Integrated photonic systems based on transformation optics enabled gradient index devices

Transcription

1 Light: Science & Applictions (), e8; doi:.8/ls..8 ß CIOMP. All rights reserved 47-78/ ORIGINAL ARTICLE Integrted photonic systems sed on trnsformtion optics enled grdient inde devices Qi Wu, Jeremih P Turpin nd Dougls H Werner Integrted photonics is epected to ply n incresingly importnt role in opticl communictions, imging, computing nd sensing with the promise for significnt reduction in the cost nd weight of these systems. Future dvncement of this technology is criticlly dependent on n ility to develop compct nd relile opticl components nd fcilitte their integrtion on common sustrte. Here we revel, with the utility of the emerging trnsformtion optics technique, tht functionl components composed of plnr grdient inde mterils cn e designed nd redily integrted into photonic circuits. The unprecedented design fleiility of trnsformtion optics llows for the cretion of numer of novel devices, such s light source collimtor, wveguide dpters nd wveguide crossing, which hve rod pplictions in integrted photonic chips nd re comptile with current friction technology. Using the finite-difference time-domin method, we perform full-wve numericl simultions to demonstrte their superior opticl performnce nd efficient integrtion with other components in n on-chip photonic system. These components only require sptilly-vrying dielectric mterils with no mgnetic properties, fcilitting low-loss, rodnd opertion in n integrted photonic environment. Light: Science & Applictions (), e8; doi:.8/ls..8; pulished online Novemer Keywords: grdient inde mteril; integrted photonic system; qusi-conforml mpping; trnsformtion optics INTRODUCTION Trnsformtion optics (TO) provides systemtic method to mnipulte light propgtion y eploiting sptil mppings nd distriutions of constituent mterils., Bsed on the property tht Mwell s equtions re invrint under coordinte trnsformtions, TO represents powerful new design tool in controlling the trjectory of light nd creting novel devices, such s invisiility cloks, field concentrtors 4 nd perfect lck hole sorers. The importnt clss of emedded coordinte trnsformtions 6 stnds out y llowing discontinuities long trnsformtion medi oundries. This unique property hs fcilitted the development of some of the more prcticl, ut nonetheless remrkle TO devices, including reflectionless em ends nd splitters, 7 polriztion rottors 8 nd vrious flt lenses. 9 Despite the mny innovtive pplictions, mterils designed using TO re generlly comple, ehiiting significnt nisotropy nd sptil dependence., Recent progress on metmterils promises pthwy for constructing TO devices; however, the ssocited sorption loss nd limited ndwidth remin s mjor chllenges for their prcticl ppliction. One wy to reduce mteril compleities is to employ qusi-conforml (QC) trnsformtions, which cn minimize the nisotropy of the constitutive mterils, llowing ll-dielectric implementtions. 4 As result, nerly-isotropic grdient inde (GRIN) mterils with rod ndwidth nd low losses cn e employed, leding to functionl QCTO devices, such s crpet cloks nd trnsformed Luneurg lenses in oth the microwve nd opticl wvelength regimes. 4 We pply emedded QC trnsformtions towrds the design of prcticl opticl components for integrted photonic systems. There hs een growing interest in the development of more comple onchip systems y integrting miniturized photonic devices of high functionlity on common sustrte. 4, Besides conventionl devices with dielectric wveguides s key elements, engineered structures including photonic crystls nd metmterils cn e employed to develop opticl integrted devices or nnocircuits. 6 8 Here, we introduce the concept of new type of photonic integrted circuit, s shown in Figure, which consists of QCTO elements tht cn perform vriety of functions, such s light collimtion, ending nd coupling. Such TO-sed GRIN components cn effectively steer light throughout the entire volume of the device, providing compct implementtion nd drmtic improvement in the control of light compred to conventionl GRIN optics with simple il, rdil nd sphericl grdient profiles. 