[1] L. Lu, J. D. Joannopoulos, M. Soljačić. Topological photonics. Nat. Photonics, 8, 821-829(2014).

[2] A. B. Khanikaev, G. Shvets. Two-dimensional topological photonics. Nat. Photonics, 11, 763-773(2017).

[3] T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, I. Carusotto. Topological photonics. Rev. Mod. Phys., 91, 015006(2019).

[4] H. Wang, S. K. Gupta, B. Xie, M. Lu. Topological photonic crystals: a review. Front. Optoelectron., 13, 50-72(2020).

[5] Z. Wang, Y. Chong, J. D. Joannopoulos, M. Soljačić. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature, 461, 772-775(2009).

[6] M. Hafezi, S. Mittal, J. Fan, A. Migdall, J. M. Taylor. Imaging topological edge states in silicon photonics. Nat. Photonics, 7, 1001-1005(2013).

[7] M. Hafezi, E. A. Demler, M. D. Lukin, J. M. Taylor. Robust optical delay lines with topological protection. Nat. Phys., 7, 907-912(2011).

[8] K. Lai, T. Ma, X. Bo, S. Anlage, G. Shvets. Experimental realization of a reflections-free compact delay line based on a photonic topological insulator. Sci. Rep., 6, 28453(2016).

[9] A. Kodigala, T. Lepetit, Q. Gu, B. Bahari, Y. Fainman, B. Kante. Lasing action from photonic bound states in continuum. Nature, 541, 196-199(2017).

[10] Z.-K. Shao, H.-Z. Chen, S. Wang, X.-R. Mao, Z.-Q. Yang, S.-L. Wang, X.-X. Wang, X. Hu, R.-M. Ma. A high-performance topological bulk laser based on band-inversion-induced reflection. Nat. Nanotechnol., 15, 67-72(2020).

[11] Y. Zeng, U. Chattopadhyay, B. Zhu, B. Qiang, J. Li, Y. Jin, L. Li, A. G. Davies, E. H. Linfield, B. Zhang, Y. Chong, Q. J. Wang. Electrically pumped topological laser with valley edge modes. Nature, 578, 246-250(2020).

[12] K. V. Klitzing, G. Dorda, M. Pepper. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett., 45, 494-497(1980).

[13] D. J. Thouless, M. Kohmoto, M. P. Nightingale, M. den Nijs. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett., 49, 405-408(1982).

[14] M. Z. Hasan, C. L. Kane. Colloquium: topological insulators. Rev. Mod. Phys., 82, 3045-3067(2010).

[15] J. E. Moore. The birth of topological insulators. Nature, 464, 194-198(2010).

[16] Y. Hatsugai. Chern number and edge states in the integer quantum Hall effect. Phys. Rev. Lett., 71, 3697-3700(1993).

[17] Y. Hatsugai. Edge states in the integer quantum Hall effect and the Riemann surface of the Bloch function. Phys. Rev. B, 48, 11851-11862(1993).

[18] X.-L. Qi, Y.-S. Wu, S.-C. Zhang. General theorem relating the bulk topological number to edge states in two-dimensional insulators. Phys. Rev. B, 74, 045125(2006).

[19] C. L. Kane, E. J. Mele. Quantum spin Hall effect in graphene. Phys. Rev. Lett., 95, 226801(2005).

[20] C. L. Kane, E. J. Mele. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett., 95, 146802(2005).

[21] B. A. Bernevig, S.-C. Zhang. Quantum spin Hall effect. Phys. Rev. Lett., 96, 106802(2006).

[22] J. E. Moore, L. Balents. Topological invariants of time-reversal-invariant band structures. Phys. Rev. B, 75, 121306(2007).

[23] L. Fu, C. L. Kane. Topological insulators with inversion symmetry. Phys. Rev. B, 76, 045302(2007).

[24] L. Fu, C. L. Kane, E. J. Mele. Topological insulators in three dimensions. Phys. Rev. Lett., 98, 106803(2007).

[25] B. A. Bernevig, T. L. Hughes, S.-C. Zhang. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science, 314, 1757-1761(2006).

[26] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, M. Z. Hasan. A topological Dirac insulator in a quantum spin Hall phase. Nature, 452, 970-974(2008).

