Skip to main content

Topological photonic crystals: a review

Frontiers of Optoelectronics volume 13, pages 50–72 (2020)Cite this article

Abstract

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.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. Yablonovitch E. Inhibited spontaneous emission in solid-state physics and electronics. Physical Review Letters, 1987, 58(20): 2059–2062

    Article  Google Scholar 

  2. John S. Strong localization of photons in certain disordered dielectric superlattices. Physical Review Letters, 1987, 58(23): 2486–2489

    Article  Google Scholar 

  3. Wang B, Cappelli M A. A plasma photonic crystal bandgap device. Applied Physics Letters, 2016, 108(16): 161101

    Google Scholar 

  4. 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

    Google Scholar 

  5. Shelby R A, Smith D R, Schultz S. Experimental verification of a negative index of refraction. Science, 2001, 292(5514): 77–79

    Google Scholar 

  6. 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

    Google Scholar 

  7. 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

    Google Scholar 

  8. 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

    Google Scholar 

  9. Kohmoto M. Topological invariant and the quantization of the Hall conductance. Annals of Physics, 1985, 160(2): 343–354

    MathSciNet  Google Scholar 

  10. Kane C L, Mele E J. Quantum spin Hall effect in graphene. Physical Review Letters, 2005, 95(22): 226801

    Google Scholar 

  11. Bernevig B A, Zhang S C. Quantum spin Hall effect. Physical Review Letters, 2006, 96(10): 106802

    Google Scholar 

  12. 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

    Google Scholar 

  13. 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

    Google Scholar 

  14. 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

    Google Scholar 

  15. 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

    Google Scholar 

  16. Wang Z, Chong Y, Joannopoulos J D, Soljacić M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature, 2009, 461(7265): 772–775

    Google Scholar 

  17. 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

    Google Scholar 

  18. Umucalılar R O, Carusotto I. Artificial gauge field for photons in coupled cavity arrays. Physical Review A, 2011, 84(4): 043804

    Google Scholar 

  19. 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

    Google Scholar 

  20. 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

    Google Scholar 

  21. Wu L H, Hu X. Scheme for achieving a topological photonic crystal by using dielectric material. Physical Review Letters, 2015, 114(22): 223901

    Google Scholar 

  22. 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

    Google Scholar 

  23. 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

    Google Scholar 

  24. 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

    Google Scholar 

  25. 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

    Google Scholar 

  26. Lumer Y, Plotnik Y, Rechtsman M C, Segev M. Self-localized states in photonic topological insulators. Physical Review Letters, 2013, 111(24): 243905

    Google Scholar 

  27. 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

    Google Scholar 

  28. Titum P, Lindner N H, Rechtsman M C, Refael G. Disorder-induced Floquet topological insulators. Physical Review Letters, 2015, 114(5): 056801

    Google Scholar 

  29. 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

    Google Scholar 

  30. Maczewsky L J, Zeuner J M, Nolte S, Szameit A. Observation of photonic anomalous Floquet topological insulators. Nature Communications, 2017, 8(1): 13756

    Google Scholar 

  31. 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

    Google Scholar 

  32. 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

    Google Scholar 

  33. 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

    Google Scholar 

  34. Nathan F, Abanin D, Berg E, Lindner N H, Rudner M S. Anomalous Floquet insulators. Physical Review B, 2019, 99(19): 195133

    Google Scholar 

  35. Ma T, Shvets G. All-Si valley-Hall photonic topological insulator. New Journal of Physics, 2016, 18(2): 025012

    Google Scholar 

  36. 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

    Google Scholar 

  37. 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

    Google Scholar 

  38. 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

    Google Scholar 

  39. 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

    Google Scholar 

  40. Yang B J, Nagaosa N. Classification of stable three-dimensional Dirac semimetals with nontrivial topology. Nature Communications, 2014, 5(1): 4898

    Google Scholar 

  41. 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

    Google Scholar 

  42. 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

    Google Scholar 

  43. 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

    Google Scholar 

  44. Burkov A A, Hook M D, Balents L. Topological nodal semimetals. Physical Review B, 2011, 84(23): 235126

    Google Scholar 

  45. Yan Z, Wang Z. Tunable Weyl points in periodically driven nodal line semimetals. Physical Review Letters, 2016, 117(8): 087402

    Google Scholar 

  46. 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

    Google Scholar 

  47. Adair R, Chase L L, Payne S A. Nonlinear refractive index of optical crystals. Physical Review B, 1989, 39(5): 3337–3350