9 Since the QCTO pproch is inherently two-dimensionl, it is felicitous nd sufficient for the design of plnr photonic devices which mnipulte the sptil propgtion of light within thin lyer. In contrst to generl emedded TO designs, the QCTO components contin non-mgnetic, dielectric-only mterils. Therefore, they cn e implemented with stndrd friction techniques, such s ptterning of ir holes or rods on, e.g., silicon-on-insultor The Pennsylvni Stte University, Deprtment of Electricl Engineering, University Prk, PA 68, USA Correspondence: Professor DH Werner, Deprtment of Electricl Engineering, The Pennsylvni Stte University, A Electricl Engineering Est, University Prk, PA 68, USA E-mil: dhw@psu.edu Received 8 Jnury ; revised 7 My ; ccepted 4 July

2 Trnsformtion optics integrted photonic systems Q Wu et l Pump Light TO Wveguide Coupler Polriztion Splitter TO Light Collimtor TO Bender TO Splitter Modultor TO Wveguide Crossing Photodetector Figure A schemtic of photonic integrted circuit composed of vrious TO components. A group of TO-sed photonic components cn e integrted with conventionl opticl nd optoelectronic devices, including wveguides nd photodetectors, on common plnr sustrte. These TO uilding locks crete comple photonic devices nd systems, which cn provide wide rnge of functionlities with pplictions in opticl communictions, informtion processing nd sensing. The red rrows represent the propgtion of light, which cn e controlled y the TO components s well s on-chip electro-optic devices. TO, trnsformtion optics. pltform,7 9, fcilitting their ppliction nd integrtion into onchip photonic systems. MATERIALS AND METHODS To design functionl devices such s light collimtors, we consider coordinte trnsformtions tht cn mp region contining circle into rectngle with flt surfces. For instnce, Figure illustrtes the geometry trnsformtion from circle with rdius R in the virtul spce to rectngle in the physicl spce. Two dditionl flt protrusions with width of w re chosen in order to fcilitte orthogonl grid genertion through QC mppings. In prticulr, the rcs on the top nd ottom oundries of the circulr domin re mpped into two stright segments long the surfces of the rectngulr domin s shown y the solid red curves. When point source is plced t the center of the virtul spce in vcuum, the diverging cylindricl wves hve equl-phse surfces s concentric circles, including those curved oundries in red. Since the circulr rcs re mpped into stright lines in the new system, the emerging EM wves from these interfces will hve plnr wve fronts, producing highly directive ems tht cn efficiently couple into neighoring components, such s opticl wveguides. In Figure, QC trnsformtion is performed over circle with four corner-like protrusions to convert it into squre, where four eqully distriuted rcs re mpped in sequence onto the four sides of the squre in the physicl spce. Consequently, n isotropiclly-rditing source t the center of the TO domin cn e morphed into four highly collimted ems propgting in the outwrd norml direction to ech fce of the device. The construction of trnsformtion medi for the TO designs in Figure would normlly require nisotropic mterils with etreme prmeters, which give rise to nrrow ndwidths nd high intrinsic losses rising from the resonnt properties of inclusions. In the present work, QC trnsformtions re employed to design TO devices composed of GRIN mterils with miniml nisotropy.4, Such QC mppings re numericlly generted orthonorml grids s shown in Figure, which cn e implemented through vriety of different techniques.9 These mppings pproimtely stisfy the Cuchy Riemnn equtions, nd cn e regrded s possessing ll the properties of conforml mpping for the purposes of the TO pproch. 