[27] H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, S.-C. Zhang. Topological insulators in Bi₂Se₃, Bi₂Te₃ and Sb₂Te₃ with a single Dirac cone on the surface. Nat. Phys., 5, 438-442(2009).

[28] Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, Z.-X. Shen. Experimental realization of a three-dimensional topological insulator, Bi₂Te₃. Science, 325, 178-181(2009).

[29] M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, S.-C. Zhang. Quantum spin Hall insulator state in HGTE quantum wells. Science, 318, 766-770(2007).

[30] M. Ezawa. Symmetry protected topological charge in symmetry broken phase: spin-Chern, spin-valley-Chern and mirror-Chern numbers. Phys. Lett. A, 378, 1180-1184(2014).

[31] A. F. Morpurgo, F. Guinea. Intervalley scattering, long-range disorder, and effective time-reversal symmetry breaking in graphene. Phys. Rev. Lett., 97, 196804(2006).

[32] A. Rycerz, J. Tworzydlo, C. W. J. Beenakker. Valley filter and valley valve in graphene. Nat. Phys., 3, 172-175(2007).

[33] L. Ju, Z. Shi, N. Nair, Y. Lv, C. Jin, J. Velasco, C. Ojeda-Aristizabal, H. A. Bechtel, M. C. Martin, A. Zettl, J. Analytis, F. Wang. Topological valley transport at bilayer graphene domain walls. Nature, 520, 650-655(2015).

[34] T. Ma, G. Shvets. All-Si valley-Hall photonic topological insulator. New J. Phys., 18, 025012(2016).

[35] J. Noh, S. Huang, K. P. Chen, M. C. Rechtsman. Observation of photonic topological valley Hall edge states. Phys. Rev. Lett., 120, 063902(2018).

[36] F. Gao, H. Xue, Z. Yang, K. Lai, Y. Yu, X. Lin, Y. Chong, G. Shvets, B. Zhang. Topologically protected refraction of robust kink states in valley photonic crystals. Nat. Phys., 14, 140-144(2018).

[37] M. Ezawa. Spin valleytronics in silicene: quantum spin Hall-quantum anomalous Hall insulators and single-valley semimetals. Phys. Rev. B, 87, 155415(2013).

[38] J.-W. Dong, X.-D. Chen, H. Zhu, Y. Wang, X. Zhang. Valley photonic crystals for control of spin and topology. Nat. Mater., 16, 298-302(2017).

[39] S. Ryu, Y. Hatsugai. Topological origin of zero-energy edge states in particle-hole symmetric systems. Phys. Rev. Lett., 89, 077002(2002).

[40] J. Zak. Berry’s phase for energy bands in solids. Phys. Rev. Lett., 62, 2747-2750(1989).

[41] W. P. Su, J. R. Schrieffer, A. J. Heeger. Solitons in polyacetylene. Phys. Rev. Lett., 42, 1698-1701(1979).

[42] J. C. Y. Teo, L. Fu, C. L. Kane. Surface states and topological invariants in three-dimensional topological insulators: application to Bi_1-xSb_x. Phys. Rev. B, 78, 045426(2008).

[43] R. Takahashi, S. Murakami. Gapless interface states between topological insulators with opposite Dirac velocities. Phys. Rev. Lett., 107, 166805(2011).

[44] T. H. Hsieh, H. Lin, J. Liu, W. Duan, A. Bansil, L. Fu. Topological crystalline insulators in the SnTe material class. Nat. Commun., 3, 982(2012).

[45] L. Fu. Topological crystalline insulators. Phys. Rev. Lett., 106, 106802(2011).

[46] F. D. M. Haldane, S. Raghu. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett., 100, 013904(2008).

[47] M. Sato, K. Hasebe, K. Esaki, M. Kohmoto. Time-reversal symmetry in non-Hermitian systems. Progr. Theoret. Phys., 127, 937-974(2012).

[48] K. Esaki, M. Sato, K. Hasebe, M. Kohmoto. Edge states and topological phases in non-Hermitian systems. Phys. Rev. B, 84, 205128(2011).

