.2) Since. ε 0 = 8.854 10 12 C 2 N 1 m 2 and μ 0 = 4π 10 7 Ns 2 C 2 (1.3) Krishna Thyagarajan and Ajoy Ghatak. 1.
1 1 Basic Optics Krishna Thyagarajan and Ajoy Ghatak 1.1 Introduction This chapter on optics provides the reader with the basic understanding of light rays and light waves, image formation and aberrations,
More informationAn Innovate Dynamic Load Balancing Algorithm Based on Task
An Innovate Dynaic Load Balancing Algorith Based on Task Classification Hong-bin Wang,,a, Zhi-yi Fang, b, Guan-nan Qu,*,c, Xiao-dan Ren,d College of Coputer Science and Technology, Jilin University, Changchun
More informationApertureless Near-Field Optical Microscopy
VI Apertureless Near-Field Optical Microscopy In recent years, several types of apertureless near-field optical microscopes have been developed 1,2,3,4,5,6,7. In such instruments, light scattered from
More informationHolographically corrected microscope with a large working distance (as appears in Applied Optics, Vol. 37, No. 10, 1849-1853, 1 April 1998)
Holographically corrected microscope with a large working distance (as appears in Applied Optics, Vol. 37, No. 10, 1849-1853, 1 April 1998) Geoff Andersen and R. J. Knize Laser and Optics Research Center
More informationUnderstanding Laser Beam Parameters Leads to Better System Performance and Can Save Money
Understanding Laser Beam Parameters Leads to Better System Performance and Can Save Money Lasers became the first choice of energy source for a steadily increasing number of applications in science, medicine
More informationAcousto-optic modulator
1 of 3 Acousto-optic modulator F An acousto-optic modulator (AOM), also called a Bragg cell, uses the acousto-optic effect to diffract and shift the frequency of light using sound waves (usually at radio-frequency).
More informationSearching strategy for multi-target discovery in wireless networks
Searching strategy for ulti-target discovery in wireless networks Zhao Cheng, Wendi B. Heinzelan Departent of Electrical and Coputer Engineering University of Rochester Rochester, NY 467 (585) 75-{878,
More informationDiffraction of a Circular Aperture
Diffraction of a Circular Aperture Diffraction can be understood by considering the wave nature of light. Huygen's principle, illustrated in the image below, states that each point on a propagating wavefront
More informationLaser expander design of highly efficient Blu-ray disc pickup head
Laser expander design of highly efficient Blu-ray disc pickup head Wen-Shing Sun, 1,* Kun-Di Liu, 1 Jui-Wen Pan, 1 Chuen-Lin Tien, 2 and Min-Sheng Hsieh 1 1 Department of Optics and Photonics, National
More informationManufacturing of an absorbing filter controlled by a broadband optical monitoring
Manufacturing of an absorbing filter controlled by a broadband optical onitoring Bruno Badoil, Fabien Learchand*, Michel Caelinaud and Michel Lequie Laboratoire Institut Fresnel, Université Paul Cézanne,
More informationSection 1.1. Introduction to R n
The Calculus of Functions of Several Variables Section. Introduction to R n Calculus is the study of functional relationships and how related quantities change with each other. In your first exposure to
More informationUsing light scattering method to find The surface tension of water
Experiment (8) Using light scattering method to find The surface tension of water The aim of work: The goals of this experiment are to confirm the relationship between angular frequency and wave vector
More informationTwo vectors are equal if they have the same length and direction. They do not
Vectors define vectors Some physical quantities, such as temperature, length, and mass, can be specified by a single number called a scalar. Other physical quantities, such as force and velocity, must
More informationScanning Near Field Optical Microscopy: Principle, Instrumentation and Applications
Scanning Near Field Optical Microscopy: Principle, Instrumentation and Applications Saulius Marcinkevičius Optics, ICT, KTH 1 Outline Optical near field. Principle of scanning near field optical microscope
More informationEnergy Efficient VM Scheduling for Cloud Data Centers: Exact allocation and migration algorithms
Energy Efficient VM Scheduling for Cloud Data Centers: Exact allocation and igration algoriths Chaia Ghribi, Makhlouf Hadji and Djaal Zeghlache Institut Mines-Téléco, Téléco SudParis UMR CNRS 5157 9, Rue
More informationLaser tweezer controlled solid immersion lens for high resolution imaging in microfluidic and biological samples
Laser tweezer controlled solid immersion lens for high resolution imaging in microfluidic and biological samples Aaron L. Birkbeck *, Sanja Zlatanovic, Mihrimah Ozkan and Sadik C. Esener University of
More informationDevelopment of Optical Wave Microphone Measuring Sound Waves with No Diaphragm
Progress In Electromagnetics Research Symposium Proceedings, Taipei, March 5 8, 3 359 Development of Optical Wave Microphone Measuring Sound Waves with No Diaphragm Yoshito Sonoda, Takashi Samatsu, and
More informationCapacity of Multiple-Antenna Systems With Both Receiver and Transmitter Channel State Information
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 49, NO., OCTOBER 23 2697 Capacity of Multiple-Antenna Systes With Both Receiver and Transitter Channel State Inforation Sudharan K. Jayaweera, Student Meber,
More informationPERFORMANCE METRICS FOR THE IT SERVICES PORTFOLIO
Bulletin of the Transilvania University of Braşov Series I: Engineering Sciences Vol. 4 (53) No. - 0 PERFORMANCE METRICS FOR THE IT SERVICES PORTFOLIO V. CAZACU I. SZÉKELY F. SANDU 3 T. BĂLAN Abstract:
More informationASIC Design Project Management Supported by Multi Agent Simulation
ASIC Design Project Manageent Supported by Multi Agent Siulation Jana Blaschke, Christian Sebeke, Wolfgang Rosenstiel Abstract The coplexity of Application Specific Integrated Circuits (ASICs) is continuously
More informationOptimal Times to Decrease Extraction Rates During Two-Stage Remediation Affected by Rate-Limited Transport Jose A. Saez, Loyola Marymount University
Optial Ties to Decrease Extraction ates During Two-Stage eediation Affected by ate-liited Transport Jose A. Saez, Loyola Maryount University Abstract Saez and Haron presented a two-stage pup and treat
More informationResearch Article Performance Evaluation of Human Resource Outsourcing in Food Processing Enterprises
Advance Journal of Food Science and Technology 9(2): 964-969, 205 ISSN: 2042-4868; e-issn: 2042-4876 205 Maxwell Scientific Publication Corp. Subitted: August 0, 205 Accepted: Septeber 3, 205 Published:
More informationLenses and Apertures of A TEM
Instructor: Dr. C.Wang EMA 6518 Course Presentation Lenses and Apertures of A TEM Group Member: Anup Kr. Keshri Srikanth Korla Sushma Amruthaluri Venkata Pasumarthi Xudong Chen Outline Electron Optics
More informationMedia Adaptation Framework in Biofeedback System for Stroke Patient Rehabilitation
Media Adaptation Fraework in Biofeedback Syste for Stroke Patient Rehabilitation Yinpeng Chen, Weiwei Xu, Hari Sundara, Thanassis Rikakis, Sheng-Min Liu Arts, Media and Engineering Progra Arizona State
More information