4 Here, the QC mppings re otined y solving Poisson s eqution with Neumnn Dirichlet oundry conditions using the Poisson trnsform lgorithm. As illustrted y Figure, the mesh grids creted y the QC mppings possess strong orthogonlity within the entire trnsformtion domin, indicting tht the nisotropy of the medium hs een minimized. The permittivity nd permeility tensors of the trnsformtion medi cn e found from the generl TO design equtions. We ssume trnsverse electric polrized wve with electric field norml to the plne of propgtion nd chrcterize the TO devices y the sptil distriution of refrctive inde. As n emple, Figure shows the computed tensor elements of the refrctive indices sed on the trnsformtion given in Figure. The nd y es indicte the normlized dimensions of the trnsformtion domin in physicl spce, while the refrctive inde distriutions re illustrted y the color mps used in the plots. It is found tht the off-digonl elements re _.4 Virtul Spce y R R. QCTO c _.4 y Physicl Spce Figure The QC trnsformtions used to design integrted photonic components. (, ) The QC mppings trnsform circulr domins with protrusions in the virtul spce into rectngulr domins in the physicl spce. () The top nd ottom surfces of circle re mpped into two stright segments long the surfces of rectngle (solid red). () Four rcs of circle re mpped onto ech side of squre (solid red). The resulting sptil grids nd their inverse from the QC mppings re illustrted y green lines within the TO domins. A point source represented y purple dot is emedded t the center of ll the devices. QC, qusi-conforml; TO, trnsformtion optics. Light: Science & Applictions _.. d _.4 nyy.4. ny y.4. W _.4 n. nzz y Figure The QC trnsformtions generte TO designs with n isotropic GRIN profile. The elements of refrctive inde tensor (, n,, ny, c, nyy, nd d, nzz) for the QC trnsformtion illustrted in Figure. The interior region of the domin in the virtul spce consists of free spce. QC, qusi-conforml; GRIN, grdient inde; TO, trnsformtion optics.

3 Trnsformtion optics integrted photonic systems QWuet l nerly zero due to the orthogonlity of the grids, nd ll the in-plne digonl elements re very close to unity ecept for n zz, which hs mimum vlue of.. Therefore, the nisotropy of the trnsformtion medium cn e neglected, llowing TO devices to e creted using only isotropic GRIN mterils. These types of TO designs composed of plnr GRIN mterils with two-dimensionl inde profiles cn e implemented in sl wveguides, such s silicon-on-insultor wfers, leding to prcticl friction nd integrtion with other photonic components in n on-chip system. For instnce, structured dielectrics comprised of suwvelength holes etched in wveguide cn e used to crete n effective medium with desired GRIN distriutions. 7 Using this technique, refrctive inde rnging from the ulk vlue of the dielectric host medium to ner unity is chievle under certin friction constrints, llowing for dvnced QCTO designs with lrge inde vrition. As result, this method hs een successfully employed for eperimentl demonstrtions of severl TO devices in the ner infrred region. 7 9,, Alterntively, the GRIN distriutions necessry for the QCTO devices cn e implemented y controlling the thickness of the guiding lyer of sl wveguide. 6,7 Since the effective mode inde of the wveguide is dependent on the thickness of the guiding lyer, the GRIN profile of TO design cn e trnslted into height mp of the guiding lyer. Bsed on this method, low-loss Luneurg lenses with strong inde vritions hve lso een demonstrted. 8,9 Refrctive Inde TO Collimtor t Wveguides RESULTS AND DISCUSSION We first design squre qud-em collimtor y following the QC mpping illustrted in Figure. Bsed on the geometry trnsformtion, wves tht emerge from ech fce of the device possess plnr equl-phse surfces, which produce collimted light ems norml to the surfces. 