[49] F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J. D. Joannopoulos, M. Soljačić, H. Chen, L. Lu, Y. Chong, B. Zhang. Probing topological protection using a designer surface plasmon structure. Nat. Commun., 7, 11619(2016).

[50] V. M. Martinez Alvarez, J. E. Barrios Vargas, M. Berdakin, L. E. F. Torres. Topological states of non-Hermitian systems. Eur. Phys. J. Spec. Top., 227, 1295-1308(2018).

[51] H. Shen, B. Zhen, L. Fu. Topological band theory for non-Hermitian Hamiltonians. Phys. Rev. Lett., 120, 146402(2018).

[52] T. Kato. Perturbation Theory in a Finite-Dimensional Space, 62-126(1995).

[53] K. Kawabata, T. Bessho, M. Sato. Classification of exceptional points and non-Hermitian topological semimetals. Phys. Rev. Lett., 123, 066405(2019).

[54] B. Peng, Å. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yılmaz, J. Wiersig, S. Rotter, L. Yang. Chiral modes and directional lasing at exceptional points. Proc. Natl. Acad. Sci. USA, 113, 6845-6850(2016).

[55] A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim. The electronic properties of graphene. Rev. Mod. Phys., 81, 109-162(2009).

[56] S. M. Young, S. Zaheer, J. C. Y. Teo, C. L. Kane, E. J. Mele, A. M. Rappe. Dirac semimetal in three dimensions. Phys. Rev. Lett., 108, 140405(2012).

[57] X. Wan, A. M. Turner, A. Vishwanath, S. Y. Savrasov. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iriyears. Phys. Rev. B, 83, 205101(2011).

[58] A. A. Burkov, L. Balents. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett., 107, 127205(2011).

[59] L. Lu, L. Fu, J. D. Joannopoulos, M. Soljačić. Weyl points and line nodes in gyroid photonic crystals. Nat. Photonics, 7, 294-299(2013).

[60] M. V. Berry. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. London A, 392, 45-57(1984).

[61] A. A. Mailybaev, O. N. Kirillov, A. P. Seyranian. Geometric phase around exceptional points. Phys. Rev. A, 72, 014104(2005).

[62] S.-D. Liang, G.-Y. Huang. Topological invariance and global Berry phase in non-Hermitian systems. Phys. Rev. A, 87, 012118(2013).

[63] L. Feng, R. El-Ganainy, L. Ge. Non-Hermitian photonics based on parity-time symmetry. Nat. Photonics, 11, 752-762(2017).

[64] R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, D. N. Christodoulides. Non-Hermitian physics and PT symmetry. Nat. Phys., 14, 11-19(2018).

[65] S. K. Ozdemir, S. Rotter, F. Nori, L. Yang. Parity-time symmetry and exceptional points in photonics. Nat. Mater., 18, 783-798(2019).

[66] D. Leykam, K. Y. Bliokh, C. Huang, Y. D. Chong, F. Nori. Edge modes, degeneracies, and topological numbers in non-Hermitian systems. Phys. Rev. Lett., 118, 040401(2017).

[67] T. E. Lee. Anomalous edge state in a non-Hermitian lattice. Phys. Rev. Lett., 116, 133903(2016).

[68] S. Lin, L. Jin, Z. Song. Symmetry protected topological phases characterized by isolated exceptional points. Phys. Rev. B, 99, 165148(2019).

[69] A. Mostafazadeh, H. Mehri-Dehnavi. Spectral singularities, biorthonormal systems and a two-parameter family of complex point interactions. J. Phys. A, 42, 125303(2009).

[70] A. Mostafazadeh. Spectral singularities of complex scattering potentials and infinite reflection and transmission coefficients at real energies. Phys. Rev. Lett., 102, 220402(2009).

[71] P. Wang, L. Jin, G. Zhang, Z. Song. Wave emission and absorption at spectral singularities. Phys. Rev. A, 94, 053834(2016).

[72] L. Jin, Z. Song. Incident direction independent wave propagation and unidirectional lasing. Phys. Rev. Lett., 121, 073901(2018).

[73] S. Yao, Z. Wang. Edge states and topological invariants of non-Hermitian systems. Phys. Rev. Lett., 121, 086803(2018).

[74] S. Yao, F. Song, Z. Wang. Non-Hermitian Chern bands. Phys. Rev. Lett., 121, 136802(2018).

