1. Hasan, M. Z. and C. L. Kane, "Colloquium: Topological insulators," Reviews of Modern Physics, Vol. 82, No. 4, 3045-3067, 2010.
doi:10.1103/RevModPhys.82.3045 Google Scholar
2. Qi, X.-L. and S.-C. Zhang, "Topological insulators and superconductors," Reviews of Modern Physics, Vol. 83, No. 4, 1057-1110, 2011.
doi:10.1103/RevModPhys.83.1057 Google Scholar
3. Lu, L., J. D. Joannopoulos, and M. Soljacic, "Topological photonics," Nature Photonics, Vol. 8, No. 11, 821-829, 2014.
doi:10.1038/nphoton.2014.248 Google Scholar
4. Haldane, F. D. M. and S. Raghu, "Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry," Physical Review Letters, Vol. 100, No. 1, 013904, 2008.
doi:10.1103/PhysRevLett.100.013904 Google Scholar
5. Wang, Z., Y. D. Chong, J. D. Joannopoulos, and M. Soljacic, "Observation of unidirectional backscattering-immune topological electromagnetic states," Nature, Vol. 461, No. 7265, 772-775, 2009.
doi:10.1038/nature08293 Google Scholar
6. Hafezi, M., S. Mittal, J. Fan, A. Migdall, and J. M. Taylor, "Imaging topological edge states in silicon photonics," Nature Photonics, Vol. 7, No. 12, 1001-1005, 2013.
doi:10.1038/nphoton.2013.274 Google Scholar
7. Khanikaev, A. B., et al., "Photonic topological insulators," Nature Materials, Vol. 12, No. 3, 233-239, 2013.
doi:10.1038/nmat3520 Google Scholar
8. Wu, L. H. and X. Hu, "Scheme for achieving a topological photonic crystal by using dielectric material," Physical Review Letters, Vol. 114, No. 22, 223901, 2015.
doi:10.1103/PhysRevLett.114.223901 Google Scholar
9. Harari, G., M. A. Bandres, Y. Lumer, M. C. Rechtsman, Y. D. Chong, M. Khajavikhan, D. N. Christodoulides, and M. Segev, "Topological insulator laser: Theory," Science, Vol. 359, No. 6381, eaar4003, 2018.
doi:10.1126/science.aar4003 Google Scholar
10. Bandres, M. A., S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, "Topological insulator laser: Experiments," Science, Vol. 359, No. 5381, eaar4005, 2018.
doi:10.1126/science.aar4005 Google Scholar
11. Rechtsman, M. C., et al., "Photonic Floquet topological insulators," Nature, Vol. 496, No. 7444, 196-200, 2013.
doi:10.1038/nature12066 Google Scholar
12. Lin, H. and L. Lu, "Dirac-vortex topological photonic crystal fibre," Light: Science & Applications, Vol. 9, No. 1, 202, 2020.
doi:10.1038/s41377-020-00432-2 Google Scholar
13. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed., Princeton University Press, 2008.
14. Yablonovitch, E., "Inhibited spontaneous emission in solid-state physics and electronics," Physical Review Letters, Vol. 58, No. 20, 2059-2062, 1987.
doi:10.1103/PhysRevLett.58.2059 Google Scholar
15. John, S., "Strong localization of photons in certain disordered dielectric superlattices," Physical Review Letters, Vol. 58, No. 23, 2486-2489, 1987.
doi:10.1103/PhysRevLett.58.2486 Google Scholar
16. Zhu, W., X. Fang, D. Li, Y. Sun, Y. Li, Y. Jing, and H. Chen, "Simultaneous observation of a topological edge state and exceptional point in an open and non-Hermitian acoustic system," Physical Review Letters, Vol. 121, No. 12, 124501, 2018.
doi:10.1103/PhysRevLett.121.124501 Google Scholar
17. Zhu, S. and X. Zhang, "Metamaterials: Artificial materials beyond nature," National Science Review, Vol. 5, No. 2, 131-131, 2018.
doi:10.1093/nsr/nwy026 Google Scholar
18. Pendry, J. B., "Negative refraction makes a perfect lens," Physical Review Letters, Vol. 85, No. 18, 3966-3969, 2000.
doi:10.1103/PhysRevLett.85.3966 Google Scholar
19. Ahn, D., J. Park, C. Kim, J. Kim, Y. Qian, and T. Itoh, "A design of the low-pass filter using the novel microstrip defected ground structure," IEEE Transactions on Microwave Theory and Techniques, Vol. 49, No. 1, 86-93, 2001.