4 4 When connected to silicon wveguides t its collimting surfces, this TO component efficiently couples light emitted from point source t the center of the device into ech wveguide. By following the generl TO design equtions, the required effective prmeters of the trnsformtion medium re clculted. As shown in Figure 4, the GRIN profile of the collimtor ehiits four-fold symmetry due to the trnsformtion geometry nd hs high inde t ech collimting surfce. The highest refrctive inde found t the edge of the device cn e djusted y controlling the geometries nd dimensions of the trnsformtion domin. Therefore, the trnsformtion is engineered such tht the indices of the silicon wveguide nd the QCTO element re mostly mtched t the oundries with n inde of.4, leding to miniml reflection. In order to chrcterize the performnce of the TO collimtor coupled with wveguides, full-wve numericl simultions re performed using the finite-difference time-domin (FDTD) method. Figure 4 demonstrtes the light intensity distriution ecited y point source with wvelength of. mm, where the emitting light is smoothly guided inside the TO collimtor efore entering the connecting wveguides. Low reflections t the interfce re evidenced s the interference fringes re firly wek inside the TO collimtor. In fct, FDTD simultions revel tht over 98% of the emitted energy is coupled into the wveguides through the TO collimtor, demonstrting high coupling efficiency nd low insertion losses. In ddition to the light source collimtor, the QC trnsformtion technique cn e employed to design mny other GRIN components with verstile functionlities. To further demonstrte the fleiility of this design tool, we present severl wveguide dpters tht re criticl components in integrted photonic systems s depicted in Figure. One emple is wveguide coupler tht cn connect different-sized Figure 4 A qud-em TO collimtor connects four silicon wveguides. () The squre qud-em collimtor mesuring 7. mm on side connects four silicon wveguides with t mm. The inset shows the refrctive inde profile of the QCTO device. () The light intensity distriution ecited y point source t the center of the device demonstrtes efficient coupling from the light source to ll the wveguides. The wvelength of the light source is. mm. QC, qusi-conforml; TO, trnsformtion optics. opticl wveguides y converting the guided modes. 44 In contrst to conventionl coupler which requires long diticlly tpering section to reduce losses, the TO-sed design pproch leds to compct devices s the light propgtion cn e controlled effectively through the GRIN distriution over the entire trnsformtion medium. The coupler is comprised of two GRIN elements, s shown y the lck dshed o in Figure. The inde distriutions of oth elements re otined sed on the QC mpping illustrted in Figure. Due to the mirror symmetry of the refrctive inde profile in Figure d, ech element of the wveguide coupler consists of hlf of the trnsformtion medium. Furthermore, the geometricl trnsformtions re chosen so tht the resulting TO coupler mtches the size nd refrctive inde of the wveguides t oth the input nd output surfces. In this wy, light crried y the input wveguide from the left is compressed into nrrow em y the first element of the coupler efore eperiencing susequent epnsion to mtch the size of the.6.4. Light: Science & Applictions

4 4 Trnsformtion optics integrted photonic systems QWuet l c Wveguide Coupler output wveguide. Figure demonstrtes the performnce of the device, through which light is smoothly guided nd coupled etween two silicon wveguides of different sizes. Despite smll mount of reflective nd scttered light, which re found to e.6% nd.4%, respectively, such compct TO wveguide coupler provides coupling efficiency with up to 9% trnsmission. Further numericl studies revel tht the TO coupler mintins high trnsmission ove 94% t wvelengths etween. mm nd. mm, covering the entire infrred telecommunictions nd. Menwhile, it is interesting to d 4 4 Power Splitter Figure TO-sed GRIN wveguide dpters. () A TO wveguide coupler connects two silicon wveguides with width of 7. mm nd.7 mm, respectively. The coupler device, illustrted in the lck dshed o, hs size of 7. mm6.7 mm. () Light