[75] F. Song, S. Yao, Z. Wang. Non-Hermitian skin effect and chiral damping in open quantum systems. Phys. Rev. Lett., 123, 170401(2019).

[76] C. H. Lee, R. Thomale. Anatomy of skin modes and topology in non-Hermitian systems. Phys. Rev. B, 99, 201103(2019).

[77] N. Okuma, K. Kawabata, K. Shiozaki, M. Sato. Topological origin of non-Hermitian skin effects. Phys. Rev. Lett., 124, 086801(2020).

[78] V. M. Martinez Alvarez, J. E. B. Vargas, L. E. F. Torres. Non-Hermitian robust edge states in one dimension: anomalous localization and eigenspace condensation at exceptional points. Phys. Rev. B, 97, 121401(2018).

[79] F. K. Kunst, E. Edvardsson, J. C. Budich, E. J. Bergholtz. Biorthogonal bulk-boundary correspondence in non-Hermitian systems. Phys. Rev. Lett., 121, 026808(2018).

[80] L. Jin, Z. Song. Bulk-boundary correspondence in a non-Hermitian system in one dimension with chiral inversion symmetry. Phys. Rev. B, 99, 081103(2019).

[81] K. Yokomizo, S. Murakami. Non-Bloch band theory of non-Hermitian systems. Phys. Rev. Lett., 123, 066404(2019).

[82] F. Song, S. Yao, Z. Wang. Non-Hermitian topological invariants in real space. Phys. Rev. Lett., 123, 246801(2019).

[83] A. Ghatak, T. Das. New topological invariants in non-Hermitian systems. J. Phys. Condens. Matter, 31, 263001(2019).

[84] K. Kawabata, K. Shiozaki, M. Ueda, M. Sato. Symmetry and topology in non-Hermitian physics. Phys. Rev. X, 9, 041015(2019).

[85] C. Yin, H. Jiang, L. Li, R. Lü, S. Chen. Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems. Phys. Rev. A, 97, 052115(2018).

[86] H. Zhou, J. Y. Lee. Periodic table for topological bands with non-Hermitian symmetries. Phys. Rev. B, 99, 235112(2019).

[87] L. Xiao, T. Deng, K. Wang, G. Zhu, Z. Wang, W. Yi, P. Xue. Non-Hermitian bulk-boundary correspondence in quantum dynamics. Nat. Phys., 16, 761-766(2020).

[88] S. Weidemann, M. Kremer, T. Helbig, T. Hofmann, A. Stegmaier, M. Greiter, R. Thomale, A. Szameit. Topological funneling of light. Science, 368, 311-314(2020).

[89] J. von Neuman, E. Wigner. Uber merkwurdige diskrete Eigenwerte. Uber das Verhalten von eigenwerten bei adiabatischen prozessen. Phys. Z., 30, 467-470(1929).

[90] H. Friedrich, D. Wintgen. Interfering resonances and bound states in the continuum. Phys. Rev. A, 32, 3231-3242(1985).

[91] C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, M. Soljačić. Bound states in the continuum. Nat. Rev. Mater., 1, 16048(2016).

[92] N. D. Mermin. The topological theory of defects in ordered media. Rev. Mod. Phys., 51, 591-648(1979).

[93] H. Zhou, C. Peng, Y. Yoon, C. W. Hsu, K. A. Nelson, L. Fu, J. D. Joannopoulos, M. Soljačić, B. Zhen. Observation of bulk Fermi arc and polarization half charge from paired exceptional points. Science, 359, 1009-1012(2018).

[94] D. C. Tsui, H. L. Stormer, A. C. Gossard. Two-dimensional magneto transport in the extreme quantum limit. Phys. Rev. Lett., 48, 1559-1562(1982).

[95] S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, M. Z. Hasan. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science, 349, 613-617(2015).

[96] L. Lu, Z. Wang, D. Ye, L. Ran, L. Fu, J. D. Joannopoulos, M. Soljačić. Experimental observation of Weyl points. Science, 349, 622-624(2015).

[97] S.-C. Zhang, J. Hu. A four-dimensional generalization of the quantum Hall effect. Science, 294, 823-828(2001).