doi:10.1109/22.899965 Google Scholar
20. Pendry, J. B., D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science, Vol. 312, No. 5781, 1780-1782, 2006.
doi:10.1126/science.1125907 Google Scholar
21. Schurig, D., J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, "Metamaterial electromagnetic cloak at microwave frequencies," Science, Vol. 314, No. 5801, 977-980, 2006.
doi:10.1126/science.1133628 Google Scholar
22. Fang, N., H. Lee, C. Sun, and X. Zhang, "Sub-diffraction-limited optical imaging with a silver superlens," Science, Vol. 308, No. 5721, 534-537, 2005.
doi:10.1126/science.1108759 Google Scholar
23. Cui, T. J., M. Q. Qi, X.Wan, J. Zhao, and Q. Cheng, "Coding metamaterials, digital metamaterials and programmable metamaterials," Light: Science & Applications, Vol. 3, e218, 2014.
doi:10.1038/lsa.2014.99 Google Scholar
24. Liu, W., Z. N. Chen, and X. Qing, "Metamaterial-based low-profile broadband mushroom antenna," IEEE Transactions on Antennas and Propagation, Vol. 62, No. 3, 1165-1172, 2014.
doi:10.1109/TAP.2013.2293788 Google Scholar
25. Hao, J., Y. Yuan, L. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, "Manipulating electromagnetic wave polarizations by anisotropic metamaterials," Physical Review Letters, Vol. 99, No. 6, 063908, 2007.
doi:10.1103/PhysRevLett.99.063908 Google Scholar
26. Cai, T., et al., "High-efficiency and full-space manipulation of electromagnetic wave fronts with metasurfaces," Physical Review Applied, Vol. 8, No. 3, 034033, 2017.
doi:10.1103/PhysRevApplied.8.034033 Google Scholar
27. Su, W. P., J. R. Schrieffer, and A. J. Heeger, "Solitons in polyacetylene," Physical Review Letters, Vol. 42, No. 25, 1698-1701, 1979.
doi:10.1103/PhysRevLett.42.1698 Google Scholar
28. Malkova, N., I. Hromada, X. Wang, G. Bryant, and Z. Chen, "Observation of optical Shockley-like surface states in photonic superlattices," Optics Letters, Vol. 34, No. 11, 1633-1635, 2009.
doi:10.1364/OL.34.001633 Google Scholar
29. Tan, W., Y. Sun, H. Chen, and S.-Q. Shen, "Photonic simulation of topological excitations in metamaterials," Scientific Reports, Vol. 4, 3842, 2014.
doi:10.1038/srep03842 Google Scholar
30. Poshakinskiy, A. V., A. N. Poddubny, L. Pilozzi, and E. L. Ivchenko, "Radiative topological states in resonant photonic crystals," Physical Review Letters, Vol. 112, No. 10, 107403, 2014.
doi:10.1103/PhysRevLett.112.107403 Google Scholar
31. Xiao, M., Z. Q. Zhang, and C. T. Chan, "Surface impedance and bulk band geometric phases in one-dimensional systems," Physical Review X, Vol. 4, No. 2, 021017, 2014.
doi:10.1103/PhysRevX.4.021017 Google Scholar
32. Poddubny, A., A. Miroshnichenko, A. Slobozhanyuk, and Y. Kivshar, "Topological Majorana states in zigzag chains of plasmonic nanoparticles," ACS Photonics, Vol. 1, No. 2, 101-105, 2014.
doi:10.1021/ph4000949 Google Scholar
33. Ling, C. W., M. Xiao, S. F. Yu, and K. H. Fung, "Topological edge plasmon modes between diatomic chains of nanoparticles," Optics Express, Vol. 23, No. 3, 2021-2031, 2015.
doi:10.1364/OE.23.002021 Google Scholar
34. Poli, C., M. Bellec, U. Kuhl, F. Mortessagne, and H. Schomerus, "Selective enhancement of topologically induced interface states," Nature Communications, Vol. 6, 6710, 2015.
doi:10.1038/ncomms7710 Google Scholar
35. Shen, S. Q., Topological Insulators: Dirac Equation in Condensed Matter, 2nd Ed., Springer, 2017.
doi:10.1007/978-981-10-4606-3
36. Guan, G., H. Jiang, H. Li, Y. Zhang, H. Chen, and S. Y. Zhu, "Tunneling modes of photonic heterostructures consisting of single-negative materials," Applied Physics Letters, Vol. 88, No. 21, 211112, 2006.