intensity distriution otined from FDTD simultions. Light from the input wveguide on the left couples well into the output wveguide through the QCTO component. (c) The refrctive inde profile of QCTO power splitter which divides light from the input wveguide (. mm) etween two output wveguides (. mm). The TO splitter within the dshed o hs footprint of.7 mm. mm. (d) FDTD simultion demonstrtes equl division of opticl power etween two output wveguides through the TO splitter. The wvelength of the light in oth () nd (d) is. mm. The color scles for (c) nd (d) re identicl to those in () nd (). FDTD, finite-difference time-domin; GRIN, grdient inde; QC, qusi-conforml; TO, trnsformtion optics. note tht the incident light is focused in the middle of the coupler, producing n enhnced electric field tht is five times stronger thn tht in the input wveguide. As result, this TO component, together with the ssocited wveguides, provides n integrted pltform tht is suitle for investigting light interction with opticl medi, such s ctive nd nonliner mterils. Another commonly used component in integrted photonics is power splitter, which eqully divides power from n input wveguide etween two output wveguides. The Y rnch nd multimode interference element re often used; however, these devices hve lrge footprints nd ehiit limited ndwidth, respectively. 4, Here, we comine properly engineered TO elements to form new type of power splitter. As shown in Figure c, the TO version of the splitter is composed of three GRIN elements, ech connecting to n opticl wveguide. The GRIN profile of ech element is found y performing the QC mpping illustrted in Figure. Light from the input wveguide is divided etween two output wveguides, which form 66 ngle with respect to ech other. Figure d illustrtes the light intensity distriution predicted y FDTD simultions. As we epect, the incident light grdully couples into the first element of the TO- GRIN splitter efore eing seprted into the two output wveguides y the second hlf of the device. Due to the mtched indices t ll the surfces of the device, the opticl power is efficiently delivered nd eqully distriuted in the output wveguides. Moreover, such comined TO splitters cn e esily djusted to integrte with wveguides tht hve different sizes nd orienttions, mking them promising cndidtes for compct, rodnd integrted photonic systems. Another essentil component in integrted photonics is the wveguide crossing, which llows opticl signls crried y wveguides to e routed nd interconnected within limited spce, providing the possiility for high-density integrtion of opticl devices in photonic circuits. 4, In order to mitigte insertion loss nd crosstlk t the intersections of opticl wveguides, either resontor or mode epnder type crossing device is needed. 4,46 By pplying n pproprite QCTO pproch to engineer the GRIN profile of the device, we design new type of wveguide crossing tht cn chnnel the light propgtion throughout the trnsformtion medium without ny wve guiding structures. Therefore, compct TO-sed crossing devices cn e relized to operte over wide ndwidth. TO devices tht cn end nd shift light ems hve een proposed nd demonstrted through oth numericl simultions nd eperimentl chrcteriztion.,, Here, we investigte GRIN elements which cn process two or more ems simultneously, nd demonstrte the crossing functionlity y connecting the TO device with set of input nd output wveguides. For the development of wveguide crossing, we hve utilized the geometricl mpping illustrted in Figure, in which circulr domin in the virtul spce is trnsformed into rectngulr domin with flt surfces in the physicl spce. Since light rys in oth spces must remin norml to the oundries (solid red lines), the light will end to pss through the origin in the physicl spce nd ehiit lterl shift when eiting the device. Insted of ssuming vcuum in the virtul spce s in most of the TO designs, we ssign Mwell fisheye lens with rdil GRIN distriution given in Eqution () to the circulr region s shown in Figure 6, where R is the rdius of the circulr region nd frfr. nr ðþ~ zðr=rþ ðþ Light: Science & Applictions