[98] Y. E. Kraus, Z. Ringel, O. Zilberberg. Four-dimensional quantum Hall effect in a two-dimensional quasicrystal. Phys. Rev. Lett., 111, 226401(2013).

[99] S. John. Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett., 58, 2486-2489(1987).

[100] E. Yablonovitch. Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett., 58, 2059-2062(1987).

[101] S. Fan, J. D. Joannopoulos. Analysis of guided resonances in photonic crystal slabs. Phys. Rev. B, 65, 235112(2002).

[102] L. Ni, Z. Wang, C. Peng, Z. Li. Tunable optical bound states in the continuum beyond in-plane symmetry protection. Phys. Rev. B, 94, 245148(2016).

[103] Y. Yang, C. Peng, Y. Liang, Z. Li, S. Noda. Analytical perspective for bound states in the continuum in photonic crystal slabs. Phys. Rev. Lett., 113, 037401(2014).

[104] W. Chen, Y. Chen, W. Liu. Singularities and Poincaré indices of electromagnetic multipoles. Phys. Rev. Lett., 122, 153907(2019).

[105] Z. Sadrieva, K. Frizyuk, M. Petrov, Y. Kivshar, A. Bogdanov. Multipolar origin of bound states in the continuum. Phys. Rev. B, 100, 115303(2019).

[106] B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, M. Soljačić. Topological nature of optical bound states in the continuum. Phys. Rev. Lett., 113, 257401(2014).

[107] E. N. Bulgakov, D. N. Maksimov. Topological bound states in the continuum in arrays of dielectric spheres. Phys. Rev. Lett., 118, 267401(2017).

[108] G. J. Gbur. Singular Optics(2016).

[109] H. M. Doeleman, F. Monticone, W. den Hollander, A. Alã, A. F. Koenderink. Experimental observation of a polarization vortex at an optical bound state in the continuum. Nat. Photonics, 12, 397-401(2018).

[110] W. Liu, B. Wang, Y. Zhang, J. Wang, M. Zhao, F. Guan, X. Liu, L. Shi, J. Zi. Circularly polarized states spawning from bound states in the continuum. Phys. Rev. Lett., 123, 116104(2019).

[111] Y. Zhang, A. Chen, W. Liu, C. W. Hsu, B. Wang, F. Guan, X. Liu, L. Shi, L. Lu, J. Zi. Observation of polarization vortices in momentum space. Phys. Rev. Lett., 120, 186103(2018).

[112] J. Mei, Y. Wu, C. T. Chan, Z.-Q. Zhang. First-principles study of Dirac and Dirac-like cones in phononic and photonic crystals. Phys. Rev. B, 86, 035141(2012).

[113] X. Yin, Y. Liang, L. Ni, Z. Wang, C. Peng, Z. Li. Analytical study of mode degeneracy in non-Hermitian photonic crystals with TM-like polarization. Phys. Rev. B, 96, 075111(2017).

[114] H.-Z. Chen, T. Liu, H.-Y. Luan, R.-J. Liu, X.-Y. Wang, X.-F. Zhu, Y.-B. Li, Z.-M. Gu, S.-J. Liang, H. Gao, L. Lu, L. Ge, S. Zhang, J. Zhu, R.-M. Ma. Revealing the missing dimension at an exceptional point. Nat. Phys., 16, 571-578(2020).

[115] A. Szameit, M. C. Rechtsman, O. Bahat-Treidel, M. Segev. PT-symmetry in honeycomb photonic lattices. Phys. Rev. A, 84, 021806(2011).

[116] Y. Xu, S.-T. Wang, L.-M. Duan. Weyl exceptional rings in a three-dimensional dissipative cold atomic gas. Phys. Rev. Lett., 118, 045701(2017).

[117] X. Huang, Y. Lai, Z. H. Hang, H. Zheng, C. T. Chan. Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials. Nat. Mater., 10, 582-586(2011).

[118] B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S.-L. Chua, J. D. Joannopoulos, M. Soljačić. Spawning rings of exceptional points out of Dirac cones. Nature, 525, 354-358(2015).