doi:10.1063/1.2207218 Google Scholar
37. Guo, J., H. Chen, H. Li, and Y. Zhang, "Effective permittivity and permeability of one dimensional dielectric photonic crystal within a band gap," Chinese Physics B, Vol. 17, No. 7, 2544-2552, 2008.
doi:10.1088/1674-1056/17/7/034 Google Scholar
38. Shi, X., C. Xue, H. Jiang, and H. Chen, "Topological description for gaps of one-dimensional symmetric all-dielectric photonic crystals," Optics Express, Vol. 24, No. 16, 18580-18581, 2016.
doi:10.1364/OE.24.018580 Google Scholar
39. Huang, Q., Z. Guo, J. Feng, C. Yu, H. Jiang, Z. Zhang, Z. Wang, and H. Chen, "Observation of a topological edge state in the X-ray band," Laser & Photonics Reviews, Vol. 13, No. 6, 1800339, 2019.
doi:10.1002/lpor.201800339 Google Scholar
40. Wang, Q., M. Xiao, H. Liu, S. N. Zhu, and C. T. Chan, "Measurement of the Zak phase of photonic bands through the interface states of a metasurface/photonic crystal," Physical Review B, Vol. 93, No. 4, 041415, 2016.
doi:10.1103/PhysRevB.93.041415 Google Scholar
41. Lemoult, F., N. Kaina, M. Fink, G. Lerosey, and , "Wave propagation control at the deep subwavelength scale in metamaterials," Nature Physics, Vol. 9, No. 1, 55-60, 2013.
doi:10.1038/nphys2480 Google Scholar
42. Fan, L., W. W. Yu, S. Y. Zhang, H. Zhang, and J. Ding, "Zak phases and band properties in acoustic metamaterials with negative modulus or negative density," Physical Review B, Vol. 94, No. 17, 174307, 2016.
doi:10.1103/PhysRevB.94.174307 Google Scholar
43. Zhu, W., Y.-Q. Ding, J. Ren, Y. Sun, Y. Li, H. Jiang, and H. Chen, "Zak phase and band inversion in dimerized one-dimensional locally resonant metamaterials," Physical Review B, Vol. 97, No. 19, 195307, 2018.
doi:10.1103/PhysRevB.97.195307 Google Scholar
44. Fan, C., X. Shi, F. Wu, Y. Li, H. Jiang, Y. Sun, and H. Chen, "Photonic topological transition in dimerized chains with the joint modulation of near-field and far-field couplings," Photonics Research, Vol. 10, No. 1, 41-49, 2022.
doi:10.1364/PRJ.441278 Google Scholar
45. Verbin, M., O. Zilberberg, Y. E. Kraus, Y. Lahini, and Y. Silberberg, "Observation of topological phase transitions in photonic quasicrystals," Physical Review Letters, Vol. 110, No. 7, 076403, 2013.
doi:10.1103/PhysRevLett.110.076403 Google Scholar
46. Lang, L., X. Cai, and S. Chen, "Edge states and topological phases in one-dimensional optical superlattices," Physical Review Letters, Vol. 108, No. 21, 220401, 2012.
doi:10.1103/PhysRevLett.108.220401 Google Scholar
47. Kraus, Y. E., Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, "Topological states and adiabatic pumping in quasicrystals," Physical Review Letters, Vol. 109, No. 10, 106402, 2012.
doi:10.1103/PhysRevLett.109.106402 Google Scholar
48. Feng, L., Y.-L. Xu, W. S. Fegadolli, M.-H. Lu, J. E. B. Oliveira, V. R. Almeida, Y.-F. Chen, and A. Scherer, "Experimental demonstration of a unidirectional reflectionless parity-time metamaterial at optical frequencies," Nature Materials, Vol. 12, No. 2, 108-113, 2013.
doi:10.1038/nmat3495 Google Scholar
49. Shi, X., Y. Sun, C. Xue, and X. Hu, "Prediction of interface states in liquid surface waves with one-dimensional modulation," Physics Letters A, Vol. 383, No. 17, 2106-2109, 2019.
doi:10.1016/j.physleta.2019.04.002 Google Scholar
50. Zhang, D., J. Ren, T. Zhou, and B. Li, "Dark state, zero-index and topology in phononic metamaterials with negative mass and negative coupling," New Journal of Physics, Vol. 21, 093033, 2019.
doi:10.1088/1367-2630/ab3f6d Google Scholar
51. Jiang, J., Z. W. Guo, Y. Q. Ding, Y. Sun, Y. H. Li, H. T. Jiang, and H. Chen, "Experimental demonstration of the robust edge states in a split-ring-resonator chain," Optics Express, Vol. 26, No. 10, 12891-12902, 2018.