    Google Scholar 

  48. Berger V. Nonlinear photonic crystals. Physical Review Letters, 1998, 81(19): 4136–4139

    Google Scholar 

  49. Mingaleev S F, Kivshar Y S. Self-trapping and stable localized modes in nonlinear photonic crystals. Physical Review Letters, 2001, 86(24): 5474–5477

    MATH  Google Scholar 

  50. Soljačić M, Luo C, Joannopoulos J D, Fan S. Nonlinear photonic crystal microdevices for optical integration. Optics Letters, 2003, 28(8): 637–639

    Google Scholar 

  51. 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

    Google Scholar 

  52. Soljačić M, Joannopoulos J D. Enhancement of nonlinear effects using photonic crystals. Nature Materials, 2004, 3(4): 211 -219

    Google Scholar 

  53. 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

    MathSciNet  Google Scholar 

  54. 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

    Google Scholar 

  55. Leykam D, Chong Y D. Edge solitons in nonlinear-photonic topological insulators. Physical Review Letters, 2016, 117(14): 143901

    Google Scholar 

  56. 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

    Google Scholar 

  57. 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

    Google Scholar 

  58. Zhou X, Wang Y, Leykam D, Chong Y D. Optical isolation with nonlinear topological photonics. New Journal of Physics, 2017, 19(9): 095002

    Google Scholar 

  59. 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

    Google Scholar 

  60. Rajesh C, Georgios T. Self-induced topological transition in phononic crystals by nonlinearity management. 2019, arXiv:1904. 09466v1

  61. Bender C M, Boettcher S. Real spectra in non-Hermitian Hamiltonians having PT symmetry. Physical Review Letters, 1998, 80(24): 5243–5246

    MathSciNet  MATH  Google Scholar 

  62. 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

    Google Scholar 

  63. 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

    Google Scholar 

  64. 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

    Google Scholar 

  65. 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

    Google Scholar 

  66. 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

    Google Scholar 

  67. 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

    Google Scholar 

  68. 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

    Google Scholar 

  69. Bulgakov E N, Maksimov D N. Topological bound states in the continuum in arrays of dielectric spheres. Physical Review Letters, 2017, 118(26): 267401

    Google Scholar 

  70. Feng L, El-Ganainy R, Ge L. Non-Hermitian photonics based on parity-time symmetry. Nature Photonics, 2017, 11(12): 752–762

    Google Scholar 

  71. 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

    Google Scholar 

  72. 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

    Google Scholar 

  73. 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

    Google Scholar 

  74. Kawabata K, Shiozaki K, Ueda M. Anomalous helical edge states in a non-Hermitian Chern insulator. Physical Review B, 2018, 98(16): 165148

    Google Scholar 

  75. 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

    Google Scholar 

  76. Lieu S. Topological phases in the non-Hermitian Su-Schrieffer-Heeger model. Physical Review B, 2018, 97(4): 045106

    MathSciNet  Google Scholar 

  77. 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

    Google Scholar 

  78. 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

    Google Scholar 

  79. Shen H, Zhen B, Fu L. Topological band theory for non-Hermitian Hamiltonians. Physical Review Letters, 2018, 120(14): 146402

    MathSciNet  Google Scholar 

  80. 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

    Google Scholar 

  81. Yao S, Song F, Wang Z. Non-Hermitian Chern bands. Physical Review Letters, 2018, 121(13): 136802

    Google Scholar 

  82. Yao S, Wang Z. Edge states and topological invariants of non-Hermitian systems. Physical Review Letters, 2018, 121(8): 086803

    Google Scholar 

  83. 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

  84. Ezawa M. Higher-order topological insulators and semimetals on the breathing kagome and pyrochlore lattices. Physical Review Letters, 2018, 120(2): 026801

    Google Scholar 

  85. Ezawa M. Minimal models for Wannier-type higher-order topological insulators and phosphorene. Physical Review B, 2018, 98(4): 045125

    MathSciNet  Google Scholar 

  86. Ezawa M. Magnetic second-order topological insulators and semimetals. Physical Review B, 2018, 97(15): 155305

    Google Scholar 

  87. 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

    Google Scholar 

  88. 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

    Google Scholar 

  89. Khalaf E. Higher-order topological insulators and superconductors protected by inversion symmetry. Physical Review B, 2018, 97(20): 205136

    Google Scholar 

  90. 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

    Google Scholar 

  91. 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

    Google Scholar 

  92. 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

    Google Scholar 

  93. van Miert G, Ortix C. Higher-order topological insulators protected by inversion and rotoinversion symmetries. Physical Review B, 2018, 98(8): 081110