5 Trnsformtion optics integrted photonic systems QWuet l. d..... Wveguide Crossing c Input Wveguide Output Wveguide e... Input Wveguide Output Wveguide Figure 6 A TO-sed GRIN wveguide crossing. () The refrctive inde profile of Mwell fisheye lens in circulr domin contining protrusions in the virtul spce. () The GRIN profile of the trnsformed rectngulr domin in the physicl spce. (c) A TO wveguide crossing connects two silicon wveguides with width of. mm on either side of the device. The crossing device, illustrted in the lck dshed o, hs size of mm mm. (d) Light intensity distriution otined with input wveguide illuminted. Light from the input wveguide ends down nd couples well into the output wveguide through the QCTO component. (e) Light intensity distriution otined with oth input wveguides nd illuminted. The wvelength of the light in oth (d) nd (e) is. mm. GRIN, grdient inde; QC, qusi-conforml; TO, trnsformtion optics. Recent pplictions of the TO pproch to conventionl GRIN optics, such s the Luneurg lens nd Mwell fisheye lens, hve led to devices with more dvntgeous functionlities.,,9 Anlogously, it is found tht the inherent focusing property of the Mwell fisheye lens cn efficiently suppress the diffrction of light in the TO crossing design nd significntly reduce loss nd crosstlk. The resulting GRIN profile of the trnsformed medium is shown in Figure 6, where the center region within the dshed lck o is truncted nd employed s crossing device. To demonstrte the wveguide crossing ehvior, the GRIN device is connected to two input nd two output wveguides with reversed order on either side of the device s shown in Figure 6c. The crossing device, illustrted y the lck dshed o, hs size of mm mm nd refrctive inde rnging from. to.4. All the connecting Si wveguides possess width of. mm, while the djcent wveguides on ech side of the device re seprted y distnce of mm. FDTD simultions were performed to illustrte the light shifting nd crossing effects throughout the TO device. In Figure 6d, only the input wveguide is illuminted. It is evident tht light is smoothly guided nd ended within the TO crossing device, which interconnects the two wveguides plced symmetriclly out the center of the device. Due to the imging property of the Mwell fisheye lens, the diffrction of light is compensted s the wve is focused right in front of the output wveguide nd the lterl epnsion of the em is well confined within the GRIN region. As result, low insertion loss nd crosstlk re relized with the numericl simultions predicting trnsmission of 98%. When oth input wveguides re illuminted, s shown in Figure 6e, the TO device provides the desired crossing performnce y routing two ems into the corresponding output wveguides in n inversed order. Although some interference fringes cn e oserved t the intersection re of the two ems, the two opticl signls re guided independently nd couple into the output wveguides with trnsmission of over 98% in ech cse. By incresing the size of the TO crossing element nd including more wveguide ports, it is possile to further etend the numer of opticl signls cross the device nd therey further enhnce the integrtion density of neighoring devices. Moreover, the TO device demonstrted cn lso e employed s directionl coupler with roder ndwidth compred to conventionl designs sed on coupled modes. 