doi:10.1364/OE.26.012891 Google Scholar
52. Bellec, M., U. Kuhl, G. Montambaux, and F. Mortessagne, "Tight-binding couplings in microwave artificial graphene," Physical Review B, Vol. 88, No. 11, 115437, 2013.
doi:10.1103/PhysRevB.88.115437 Google Scholar
53. Atala, M., M. Aidelsburger, J. T. Barreiro, D. Abanin, T. Kitagawa, E. Demler, and I. Bloch, "Direct measurement of the Zak phase in topological Bloch bands," Nature Physics, Vol. 9, No. 12, 795-800, 2013.
doi:10.1038/nphys2790 Google Scholar
54. Xiao, M., G. Ma, Z. Yang, P. Sheng, Z. Q. Zhang, and C. T. Chan, "Geometric phase and band inversion in periodic acoustic systems," Nature Physics, Vol. 11, No. 3, 240-244, 2015.
doi:10.1038/nphys3228 Google Scholar
55. Jiang, J., J. Ren, Z. W. Guo, W. W. Zhu, Y. Long, H. T. Jiang, and H. Chen, "Seeing topological winding number and band inversion in photonic dimer chain of split-ring resonators," Physical Review B, Vol. 101, No. 16, 165427, 2020.
doi:10.1103/PhysRevB.101.165427 Google Scholar
56. Ashcroft, N. W. and N. D. Mermin, Solid State Physics, Saunders College Publishing, 1976.
57. Guo, Z. W., J. Jiang, H. T. Jiang, J. Ren, and H. Chen, "Observation of topological bound states in a double Su-Schrieffer-Heeger chain composed of split ring resonators," Physical Review Research, Vol. 3, No. 1, 013122, 2021.
doi:10.1103/PhysRevResearch.3.013122 Google Scholar
58. Guo, Z. W., H. T. Jiang, Y. Sun, Y. H. Li, and H. Chen, "Asymmetric topological edge states in a quasiperiodic Harper chain composed of split-ring resonators," Optics Letters, Vol. 43, No. 20, 5142-5145, 2018.
doi:10.1364/OL.43.005142 Google Scholar
59. Hafezi, M., E. A. Delmer, M. D. Lukin, and J. M. Taylor, "Robust optical delay lines with topological protection," Nature Physics, Vol. 7, No. 11, 907-912, 2011.
doi:10.1038/nphys2063 Google Scholar
60. Song, J., F. Yang, Z. Guo, X.Wu, K. Zhu, J. Jiang, Y. Sun, Y. Li, H. Jiang, and H. Chen, "Wireless power transfer via topological modes in dimer chains," Physical Review Applied, Vol. 15, No. 1, 014009, 2021.
doi:10.1103/PhysRevApplied.15.014009 Google Scholar
61. Zhang, L., et al., "Demonstration of topological wireless power transfer," Science Bulletin, Vol. 66, No. 10, 974-980, 2021.
doi:10.1016/j.scib.2021.01.028 Google Scholar
62. Zeng, C., Y. Sun, G. Li, Y. Li, H. Jiang, Y. Yang, and H. Chen, "Enhanced sensitivity at high-order exceptional points in a passive wireless sensing system," Optics Express, Vol. 27, No. 20, 27562-27572, 2019.
doi:10.1364/OE.27.027562 Google Scholar
63. Yang, F., et al., "Actively controlled asymmetric edge states for directional wireless power transfer," Optics Express, Vol. 29, No. 5, 7844-7857, 2021.
doi:10.1364/OE.417887 Google Scholar
64. Hodaei, H., A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-Ganainy, D. N. Christodoulides, and M. Khajavikhan, "Enhanced sensitivity at higher-order exceptional points," Nature, Vol. 548, No. 7666, 187-191, 2017.
doi:10.1038/nature23280 Google Scholar
65. Chen, W. J., S. K. Ozdemir, G. M. Zhao, J. Wiersig, and L. Yang, "Exceptional points enhance sensing in an optical microcavity," Nature, Vol. 548, No. 7666, 192-196, 2017.
doi:10.1038/nature23281 Google Scholar
66. Chen, P. Y. and R. El-Ganainy, "Exceptional points enhance wireless readout," Nature Electronics, Vol. 2, 323-324, 2019.
doi:10.1038/s41928-019-0293-3 Google Scholar
67. Guo, Z. W., T. Zhang, J. Song, H. Jiang, and H. Chen, "Sensitivity of topological edge states in a non-Hermitian dimer chain," Photonics Research, Vol. 9, No. 4, 574-582, 2021.
