Topological photonic crystals: a review

Frontiers of Optoelectronics - Tập 13 - Trang 50-72 - 2020
Hongfei Wang1, Samit Kumar Gupta1, Biye Xie1, Minghui Lu1,2,3
1National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing, China
2Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
3Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, China

Tóm tắt

The field of topological photonic crystals has attracted growing interest since the inception of optical analog of quantum Hall effect proposed in 2008. Photonic band structures embraced topological phases of matter, have spawned a novel platform for studying topological phase transitions and designing topological optical devices. Here, we present a brief review of topological photonic crystals based on different material platforms, including all-dielectric systems, metallic materials, optical resonators, coupled waveguide systems, and other platforms. Furthermore, this review summarizes recent progress on topological photonic crystals, such as higherorder topological photonic crystals, non-Hermitian photonic crystals, and nonlinear photonic crystals. These studies indicate that topological photonic crystals as versatile platforms have enormous potential applications in maneuvering the flow of light.

Tài liệu tham khảo

Yablonovitch E. Inhibited spontaneous emission in solid-state physics and electronics. Physical Review Letters, 1987, 58(20): 2059–2062 John S. Strong localization of photons in certain disordered dielectric superlattices. Physical Review Letters, 1987, 58(23): 2486–2489 Wang B, Cappelli M A. A plasma photonic crystal bandgap device. Applied Physics Letters, 2016, 108(16): 161101 Akahane Y, Asano T, Song B S, Noda S. High-Q photonic nanocavity in a two-dimensional photonic crystal. Nature, 2003, 425(6961): 944–947 Shelby R A, Smith D R, Schultz S. Experimental verification of a negative index of refraction. Science, 2001, 292(5514): 77–79 Shalaev V M, Cai W, Chettiar U K, Yuan H K, Sarychev A K, Drachev V P, Kildishev A V. Negative index of refraction in optical metamaterials. Optics Letters, 2005, 30(24): 3356–3358 Klitzing K, Dorda G, Pepper M. New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance. Physical Review Letters, 1980, 45(6): 494–497 Thouless D J, Kohmoto M, Nightingale M P, den Nijs M. Quantized hall conductance in a two-dimensional periodic potential. Physical Review Letters, 1982, 49(6): 405–408 Kohmoto M. Topological invariant and the quantization of the Hall conductance. Annals of Physics, 1985, 160(2): 343–354 Kane C L, Mele E J. Quantum spin Hall effect in graphene. Physical Review Letters, 2005, 95(22): 226801 Bernevig B A, Zhang S C. Quantum spin Hall effect. Physical Review Letters, 2006, 96(10): 106802 Bernevig B A, Hughes T L, Zhang S C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science, 2006, 314(5806): 1757–1761 König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C. Quantum spin hall insulator state in HgTe quantum wells. Science, 2007, 318(5851): 766–770 Haldane F D, Raghu S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Physical Review Letters, 2008, 100(1): 013904 Wang Z, Chong Y D, Joannopoulos J D, Soljacić M. Reflection-free one-way edge modes in a gyromagnetic photonic crystal. Physical Review Letters, 2008, 100(1): 013905 Wang Z, Chong Y, Joannopoulos J D, Soljacić M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature, 2009, 461(7265): 772–775 Hafezi M, Demler E A, Lukin M D, Taylor J M. Robust optical delay lines with topological protection. Nature Physics, 2011, 7(11): 907–912 Umucalılar R O, Carusotto I. Artificial gauge field for photons in