    Google Scholar 

  94. 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

    Google Scholar 

  95. 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

    Google Scholar 

  96. 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

  97. Călugăru D, Juričić V, Roy B. Higher-order topological phases: a general principle of construction. Physical Review B, 2019, 99(4): 041301

    Google Scholar 

  98. Hu H, Huang B, Zhao E, Liu W V. Dynamical singularities of Floquet higher-order topological insulators. 2019, arXiv:1905. 03727v1

  99. 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

    Google Scholar 

  100. Kleinman D A. Nonlinear dielectric polarization in optical media. Physical Review, 1962, 126(6): 1977–1979

    Google Scholar 

  101. Adler E. Nonlinear optical frequency polarization in a dielectric. Physical Review, 1964, 134(3A): A728–A733

    Google Scholar 

  102. Miller R C. Optical second harmonic generation in piezoelectric crystals. Applied Physics Letters, 1964, 5(1): 17–19

    Google Scholar 

  103. 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

    Google Scholar 

  104. 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

    Google Scholar 

  105. 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

    Google Scholar 

  106. 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

    Google Scholar 

  107. 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

    Google Scholar 

  108. 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

    Google Scholar 

  109. 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

    Google Scholar 

  110. 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

    Google Scholar 

  111. 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

    Google Scholar 

  112. 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

    Google Scholar 

  113. 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

    Google Scholar 

  114. Zhu S, Zhu Y, Ming N. Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice. Science, 1997, 278(5339): 843–846

    Google Scholar 

  115. 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

    Google Scholar 

  116. 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

    Google Scholar 

  117. 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

    Google Scholar 

  118. 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

    Google Scholar 

  119. 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

    Google Scholar 

  120. 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

    Google Scholar 

  121. 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

    Google Scholar 

  122. 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

    MathSciNet  Google Scholar 

  123. 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

    MATH  Google Scholar 

  124. 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

    MathSciNet  Google Scholar 

  125. 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

    Google Scholar 

  126. 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

    MathSciNet  MATH  Google Scholar 

  127. Xiao M, Lin Q, Fan S. Hyperbolic Weyl point in reciprocal chiral metamaterials. Physical Review Letters, 2016, 117(5): 057401

    Google Scholar 

  128. 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

    Google Scholar 

  129. Fang C, Weng H, Dai X, Fang Z. Topological nodal line semimetals. Chinese Physics B, 2016, 25(11): 117106

    Google Scholar 

  130. 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

    Google Scholar 

  131. 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

    MathSciNet  MATH  Google Scholar 

  132. 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

    Google Scholar 

  133. 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

    Google Scholar 

  134. 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

    Google Scholar 

  135. 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

    Google Scholar 

  136. 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

    Google Scholar 

  137. 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

    Google Scholar 

  138. 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

    Google Scholar 

  139. 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

    Google Scholar 

  140. Chen Y, Chen H, Cai G. High transmission in a metal-based photonic crystal. Applied Physics Letters, 2018, 112(1): 013504

    Google Scholar 

  141. 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

    Google Scholar 

  142. 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

    Google Scholar 

  143. 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

    Google Scholar 

  144. 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

    Google Scholar 

  145. Karch A. Surface plasmons and topological insulators. Physical Review B, 2011, 83(24): 245432

    Google Scholar 

  146. 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

    Google Scholar 

  147. 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

    Google Scholar 

  148. 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

    Google Scholar 

  149. 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

    Google Scholar 

  150. Midya B, Zhao H, Feng L. Non-Hermitian photonics promises exceptional topology of light. Nature Communications, 2018, 9(1): 2674

    Google Scholar 

  151. 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

    MathSciNet  MATH  Google Scholar 

  152. Blanco-Redondo A, Bell B, Oren D, Eggleton B J, Segev M. Topological protection of biphoton states. Science, 2018, 362(6414): 568–571

    MathSciNet  MATH  Google Scholar 

  153. 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

    Google Scholar 

  154. 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

    Google Scholar 

  155. Heeger A J, Kivelson S, Schrieffer J R, Su W P. Solitons in conducting polymers. Reviews of Modern Physics, 1988, 60(3): 781–850