4 By eploiting the fleiility of the emedded QCTO pproch, compct GRIN components such s the wveguide dpters nd crossings hve een relized nd provide superior performnce compred to their stte-of-the-rt counterprts. Furthermore, the TO components cn introduce new functionlities to conventionl GRIN optics nd significntly improve the system level integrtion of photonic devices. For instnce, the TO collimtors, which effectively couple micro- nd nno-scle photon sources (i.e., quntum dots) with photonic wveguides, provide pth to integrte on-chip light sources with high efficiency nd thus roden their rnge of pplictions. In fct, the emedded QCTO pproch enles clss of ll-dielectric GRIN components, such s em shifters, enders nd even polriztion splitters, in which light with oth polriztions cn e independently controlled, 47 which re promising for integrted photonic systems with enhnced functionlities nd compct size. By utilizing the focusing nd enhncement of light offered y some TO devices, integrted opticl sensors nd modultors with stronger light mtter interction cn lso e relized. Moreover, the recent development of plsmon nno-lsers offers the possiility of ctive photonic circuits; however, their integrtion nd ppliction hve een hindered due to the lck of collimted emission of lser light. 48,49 In view of the recent interest in TO techniques for plsmonics, we envision tht the pproch nd devices demonstrted here could provide n enling technology for Light: Science & Applictions

6 6 Trnsformtion optics integrted photonic systems QWuet l efficient coupling of nnoscopic light, leding to new type of nnocircuit rchitecture sed on controlling surfce plsmons. CONCLUSIONS In summry, we hve designed nd demonstrted severl TO-inspired GRIN components for integrted photonic systems using full-wve FDTD simultions. An emedded QC trnsformtion pproch is employed, yielding devices comprised of isotropic, dielectric-only mterils. These TO components were shown to e le to chieve efficient light coupling etween photonic elements, such s opticl sources nd wveguides, while ehiiting gret design fleiility. Such TO-sed GRIN devices, with low losses nd rodnd opertion, hve wide rnge of pplictions including opticl communictions, computing nd sensing. Our design pproch nd emples illustrte the power of the TO methodology to ring GRIN optics into their full potentil for dvncing prcticl opticl devices nd integrted photonic systems. ACKNOWLEDGMENTS Prtil support for this work ws provided y the NSF MRSEC (Grnt No. DMR-844). We thnk Peter Sieer for his ssistnce with some of the figure visuliztions. Pendry JB, Schurig D, Smith DR. Controlling electromgnetic fields. Science 6; : Leonhrdt U. Opticl conforml mpping. Science 6; : Schurig D, Mock JJ, Justice BJ, Cummer SA, Pendry JB et l. Metmteril electromgnetic clok t microwve frequencies. Science 6; 4: Rhm M, Schurig D, Roerts DA, Cummer SA, Smith DR et l. Design of electromgnetic cloks nd concentrtors using form-invrint coordinte trnsformtions of Mwell s equtions. Photon Nnostruct Fundm Appl 7; 6: Nrimnov EE, Kildishev AV. Opticl lck hole: rodnd omnidirectionl light sorer. Appl Phys Lett 9; 9: 46/. 6 Rhm M, Cummer SA, Schurig D, Pendry JB, Smith DR. Opticl design of reflectionless comple medi y finite emedded coordinte trnsformtions. Phys Rev Lett 8; : 69/ 4. 7 RhmM, Roerts DA, PendryJB, Smith DR. Trnsformtion-opticl design of dptive em ends nd em epnders. Opt Epress 8; 6: Kwon DH, Werner DH. Polriztion splitter nd polriztion rottor designs sed on trnsformtion optics. Opt Epress 8; 6: Vkil A, Enght N. Trnsformtionl optics using grphene. Science ; : Kwon DH, WernerDH. Trnsformtionopticl designsfor wve collimtors, flt lenses, nd right-ngle ends. New J Phys 8; : /. Tng W, Argyropoulos C, Kllos E, Song W, Ho Y. Discrete coordinte trnsformtion for designing ll-dielectric flt ntenns. IEEE Trns Antenn Propg ; 8: Chen HY, Chn CT, Sheng P. Trnsformtion optics nd metmterils. Nt Mter ; 9: Kwon DH, Werner DH. Trnsformtion electromgnetics: n overview of the theory nd its ppliction. IEEE Antenns Propg Mg ; : Li J, Pendry JB. Hiding under the crpet: new strtegy for cloking. Phys Rev Lett 8; : 9/ 4. Liu R, Ji C, Mock JJ, Chin JY, Cui TJ et l. Brodnd ground-plne clok. Science 9; : M HF, Cui TJ. Three-dimensionl rodnd ground-plne clok mde of metmterils. Nt Commun ; : 6. 