coupled cavity arrays. Physical Review A, 2011, 84(4): 043804 Khanikaev A B, Mousavi S H, Tse W K, Kargarian M, MacDonald A H, Shvets G. Photonic topological insulators. Nature Materials, 2013, 12(3): 233–239 Nalitov A V, Malpuech G, Terças H, Solnyshkov D D. Spin-orbit coupling and the optical spin Hall effect in photonic graphene. Physical Review Letters, 2015, 114(2): 026803 Wu L H, Hu X. Scheme for achieving a topological photonic crystal by using dielectric material. Physical Review Letters, 2015, 114(22): 223901 Cheng X, Jouvaud C, Ni X, Mousavi S H, Genack A Z, Khanikaev A B. Robust reconfigurable electromagnetic pathways within a photonic topological insulator. Nature Materials, 2016, 15(5): 542–548 Dong J W, Chen X D, Zhu H, Wang Y, Zhang X. Valley photonic crystals for control of spin and topology. Nature Materials, 2017, 16(3): 298–302 Yang Y, Xu Y F, Xu T, Wang H X, Jiang J H, Hu X, Hang Z H. Visualization of a unidirectional electromagnetic waveguide using topological photonic crystals made of dielectric materials. Physical Review Letters, 2018, 120(21): 217401 Fang K, Yu Z, Fan S. Realizing effective magnetic field for photons by controlling the phase of dynamic modulation. Nature Photonics, 2012, 6(11): 782–787 Lumer Y, Plotnik Y, Rechtsman M C, Segev M. Self-localized states in photonic topological insulators. Physical Review Letters, 2013, 111(24): 243905 Rechtsman M C, Zeuner J M, Plotnik Y, Lumer Y, Podolsky D, Dreisow F, Nolte S, Segev M, Szameit A. Photonic Floquet topological insulators. Nature, 2013, 496(7444): 196–200 Titum P, Lindner N H, Rechtsman M C, Refael G. Disorder-induced Floquet topological insulators. Physical Review Letters, 2015, 114(5): 056801 Leykam D, Rechtsman M C, Chong Y D. Anomalous topological phases and unpaired dirac cones in photonic Floquet topological insulators. Physical Review Letters, 2016, 117(1): 013902 Maczewsky L J, Zeuner J M, Nolte S, Szameit A. Observation of photonic anomalous Floquet topological insulators. Nature Communications, 2017, 8(1): 13756 Mukherjee S, Spracklen A, Valiente M, Andersson E, Öhberg P, Goldman N, Thomson R R. Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice. Nature Communications, 2017, 8(1): 13918 Mukherjee S, Chandrasekharan H K, Öhberg P, Goldman N, Thomson R R. State-recycling and time-resolved imaging in topological photonic lattices. Nature Communications, 2018, 9(1): 4209 Zhu B, Zhong H, Ke Y, Qin X, Sukhorukov A A, Kivshar Y S, Lee C. Topological Floquet edge states in periodically curved waveguides. Physical Review A, 2018, 98(1): 013855 Nathan F, Abanin D, Berg E, Lindner N H, Rudner M S. Anomalous Floquet insulators. Physical Review B, 2019, 99(19): 195133 Ma T, Shvets G. All-Si valley-Hall photonic topological insulator. New Journal of Physics, 2016, 18(2): 025012 Wu X, Meng Y, Tian J, Huang Y, Xiang H, Han D, Wen W. Direct observation of valley-polarized topological edge states in designer surface plasmon crystals. Nature Communications, 2017, 8(1): 1304 Slobozhanyuk A, Mousavi S H, Ni X, Smirnova D, Kivshar Y S, Khanikaev A B. Three-dimensional all-dielectric photonic topological insulator. Nature Photonics, 2017, 11(2): 130–136 Yang Y, Gao Z, Xue H, Zhang L, He M, Yang Z, Singh R, Chong Y, Zhang B, Chen H. Realization of a three-dimensional photonic topological insulator. Nature, 2019, 565(7741): 622–626 Young S M, Zaheer S, Teo J C, Kane C L, Mele E J, Rappe A M. Dirac semimetal in three dimensions. Physical Review Letters, 2012, 108(14): 140405 Yang B J, Nagaosa N. Classification of stable three-dimensional Dirac semimetals with nontrivial topology. Nature Communications, 2014, 5(1): 4898 Liu Z K, Zhou B, Zhang Y, Wang Z J, Weng H M, Prabhakaran D, Mo S K, Shen Z X, Fang Z, Dai X, Hussain Z, Chen Y L. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science, 2014, 343(6173): 864–867 Yang B, Guo Q, Tremain B, Barr L E, Gao W, Liu H, Béri B, Xiang Y, Fan D, Hibbins A P, Zhang S. Direct observation of topological surface-state arcs in photonic metamaterials. Nature Communications, 2017, 8(1): 97 Li F, Huang X, Lu J, Ma J, Liu Z. Weyl points and Fermi arcs in a chiral phononic crystal. Nature Physics, 2018, 14(1): 30–34 Burkov A A, Hook M D, Balents L. Topological nodal semimetals. Physical Review B, 2011, 84(23): 235126 Yan Z, Wang Z. Tunable Weyl points in periodically driven nodal line semimetals. Physical Review Letters, 2016, 117(8): 087402 He H, Qiu C, Ye L, Cai X, Fan X, Ke M, Zhang F, Liu Z. Topological negative refraction of surface acoustic waves in a Weyl phononic crystal. Nature, 2018, 560(7716): 61–64 Adair R, Chase L L, Payne S A. Nonlinear refractive index of optical crystals. Physical Review B, 1989, 39(5): 3337–3350 Berger V. Nonlinear photonic crystals. Physical Review Letters, 1998, 81(19): 4136–4139 Mingaleev S F, Kivshar Y S. Self-trapping and stable localized modes in nonlinear photonic crystals. Physical Review Letters, 2001, 86(24): 5474–5477 Soljačić M, Luo C, Joannopoulos J D, Fan S. Nonlinear photonic crystal microdevices for optical integration. Optics Letters, 2003, 28(8): 637–639 Fleischer J W, Segev M, Efremidis N K, Christodoulides D N. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature, 2003, 422(6928): 147–150 Soljačić M, Joannopoulos J D. Enhancement of nonlinear effects using photonic crystals. Nature Materials, 2004, 3(4): 211 -219 Haddad L H, Weaver C M, Carr L D. The nonlinear Dirac equation in Bose-Einstein condensates: I. Relativistic solitons in armchair nanoribbon optical lattices. New Journal of Physics, 2015, 17(6): 063033 Hadad Y, Khanikaev A B, Alù A. Self-induced topological transitions and edge states supported by nonlinear staggered potentials. Physical Review B, 2016, 93(15): 155112 Leykam D, Chong Y D. Edge solitons in nonlinear-photonic topological insulators. Physical Review Letters, 2016, 117(14): 143901 Roushan P, Neill C, Megrant A, Chen Y, Babbush R, Barends R, Campbell B, Chen Z, Chiaro B, Dunsworth A, Fowler A, Jeffrey E, Kelly J, Lucero E, Mutus J, O’Malley P J J, Neeley M, Quintana C, Sank D, Vainsencher A, Wenner J, White T, Kapit E, Neven H, Martinis J. Chiral ground-state currents of interacting photons in a synthetic magnetic field. Nature Physics, 2017, 13(2): 146–151 Tai M E, Lukin A, Rispoli M, Schittko R, Menke T, Dan Borgnia, Preiss P M, Grusdt F, Kaufman A M, Greiner M. Microscopy of the interacting Harper-Hofstadter model in the two-body limit. Nature, 2017, 546(7659): 519–523 Zhou X, Wang Y, Leykam D, Chong Y D. Optical isolation with nonlinear topological photonics. New Journal of Physics, 2017, 19(9): 095002 Dobrykh D A, Yulin A V, Slobozhanyuk A P, Poddubny A N, Kivshar Y S. Nonlinear control of electromagnetic topological edge states. Physical Review Letters, 2018, 121(16): 163901 Rajesh C, Georgios T. Self-induced topological transition in phononic crystals by nonlinearity management. 2019, arXiv:1904. 09466v1 Bender C M, Boettcher S. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Physical Review Letters, 1998, 80(24): 5243–5246 Regensburger A, Bersch C, Miri M A, Onishchukov G, Christodoulides D N, Peschel U. Parity-time synthetic photonic lattices. Nature, 2012, 488(7410): 167–171 Yang Y, Peng C, Liang Y, Li Z, Noda S. Analytical perspective for bound states in the continuum in photonic crystal slabs. Physical Review Letters, 2014, 113(3): 037401 Zhen B, Hsu C W, Lu L, Stone A D, Soljačić M. Topological nature of optical bound states in the continuum. Physical Review Letters, 2014, 113(25): 257401 Malzard S, Poli C, Schomerus H. Topologically protected defect states in open photonic systems with non-Hermitian charge-conjugation and parity-time symmetry. Physical Review Letters, 2015, 115(20): 200402 Zeuner J M, Rechtsman M C, Plotnik Y, Lumer Y, Nolte S, Rudner M S, Segev M, Szameit A. Observation of a topological transition in the bulk of a non-Hermitian system. Physical Review Letters, 2015, 115(4): 040402 Zhen B, Hsu C W, Igarashi Y, Lu L, Kaminer I, Pick A, Chua S L, Joannopoulos J D, Soljačić M. Spawning rings of exceptional points out of Dirac cones. Nature, 2015, 525(7569): 354–358 Cerjan A, Raman A, Fan S. Exceptional contours and band structure design in parity-time symmetric photonic crystals. Physical Review Letters, 2016, 116(20): 203902 Bulgakov E N, Maksimov D N. Topological bound states in the continuum in arrays of dielectric spheres. Physical Review Letters, 2017, 118(26): 267401 Feng L, El-Ganainy R, Ge L. Non-Hermitian photonics based on parity-time symmetry. Nature Photonics, 2017, 11(12): 752–762 Kodigala A, Lepetit T, Gu Q, Bahari B, Fainman Y, Kanté B. Lasing action from photonic bound states in continuum. Nature, 2017, 541(7636): 196–199 Weimann S, Kremer M, Plotnik Y, Lumer Y, Nolte S, Makris K G, Segev M, Rechtsman M C, Szameit A. Topologically protected bound states in photonic parity-time-symmetric crystals. Nature Materials, 2017, 16(4): 433–438 El-Ganainy R, Makris K G, Khajavikhan M, Musslimani Z H, Rotter S, Christodoulides D N. Non-Hermitian physics and PT symmetry. Nature Physics, 2018, 14(1): 11–19 Kawabata K, Shiozaki K, Ueda M. Anomalous helical edge states in a non-Hermitian Chern insulator. Physical Review B, 2018, 98(16): 165148 Kunst F K, Edvardsson E, Budich J C, Bergholtz E J. Biorthogonal bulk-boundary correspondence in non-Hermitian systems. Physical Review Letters, 2018, 121(2): 026808 Lieu S. Topological phases in the non-Hermitian Su-Schrieffer-Heeger model. Physical Review B, 2018, 97(4): 045106 Pan M, Zhao H, Miao P, Longhi S, Feng L. Photonic zero mode in a non-Hermitian photonic lattice. Nature Communications, 2018, 9(1): 1308 Qi B, Zhang L, Ge L. Defect states emerging from a non-Hermitian flatband of photonic zero modes. Physical Review Letters, 2018, 120(9): 093901 Shen H, Zhen B, Fu L. Topological band theory for non-Hermitian Hamiltonians. Physical Review Letters, 2018, 120(14): 146402 Wang H F, Gupta S K, Zhu X Y, Lu M H, Liu X P, Chen Y F. Bound states in the continuum in a bilayer photonic crystal with TE-TM cross coupling. Physical Review. B, 2018, 98(21): 214101 Yao S, Song F, Wang Z. Non-Hermitian Chern bands. Physical Review Letters, 2018, 121(13): 136802 Yao S, Wang Z. Edge states and topological invariants of non-Hermitian systems. Physical Review Letters, 2018, 121(8): 086803 Chen X D, Deng W M, Shi F L, Zhao F L, Chen M, Dong J W. Direct observation of corner states in second-order topological photonic crystal slabs. 