[119] Y. Li, S. Kita, P. Muñoz, O. Reshef, D. I. Vulis, M. Yin, M. Lončar, E. Mazur. On-chip zero-index metamaterials. Nat. Photonics, 9, 738-742(2015).

[120] B. Yang, Q. Guo, B. Tremain, L. E. Barr, W. Gao, H. Liu, B. Barr, Y. Xiang, D. Fan, A. P. Hibbins, S. Zhang. Direct observation of topological surface-state arcs in photonic metamaterials. Nat. Commun., 8, 97(2017).

[121] J. Noh, S. Huang, D. Leykam, Y. Chong, K. P. Chen, M. Rechtsman. Experimental observation of optical Weyl points and Fermi arc-like surface states. Nat. Phys., 13, 611-617(2017).

[122] F. Li, X. Huang, J. Lu, J. Ma, Z. Liu. Weyl points and Fermi arcs in a chiral phononic crystal. Nat. Phys., 14, 30-34(2018).

[123] Y. Lu, N. Jia, L. Su, C. Owens, G. Juzeliūnas, D. I. Schuster, J. Simon. Probing the Berry curvature and Fermi arcs of a Weyl circuit. Phys. Rev. B, 99, 020302(2019).

[124] J. Jin, X. Yin, L. Ni, M. Soljačić, B. Zhen, C. Peng. Topologically enabled ultrahigh-Q guided resonances robust to out-of-plane scattering. Nature, 574, 501-504(2019).

[125] C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, M. Soljačić. Observation of trapped light within the radiation continuum. Nature, 499, 188-191(2013).

[126] K. Hirose, Y. Liang, Y. Kurosaka, A. Watanabe, T. Sugiyama, S. Noda. Watt-class high-power, high-beam-quality photonic-crystal lasers. Nat. Photonics, 8, 406-411(2014).

[127] Z. Liu, Y. Xu, Y. Lin, J. Xiang, T. Feng, Q. Cao, J. Li, S. Lan, J. Liu. High-Q quasibound states in the continuum for nonlinear metasurfaces. Phys. Rev. Lett., 123, 253901(2019).

[128] X. Yin, J. Jin, M. Soljačić, C. Peng, B. Zhen. Observation of topologically enabled unidirectional guided resonances. Nature, 580, 467-471(2020).

[129] D. Taillaert, P. Bienstman, R. Baets. Compact efficient broadband grating coupler for silicon-on-insulator waveguides. Opt. Lett., 29, 2749-2751(2004).

[130] H. Zhou, B. Zhen, C. W. Hsu, O. D. Miller, S. G. Johnson, J. D. Joannopoulos, M. Soljačić. Perfect single-sided radiation and absorption without mirrors. Optica, 3, 1079-1086(2016).

[131] L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman. Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys. Rev. A, 45, 8185-8189(1992).

[132] S. Iwahashi, Y. Kurosaka, K. Sakai, K. Kitamura, N. Takayama, S. Noda. Higher-order vector beams produced by photonic-crystal lasers. Opt. Express, 19, 11963-11968(2011).

[133] C. Huang, C. Zhang, S. Xiao, Y. Wang, Y. Fan, Y. Liu, N. Zhang, G. Qu, H. Ji, J. Han, L. Ge, Y. Kivshar, Q. Song. Ultrafast control of vortex microlasers. Science, 367, 1018-1021(2020).

[134] B. Wang, W. Liu, M. Zhao, J. Wang, Y. Zhang, A. Chen, F. Guan, X. Liu, L. Shi, J. Zi. Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum. Nat. Photonics, 14, 623-628(2020).

[135] Z.-Q. Yang, Z.-K. Shao, H.-Z. Chen, X.-R. Mao, R.-M. Ma. Spin-momentum-locked edge mode for topological vortex lasing. Phys. Rev. Lett., 125, 013903(2020).

[136] L.-H. Wu, X. Hu. Scheme for achieving a topological photonic crystal by using dielectric material. Phys. Rev. Lett., 114, 223901(2015).

[137] Z. Zhang, X. Qiao, B. Midya, K. Liu, J. Sun, T. Wu, W. Liu, R. Agarwal, J. M. Jornet, S. Longhi, N. M. Litchinitser, L. Feng. Tunable topological charge vortex microlaser. Science, 368, 760-763(2020).