7 Vlentine J, Li J, Zentgrf T, Brtl G, Zhng X. An opticl clok mde of dielectrics. Nt Mter 9; 8: Grielli LH, Crdens J, Poitrs CB, Lipson M. Silicon nnostructure clok operting t opticl frequencies. Nt Photon 9; : Lee J, Blir J, Tmm VA, Wu Q, Rhee SJ et l. Direct visuliztion of opticl frequency invisiility clok sed on silicon nnorod rry. Opt Epress 9; 7: Ergin T, Stenger N, Brenner P, Pendry JB, Wegener M. Three-dimensionl invisiility clok t opticl wvelengths. Science ; 8: 7 9. Kundtz N, Smith DR. Etreme-ngle rodnd metmteril lens. Nt Mter ; 9: 9. M HF, Cui TJ. Three-dimensionl rodnd nd rod-ngle trnsformtion-optics lens. Nt Commun ; : 4/ 7. Zentgrf T, Vlentine J, Tpi N, Li J, Zhng X. An opticl Jnus device for integrted photonics. Adv Mter ; : Lifnte G. Integrted photonics: fundmentls. Chichester: Wiley,. Pollock CR, Lipson M. Integrted photonics. Norwell, MA: Kluwer Acdemic Pulishers,. 6 Jonnopoulos JD, Villeneuve PR, Fn S. Photonic crystl: put new twist on light. Nture 997; 86: Vlsov YA, O Boyle M, Hmnn HF, McN SJ. Active control of slow light on chip with photonic crystl wveguides. Nture ; 48: Enghet N. Circuits with light t nnoscles: opticl nnocircuits inspired y metmterils. Science 7; 7: Smith DR, Urzhumov Y, Kundtz NB, Lndy NI. Enhncing imging systems using trnsformtion optics. Opt Epress ; 8: 8. Thompson JF, Soni BK, Wetherill NP. Hndook of grid genertion. Boc Rton, FL: CRC Press, 999. Chng Z, Zhou X, Hu J, Hu G. Design method for qusi-isotropic trnsformtion mterils sed on inverse Lplce s eqution with sliding oundries. Opt Epress ; 8: Lndy NI, Pdill WJ. Guiding light with conforml trnsformtions. Opt Epress 9; 7: Turpin JP, Mssoud AT, Jing ZH, Werner PL, Werner DH. Conforml mppings to chieve simple mteril prmeters for trnsformtion optics devices. Opt Epress ; 8: Tng L, Yin J, Yun G, Du J, Go H et l. Generl conforml trnsformtion method sed on Schwrz Christoffel pproch. Opt Epress ; 9: 9 6. Hunt J, Tyler R, Dhr S, Tsi YJ, Bowen P et l. Plnr, flttened Luneurg lens t infrred wvelengths. Opt Epress ; : Zernike F. Luneurg lens for opticl wveguide use. Opt Commun 974; : Yo SK, Anderson DB, August RR, Youmns BR, Oni CM. Guided-wve opticl thinfilm Luneurg lenses: friction technique nd properties. Appl Opt 979; 8: Di Flco A, Kehr SC, Leonhrdt U. Luneurg lens in silicon photonics. Opt Epress ; 9: Grielli LH, Lipson M. Integrted Luneurg lens vi ultr-strong inde grdient on silicon. Opt Epress ; 9: 7. 4 Jing WX, Cui TJ, M HF, Zhou XY, Cheng Q. Cylindricl-to-plne-wve conversion vi emedded opticl trnsformtion. Appl Phys Lett 8; 9: 69/. 4 Schmiele M, Vrm VS, Rockstuhl C, Lederer F. Designing opticl elements from isotropic mterils y using trnsformtion optics. Phys Rev A ; 8: 87/. 4 Grcí-Mec C, Mrtínez A, Leonhrdt U. Engineering ntenn rdition ptterns vi qusi-conforml mppings. Opt Epress ; 9: Jing ZH, Gregory MD, Werner DH. Eperimentl demonstrtion of rodnd trnsformtion optics lens for highly directive multiem emission. Phys Rev B ; 84: 6/ Tichit PH, Burokur SN, de Lustrc A. Wveguide tper engineering using coordinte trnsformtion technology. Opt Epress ; 8: Johnson SG, Mnoltou C, Fn S, Villeneuve PR, Jonnopoulos JD et l. Elimintion of cross tlk in wveguide intersections. Opt Lett 998; : Bogerts W, Dumon P, Thourhout D, Bets R. Low-loss, low cross-tlk crossings for silicon-on-insultor nnophotonic wveguides. Opt Lett 7; : Dnner AJ, Tyc T, Leonhrdt U. Controlling irefringence in dielectrics. Nt Photon ; : Oulton RF, Sorger VJ, Zentgrf T, M RM, Gldden C et l. Plsmon lsers t deep suwvelength scle. Nture 9; 46: Noginov MA, Zhu G, Belgrve AM, Bkker R, Shlev VM et l. Demonstrtion of spser-sed nnolser. Nture 9; 46:. Huidoro PA, Nesterov ML, Mrtin-Moreno L, Grci-Vidl FJ. Trnsformtion optics for plsmonics. Nno Lett ; : Liu Y, Zentgrf T, Brtl G, Zhng X. Trnsformtionl plsmon optics. Nno Lett ; : Zentgrf T, Liu Y, Mikkelsen MH, Vlentine J, Zhng X. Plsmonic Luneurg nd Eton lenses. Nt Nnotechnol ; 6:. This work is licensed under Cretive Commons Attriution-NonCommercil-NoDerivtive Works. Unported License. To view copy of this license, visit cretivecommons.org/licenses/y-nc-nd/. Light: Science & Applictions