2018, arXiv:1812.08326 Ezawa M. Higher-order topological insulators and semimetals on the breathing kagome and pyrochlore lattices. Physical Review Letters, 2018, 120(2): 026801 Ezawa M. Minimal models for Wannier-type higher-order topological insulators and phosphorene. Physical Review B, 2018, 98(4): 045125 Ezawa M. Magnetic second-order topological insulators and semimetals. Physical Review B, 2018, 97(15): 155305 Ezawa M. Higher-order topological electric circuits and topological corner resonance on the breathing kagome and pyrochlore lattices. Physical Review B, 2018, 98(20): 201402 Geier M, Trifunovic L, Hoskam M, Brouwer P W. Second-order topological insulators and superconductors with an order-two crystalline symmetry. Physical Review B, 2018, 97(20): 205135 Khalaf E. Higher-order topological insulators and superconductors protected by inversion symmetry. Physical Review B, 2018, 97(20): 205136 Kunst F K, van Miert G, Bergholtz E J. Lattice models with exactly solvable topological hinge and corner states. Physical Review B, 2018, 97(24): 241405 Peterson C W, Benalcazar W A, Hughes T L, Bahl G. A quantized microwave quadrupole insulator with topologically protected corner states. Nature, 2018, 555(7696): 346–350 Schindler F, Cook A M, Vergniory M G, Wang Z, Parkin S S, Bernevig B A, Neupert T. Higher-order topological insulators. Science Advances, 2018, 4(6): eaat0346 van Miert G, Ortix C. Higher-order topological insulators protected by inversion and rotoinversion symmetries. Physical Review B, 2018, 98(8): 081110 Xie B Y, Wang H F, Wang H X, Zhu X Y, Jiang J H, Lu M H, Chen Y F. Second-order photonic topological insulator with corner states. Physical Review B, 2018, 98(20): 205147 Xie B Y, Su G X, Wang H F, Su H, Shen X P, Zhan P, Lu M H, Wang Z L, Chen Y F. Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals. Physical Review Letters, 2019, 122(23): 233903 Yasutomo O, Feng L, Ryota K, Katsuyuki W, Katsunori W, Yasuhiko A, Satoshi I. Photonic crystal nanocavity based on a topological corner state. 2018, arXiv:1812.10171 Călugăru D, Juričić V, Roy B. Higher-order topological phases: a general principle of construction. Physical Review B, 2019, 99(4): 041301 Hu H, Huang B, Zhao E, Liu W V. Dynamical singularities of Floquet higher-order topological insulators. 2019, arXiv:1905. 03727v1 Armstrong J A, Bloembergen N, Ducuing J, Pershan P S. Interactions between light waves in a nonlinear dielectric. Physical Review, 1962, 127(6): 1918–1939 Kleinman D A. Nonlinear dielectric polarization in optical media. Physical Review, 1962, 126(6): 1977–1979 Adler E. Nonlinear optical frequency polarization in a dielectric. Physical Review, 1964, 134(3A): A728–A733 Miller R C. Optical second harmonic generation in piezoelectric crystals. Applied Physics Letters, 1964, 5(1): 17–19 Fejer M M, Magel G, Jundt D H, Byer R L. Quasi-phase-matched second harmonic generation: tuning and tolerances. IEEE Journal of Quantum Electronics, 1992, 28(11): 2631–2654 Yamada M, Nada N, Saitoh M, Watanabe K. First-order quasiphase matched LiNbO3waveguide periodically poled by applying an external field for efficient blue second-harmonic generation. Applied Physics Letters, 1993, 62(5): 435–436 Celebrano M, Wu X, Baselli M, Großmann S, Biagioni P, Locatelli A, De Angelis C, Cerullo G, Osellame R, Hecht B, Duó L, Ciccacci F, Finazzi M. Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation. Nature Nanotechnology, 2015, 10(5): 412–417 Rubin M H, Klyshko D N, Shih Y H, Sergienko A V. Theory of two-photon entanglement in type-II optical parametric down-conversion. Physical Review A, 1994, 50(6): 5122–5133 Monken C H, Ribeiro P S, Pádua S. Transfer of angular spectrum and image formation in spontaneous parametric down-conversion. Physical Review A, 1998, 57(4): 3123–3126 Arnaut H H, Barbosa G A. Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion. Physical Review Letters, 2000, 85(2): 286–289 Howell J C, Bennink R S, Bentley S J, Boyd R W. Realization of the Einstein-Podolsky-Rosen paradox using momentum- and position-entangled photons from spontaneous parametric down conversion. Physical Review Letters, 2004, 92(21): 210403 Harder G, Bartley T J, Lita A E, Nam S W, Gerrits T, Silberhorn C. Single-mode parametric-down-conversion states with 50 photons as a source for mesoscopic quantum optics. Physical Review Letters, 2016, 116(14): 143601 Carriles R, Schafer D N, Sheetz K E, Field J J, Cisek R, Barzda V, Sylvester A W, Squier J A. Imaging techniques for harmonic and multiphoton absorption fluorescence microscopy. Review of Scientific Instruments, 2009, 80(8): 081101 Grinblat G, Li Y, Nielsen M P, Oulton R F, Maier S A. Enhanced third harmonic generation in single germanium nanodisks excited at the anapole mode. Nano Letters, 2016, 16(7): 4635–4640 Sipe J E, Moss D J, van Driel H. Phenomenological theory of optical second- and third-harmonic generation from cubic centrosymmetric crystals. Physical Review B, 1987, 35(3): 1129–1141 Zhu S, Zhu Y, Ming N. Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice. Science, 1997, 278(5339): 843–846 Soavi G, Wang G, Rostami H, Purdie D G, De Fazio D, Ma T, Luo B, Wang J, Ott A K, Yoon D, Bourelle S A, Muench J E, Goykhman I, Dal Conte S, Celebrano M, Tomadin A, Polini M, Cerullo G, Ferrari A C. Broadband, electrically tunable third-harmonic generation in graphene. Nature Nanotechnology, 2018, 13(7): 583–588 Slusher R E, Hollberg L W, Yurke B, Mertz J C, Valley J F. Observation of squeezed states generated by four-wave mixing in an optical cavity. Physical Review Letters, 1985, 55(22): 2409–2412 Deng L, Hagley E W, Wen J, Trippenbach M, Band Y, Julienne P S, Simsarian J, Helmerson K, Rolston S, Phillips W D. Four-wave mixing with matter waves. Nature, 1999, 398(6724): 218–220 Bencivenga F, Cucini R, Capotondi F, Battistoni A, Mincigrucci R, Giangrisostomi E, Gessini A, Manfredda M, Nikolov I P, Pedersoli E, Principi E, Svetina C, Parisse P, Casolari F, Danailov M B, Kiskinova M, Masciovecchio C. Four-wave mixing experiments with extreme ultraviolet transient gratings. Nature, 2015, 520(7546): 205–208 Singh S K, Abak M K, Tasgin M E. Enhancement of four-wave mixing via interference of multiple plasmonic conversion paths. Physical Review B, 2016, 93(3): 035410 Zhang H, Virally S, Bao Q, Ping L K, Massar S, Godbout N, Kockaert P. Z-scan measurement of the nonlinear refractive index of graphene. Optics Letters, 2012, 37(11): 1856–1858 Alam M Z, De Leon I, Boyd R W. Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region. Science, 2016, 352(6287): 795–797 Ozawa T, Price H M, Amo A, Goldman N, Hafezi M, Lu L, Rechtsman M C, Schuster D, Simon J, Zilberberg O, Carusotto I. Topological photonics. Reviews of Modern Physics, 2019, 91(1): 015006 Berry M V. Quantal phase factors accompanying adiabatic changes. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 1802, 1984(392): 45–57 Pancharatnam S. Generalized theory of interference and its applications. Proceedings of the Indian Academy of Sciences, Section A, Physical Sciences, 1956, 44(6): 398–417 Skirlo S A, Lu L, Igarashi Y, Yan Q, Joannopoulos J, Soljačić M. Experimental observation of large Chern numbers in photonic crystals. Physical Review Letters, 2015, 115(25): 253901 Lu L, Wang Z, Ye D, Ran L, Fu L, Joannopoulos J D, Soljačić M. Experimental observation of Weyl points. Science, 2015, 349(6248): 622–624 Xiao M, Lin Q, Fan S. Hyperbolic Weyl point in reciprocal chiral metamaterials. Physical Review Letters, 2016, 117(5): 057401 Lin Q, Xiao M, Yuan L, Fan S. Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension. Nature Communications, 2016, 7(1): 13731 Fang C, Weng H, Dai X, Fang Z. Topological nodal line semimetals. Chinese Physics B, 2016, 25(11): 117106 Lu L, Fu L, Joannopoulos J D, Soljačić M. Weyl points and line nodes in gyroid photonic crystals. Nature Photonics, 2013, 7(4): 294–299 Yang B, Guo Q, Tremain B, Liu R, Barr L E, Yan Q, Gao W, Liu H, Xiang Y, Chen J, Fang C, Hibbins A, Lu L, Zhang S. Ideal Weyl points and helicoid surface states in artificial photonic crystal structures. Science, 2018, 359(6379): 1013–1016 Chen W J, Jiang S J, Chen X D, Zhu B, Zhou L, Dong J W, Chan C T. Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide. Nature Communications, 2014, 5(1): 5782 Slobozhanyuk A P, Khanikaev A B, Filonov D S, Smirnova D A, Miroshnichenko A E, Kivshar Y S. Experimental demonstration of topological effects in bianisotropic metamaterials. Scientific Reports, 2016, 6(1): 22270 Shalaev M I, Walasik W, Tsukernik A, Xu Y, Litchinitser N M. Robust topologically protected transport in photonic crystals at telecommunication wavelengths. Nature Nanotechnology, 2019, 14(1): 31–34 Chen X D, Zhao F L, Chen M, Dong J W. Valley-contrasting physics in all-dielectric photonic crystals: orbital angular momentum and topological propagation. Physical Review B, 2017, 96(2): 020202 Chen X D, Shi F L, Liu H, Lu J C, Deng W M, Dai J Y, Cheng Q, Dong J W. Tunable electromagnetic flow control in valley photonic crystal waveguides. Physical Review Applied, 2018, 10(4): 044002 He M, Zhang L, Wang H. Two-dimensional photonic crystal with ring degeneracy and its topological protected edge states. Scientific Reports, 2019, 9(1): 3815 Ma T, Khanikaev A B, Mousavi S H, Shvets G. Guiding electromagnetic waves around sharp corners: topologically protected photonic transport in metawaveguides. Physical Review Letters, 2015, 114(12): 127401 Chen W J, Xiao M, Chan C T. Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states. Nature Communications, 2016, 7(1): 13038 Chen Y, Chen H, Cai G. High transmission in a metal-based photonic crystal. Applied Physics Letters, 2018, 112(1): 013504 El-Kady I, Sigalas M, Biswas R, Ho K, Soukoulis C. Metallic photonic crystals at optical wavelengths. Physical Review B, 2000, 62(23): 15299–15302 Gao F, Gao Z, Shi X, Yang Z, Lin X, Xu H, Joannopoulos J D, Soljačić M, Chen H, Lu L, Chong Y, Zhang B. Probing topological protection using a designer surface plasmon structure. Nature Communications, 2016, 7(1): 11619 Gao W, Yang B, Tremain B, Liu H, Guo Q, Xia L, Hibbins A P, Zhang S. Experimental observation of photonic nodal line degeneracies in metacrystals. Nature Communications, 2018, 9(1): 950 Gao F, Xue H, Yang Z, Lai K, Yu Y, Lin X, Chong Y, Shvets G, Zhang B. Topologically protected refraction ofrobustkinkstates in valley photonic crystals. Nature Physics, 2018, 14(2): 140–144 Karch A. Surface plasmons and topological insulators. Physical Review B, 2011, 83(24): 245432 Hafezi M, Mittal S, Fan J, Migdall A, Taylor J M. Imaging topological edge states in silicon photonics. Nature Photonics, 2013, 7(12): 1001–1005 Mittal S, Ganeshan S, Fan J, Vaezi A, Hafezi M. Measurement of topological invariants in a 2D photonic system. Nature Photonics, 2016, 10(3): 180–183 Harari G, Bandres M A, Lumer Y, Rechtsman M C, Chong Y D, Khajavikhan M, Christodoulides D N, Segev M. Topological insulator laser: theory. Science, 2018, 359(6381): eaar4003 Bandres M A, Wittek S, Harari G, Parto M, Ren J, Segev M, Christodoulides D N, Khajavikhan M. Topological insulator laser: experiments. Science, 2018, 359(6381): eaar4005 Midya B, Zhao H, Feng L. Non-Hermitian photonics promises exceptional topology of light. Nature Communications, 2018, 9(1): 2674 Barik S, Karasahin A, Flower C, Cai T, Miyake H, DeGottardi W, Hafezi M, Waks E. A topological quantum optics interface. Science, 2018, 359(6376): 666–668 Blanco-Redondo A, Bell B, Oren D, Eggleton B J, Segev M. Topological protection of biphoton states. Science, 2018, 362(6414): 568–571 Piper J R, Fan S. Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance. ACS Photonics, 2014, 1(4): 347–353 Gan X, Mak K F, Gao Y, You Y, Hatami F, Hone J, Heinz T F, Englund D. Strong enhancement of light-matter interaction in graphene coupled to a photonic crystal nanocavity. Nano Letters, 2012, 12(11): 5626–5631 Heeger A J, Kivelson S, Schrieffer J R, Su W P. Solitons in conducting polymers. Reviews of Modern Physics, 1988, 60(3): 781–850 Su W P, Schrieffer J R, Heeger A J. Solitons in Polyacetylene. Physical Review Letters, 1979, 42(25): 1698–1701 Miri M-A, Alù A. Exceptional points in optics and photonics. Science, 2019, 363(6422): eaar7709 Gupta S K, Zou Y, Zhu X Y, Lu M H, Zhang L, Liu X P, Chen Y F. Parity-time symmetry in Non-Hermitian complex media. 2018, arXiv:1803.00794 Lee T E. Anomalous edge state in a non-Hermitian lattice. Physical Review Letters, 2016, 116(13): 133903 Ghatak A, Das T. New topological invariants in non-Hermitian systems. Journal of Physics Condensed Matter, 2019, 31(26): 263001 St-Jean P, Goblot V, Galopin E, Lemaître A, Ozawa T, Le Gratiet L, Sagnes I, Bloch J, Amo A. Lasing in topological edge states of a one-dimensional lattice. Nature Photonics, 2017, 11(10): 651–656 Parto M, Wittek S, Hodaei H, Harari G, Bandres M A, Ren J, Rechtsman M C, Segev M, Christodoulides D N, Khajavikhan M. Edge-mode lasing in 1D topological active arrays. Physical Review Letters, 2018, 120(11): 113901 Zhao H, Miao P, Teimourpour M H, Malzard S, El-Ganainy R, Schomerus H, Feng L. Topological hybrid silicon microlasers. Nature Communications, 2018, 9(1): 981 Ota Y, Katsumi R, Watanabe K, Iwamoto S, Arakawa Y. Topological photonic crystal nanocavity laser. Communications on Physics, 2018, 1(1): 86 Haldane F D M. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “parity anomaly”. Physical Review Letters, 1988, 61(18): 2015–2018 Schmidt J, Marques M R G, Botti S, Marques M A L. Recent advances and applications of machine learning in solid-state materials science. NPJ Computational Materials, 2019, 5(1): 83 Pilozzi L, Farrelly F A, Marcucci G, Conti C. Machine learning inrerse problem for topological photonics. Communications Physics, 2018, 1(1): 57 Long Y, Ren J, Li Y, Chen H. Inverse design of photonic topological state via machine learning. Applied Physics Letters, 2019, 114(18): 181105 Barth C, Becker C. Machine learning classification for field distributions of photonic modes. Communications on Physics, 2018, 1(1): 58 Fano U. Effects of configuration interaction on intensities and phase shifts. Physical Review, 1961, 124(6): 1866–1878 Limonov M F, Rybin M V, Poddubny A N, Kivshar Y S. Fano resonances in photonics. Nature Photonics, 2017, 11(9): 543–554 Miroshnichenko A E, Flach S, Kivshar Y S. Fano resonances in nanoscale structures. Reviews of Modern Physics, 2010, 82(3): 2257–2298 Luk’yanchuk B S, Miroshnichenko A E, Kivshar Y S. Fano resonances and topological optics: an interplay of far- and near-field interference phenomena. Journal of Optics, 2013, 15(7): 073001 Gao W, Hu X, Li C, Yang J, Chai Z, Xie J, Gong Q. Fano-resonance in one-dimensional topological photonic crystal hetero-structure. Optics Express, 2018, 26(7): 8634–8644 Zangeneh-Nejad F, Fleury R. Topological Fano resonances. Physical Review Letters, 2019, 122(1): 014301 Liang G Q, Chong Y D. Optical resonator analog of a two-dimensional topological insulator. Physical Review Letters, 2013, 110(20): 203904