    Google Scholar 

  156. Su W P, Schrieffer J R, Heeger A J. Solitons in Polyacetylene. Physical Review Letters, 1979, 42(25): 1698–1701

    Google Scholar 

  157. Miri M-A, Alù A. Exceptional points in optics and photonics. Science, 2019, 363(6422): eaar7709

    MathSciNet  MATH  Google Scholar 

  158. 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

  159. Lee T E. Anomalous edge state in a non-Hermitian lattice. Physical Review Letters, 2016, 116(13): 133903

    Google Scholar 

  160. Ghatak A, Das T. New topological invariants in non-Hermitian systems. Journal of Physics Condensed Matter, 2019, 31(26): 263001

    Google Scholar 

  161. 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

    Google Scholar 

  162. 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

    Google Scholar 

  163. 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

    Google Scholar 

  164. Ota Y, Katsumi R, Watanabe K, Iwamoto S, Arakawa Y. Topological photonic crystal nanocavity laser. Communications on Physics, 2018, 1(1): 86

    Google Scholar 

  165. 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

    MathSciNet  Google Scholar 

  166. 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

    Google Scholar 

  167. Pilozzi L, Farrelly F A, Marcucci G, Conti C. Machine learning inrerse problem for topological photonics. Communications Physics, 2018, 1(1): 57

    Google Scholar 

  168. Long Y, Ren J, Li Y, Chen H. Inverse design of photonic topological state via machine learning. Applied Physics Letters, 2019, 114(18): 181105

    Google Scholar 

  169. Barth C, Becker C. Machine learning classification for field distributions of photonic modes. Communications on Physics, 2018, 1(1): 58

    Google Scholar 

  170. Fano U. Effects of configuration interaction on intensities and phase shifts. Physical Review, 1961, 124(6): 1866–1878

    MATH  Google Scholar 

  171. Limonov M F, Rybin M V, Poddubny A N, Kivshar Y S. Fano resonances in photonics. Nature Photonics, 2017, 11(9): 543–554

    Google Scholar 

  172. Miroshnichenko A E, Flach S, Kivshar Y S. Fano resonances in nanoscale structures. Reviews of Modern Physics, 2010, 82(3): 2257–2298

    Google Scholar 

  173. 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

    Google Scholar 

  174. 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

    Google Scholar 

  175. Zangeneh-Nejad F, Fleury R. Topological Fano resonances. Physical Review Letters, 2019, 122(1): 014301

    Google Scholar 

  176. Liang G Q, Chong Y D. Optical resonator analog of a two-dimensional topological insulator. Physical Review Letters, 2013, 110(20): 203904

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Key R&D Program of China (Nos. 2018YFA0306200, and 2017YFA0303702) and the National Natural Science Foundation of China (Grant Nos. 11625418, 51732006, and 11890700), as well as the Academic Program Development of Jiangsu Higher Education (PAPD).

Author information

Authors and Affiliations

  1. National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing, 210093, China

    Hongfei Wang, Samit Kumar Gupta, Biye Xie & Minghui Lu

  2. Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China

    Minghui Lu

  3. Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, 210093, China

    Minghui Lu

Authors
  1. Hongfei Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Samit Kumar Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Biye Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Minghui Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Minghui Lu.

Additional information

Hongfei Wang is a Ph.D. candidate in the Department of Materials Science and Engineering at Nanjing University. He spent his bachelor time at Anhui University during 2011–2015. His research topics include topological photonics, non-Hermitian photonics, and computational physics.

Dr. Samit Kumar Gupta received his Ph.D. in 2016 from the Department of Physics, Indian Institute of Technology Guwahati, India. Afterward, in 2017 he joined the College of Engineering and Applied Sciences, National Laboratory of Solid State Microstructures, Nanjing University as a Postdoc Fellow. His research interests include fundamental and applied aspects of nonlinear optics, nonlinear waves, non-Hermitianp hysics, and topological photonics.

Dr. Biye Xie spent his bachelor time at the University of Science and Technology of China. He received his Ph.D. degree in Physics from the University of Hong Kong, China. His research interest includes topological photonics, topological phononics, metamaterials, and quantum information.

Prof. Minghui Lu received his Ph.D. degree from Nanjing University in 2007. He is an Associate Professor at Nanjing University since 2009 and a Professor in 2013. He had been a visiting scholar at SIMES, Stanford University during 2011–2012. His current research interests mainly focus on fundamental study of photonic and acoustic artificial structures and metamaterials as well as their related applications.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wang, H., Gupta, S.K., Xie, B. et al. Topological photonic crystals: a review. Front. Optoelectron. 13, 50–72 (2020). https://doi.org/10.1007/s12200-019-0949-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12200-019-0949-7

Keywords

  • topological photonic crystals
  • topological phase transitions
  • non-Hermitian photonics
  • higher-order topological photonic crystals