doi:10.1364/PRJ.413873 Google Scholar
68. Wu, J., F. Wu, K. Lv, Z. Guo, H. Jiang, Y. Sun, Y. Li, and H. Chen, "Giant Goos-Hanchen shift with a high reflectance assisted by interface states in photonic heterostructures," Physical Review A, Vol. 101, No. 5, 053838, 2020.
doi:10.1103/PhysRevA.101.053838 Google Scholar
69. Wang, Q., M. Xiao, H. Liu, S. Zhu, and C. T. Chan, "Optical interface states protected by synthetic weyl points," Physical Review X, Vol. 7, No. 3, 031032, 2017.
doi:10.1103/PhysRevX.7.031032 Google Scholar
70. Dong, L., H. Jiang, H. Chen, and Y. Shi, "Enhancement of Faraday rotation effect in heterostructures with magneto-optical metals," Journal of Applied Physics, Vol. 107, No. 9, 093101, 2010.
doi:10.1063/1.3406152 Google Scholar
71. Du, G., H. Jiang, Z. Wang, and H. Chen, "Optical nonlinearity enhancement in heterostructures with thick metallic film and truncated photonic crystals," Optics Letters, Vol. 34, No. 5, 578-580, 2009.
doi:10.1364/OL.34.000578 Google Scholar
72. Bergholtz, E. J., J. C. Budich, and F. K. Kunst, "Exceptional topology of non-Hermitian systems," Review of Modern Physics, Vol. 93, No. 1, 015005, 2021.
doi:10.1103/RevModPhys.93.015005 Google Scholar
73. Yao, S. Y. and Z. Wang, "Edge states and topological invariants of non-Hermitian systems," Physical Review Letters, Vol. 121, No. 8, 086803, 2018.
doi:10.1103/PhysRevLett.121.086803 Google Scholar
74. Lee, T. E., "Anomalous edge state in a non-Hermitian lattice," Physical Review Letters, Vol. 116, No. 13, 133903, 2016.
doi:10.1103/PhysRevLett.116.133903 Google Scholar
75. Xiong, Y., "Why does bulk boundary correspondence fail in some non-Hermitian topological models," Journal of Physics Communications, Vol. 2, No. 3, 035043, 2018.
doi:10.1088/2399-6528/aab64a Google Scholar
76. Helbig, T., et al., "Generalized bulk-boundary correspondence in non-Hermitian topolectrical circuits," Nature Physics, Vol. 16, No. 7, 747, 2020.
doi:10.1038/s41567-020-0922-9 Google Scholar
77. Okuma, N. and M. Sato, "Hermitian zero modes protected by nonnormality: Application of pseudospectra," Physical Review B, Vol. 102, No. 1, 014203, 2020.
doi:10.1103/PhysRevB.102.014203 Google Scholar
78. Budich, J. C. and E. J. Bergholtz, "Non-Hermitian topological sensors," Physical Review Letters, Vol. 125, No. 18, 180403, 2020.
doi:10.1103/PhysRevLett.125.180403 Google Scholar
79. Li, J., R. Chu, J. Jain, and S.-Q. Shen, "Topological anderson insulator," Physical Review Letters, Vol. 102, No. 13, 136806, 2009.
doi:10.1103/PhysRevLett.102.136806 Google Scholar
80. Zhang, Z., B. Wu, J. Song, and H. Jiang, "Topological anderson insulator in electric circuits," Physical Review B, Vol. 100, No. 18, 184202, 2019.
doi:10.1103/PhysRevB.100.184202 Google Scholar
81. Stutzer, S., et al., "Photonic topological Anderson insulators," Nature, Vol. 560, 461-465, 2018.
doi:10.1038/s41586-018-0418-2 Google Scholar
82. Liu, G., e al., "Topological Anderson insulator in disordered photonic crystals," Physical Review Letters, Vol. 125, No. 13, 133603, 2020.
doi:10.1103/PhysRevLett.125.133603 Google Scholar
83. Meier, E. J., F. A. An, A. Dauphin, M. Maffei, P. Massignan, T. L. Hughes, and B. Gadway, "Observation of the topological Anderson insulator in disordered atomic wires," Science, Vol. 362, 929, 2018.
doi:10.1126/science.aat3406 Google Scholar
84. Lin, Q., T. Lin, L. Xiao, K. Wang, W. Yi, and P. Xue, "Observation of non-Hermitian topological Anderson insulator in quantum dynamics," Nature Communications, Vol. 13, 3229, 2022.
doi:10.1038/s41467-022-30938-9 Google Scholar