| [1] | Haldane, F. D. M. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008). doi: 10.1103/PhysRevLett.100.013904 |
| [2] | Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological photonics. Nat. Photonics 8, 821–829 (2014). doi: 10.1038/nphoton.2014.248 |
| [3] | Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019). doi: 10.1103/RevModPhys.91.015006 |
| [4] | Wang, Z. et al. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009). doi: 10.1038/nature08293 |
| [5] | Rechtsman, M. C. et al. Photonic floquet topological insulators. Nature 496, 196–200 (2013). doi: 10.1038/nature12066 |
| [6] | Khanikaev, A. B. et al. Photonic topological insulators. Nat. Mater. 12, 233–239 (2013). doi: 10.1038/nmat3520 |
| [7] | Hafezi, M. et al. Imaging topological edge states in silicon photonics. Nat. Photonics 7, 1001–1005 (2013). doi: 10.1038/nphoton.2013.274 |
| [8] | Wu, L. H. & Hu, X. Scheme for achieving a topological photonic crystal by using dielectric material. Phys. Rev. Lett. 114, 223901 (2015). doi: 10.1103/PhysRevLett.114.223901 |
| [9] | Barik, S. et al. A topological quantum optics interface. Science 359, 666–668 (2018). doi: 10.1126/science.aaq0327 |
| [10] | Mittal, S., Goldschmidt, E. A. & Hafezi, M. A topological source of quantum light. Nature 561, 502–506 (2018). doi: 10.1038/s41586-018-0478-3 |
| [11] | Tambasco, J. L. et al. Quantum interference of topological states of light. Sci. Adv. 4, eaat3187 (2018). doi: 10.1126/sciadv.aat3187 |
| [12] | Wang, Y. et al. Direct observation of topology from single-photon dynamics. Phys. Rev. Lett. 122, 193903 (2019). doi: 10.1103/PhysRevLett.122.193903 |
| [13] | Bahari, B. et al. Nonreciprocal lasing in topological cavities of arbitrary geometries. Science 358, 636–640 (2017). doi: 10.1126/science.aao4551 |
| [14] | Harari, G. et al. Topological insulator laser: theory. Science 359, eaar4003 (2018). doi: 10.1126/science.aar4003 |
| [15] | Bandres, M. A. et al. Topological insulator laser: experiments. Science 359, eaar4005 (2018). doi: 10.1126/science.aar4005 |
| [16] | Zhao, H. et al. Topological hybrid silicon microlasers. Nat. Commun. 9, 981 (2018). doi: 10.1038/s41467-018-03434-2 |
| [17] | Parto, M. et al. Edge-mode lasing in 1D topological active arrays. Phys. Rev. Lett. 120, 113901 (2018). doi: 10.1103/PhysRevLett.120.113901 |
| [18] | St-Jean, P. et al. Lasing in topological edge states of a one-dimensional lattice. Nat. Photonics 11, 651–656 (2017). doi: 10.1038/s41566-017-0006-2 |
| [19] | Ota, Y. et al. Topological photonic crystal nanocavity laser. Commun. Phys. 1, 86 (2018). doi: 10.1038/s42005-018-0083-7 |
| [20] | Han, C. et al. Lasing at topological edge states in a photonic crystal L3 nanocavity dimer array. Light 8, 40 (2019). doi: 10.1038/s41377-019-0149-7 |
| [21] | Shao, Z. K. et al. A high-performance topological bulk laser based on band-inversion-induced reflection. Nat. Nanotechnol. 15, 67–72 (2020). http://www.researchgate.net/publication/337955188_A_high-performance_topological_bulk_laser_based_on_band-inversion-induced_reflection |
| [22] | Zeng, Y. Q. et al. Electrically pumped topological laser with valley edge modes. Nature 578, 246–250 (2020). doi: 10.1038/s41586-020-1981-x |
| [23] | Smirnova, D. et al. Nonlinear topological photonics. Appl. Phys. Rev. 7, 021306 (2020). doi: 10.1063/1.5142397 |
| [24] | Ota, Y. et al. Thresholdless quantum dot nanolaser. Opt. Express 25, 19981–19994 (2017). doi: 10.1364/OE.25.019981 |
| [25] | Jang, H. et al. Sub-microwatt threshold nanoisland lasers. Nat. Commun. 6, 8276 (2015). doi: 10.1038/ncomms9276 |
| [26] | Takiguchi, M. et al. Systematic study of thresholdless oscillation in high-β buried multiple-quantum-well photonic crystal nanocavity lasers. Opt. Express 24, 3441–3450 (2016). doi: 10.1364/OE.24.003441 |
| [27] | Strauf, S. & Jahnke, F. Single quantum dot nanolaser. Laser Photonics Rev. 5, 607–633 (2011). doi: 10.1002/lpor.201000039 |
| [28] | Painter, O. et al. Two-dimensional photonic band-gap defect mode laser. Science 284, 1819–1821 (1999). doi: 10.1126/science.284.5421.1819 |
| [29] | Hamel, P. et al. Spontaneous mirror-symmetry breaking in coupled photonic-crystal nanolasers. Nat. Photonics 9, 311–315 (2015). doi: 10.1038/nphoton.2015.65 |
| [30] | Cao, Q. T. et al. Reconfigurable symmetry-broken laser in a symmetric microcavity. Nat. Commun. 11, 1136 (2020). doi: 10.1038/s41467-020-14861-5 |
| [31] | Huang, C. et al. Ultrafast control of vortex microlasers. Science 367, 1018–1021 (2020). doi: 10.1126/science.aba4597 |
| [32] | Benalcazar, W. A., Bernevig, B. A. & Hughes, T. L. Quantized electric multipole insulators. Science 357, 61–66 (2017). doi: 10.1126/science.aah6442 |
| [33] | Imhof, S. et al. Topolectrical-circuit realization of topological corner modes. Nat. Phys. 14, 925–929 (2018). doi: 10.1038/s41567-018-0246-1 |
| [34] | Peterson, C. W. et al. A quantized microwave quadrupole insulator with topologically protected corner states. Nature 555, 346–350 (2018). doi: 10.1038/nature25777 |
| [35] | Serra-Garcia, M. et al. Observation of a phononic quadrupole topological insulator. Nature 555, 342–345 (2018). doi: 10.1038/nature25156 |
| [36] | Mittal, S. et al. Photonic quadrupole topological phases. Nat. Photonics 13, 692–696 (2019). doi: 10.1038/s41566-019-0452-0 |
| [37] | Dutt, A., Minkov, M. & Fan, S. H. Higher-order topological insulators in synthetic dimensions. Preprint at https://arxiv.org/abs/1911.11310 (2019). |
| [38] | Langbehn, J. et al. Reflection-symmetric second-order topological insulators and superconductors. Phys. Rev. Lett. 119, 246401 (2017). doi: 10.1103/PhysRevLett.119.246401 |
| [39] | Xie, B. Y. et al. Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals. Phys. Rev. Lett. 122, 233903 (2019). doi: 10.1103/PhysRevLett.122.233903 |
| [40] | Chen, X. D. et al. Direct observation of corner states in second-order topological photonic crystal slabs. Phys. Rev. Lett. 122, 233902 (2019). doi: 10.1103/PhysRevLett.122.233902 |
| [41] | Ota, Y. et al. Photonic crystal nanocavity based on a topological corner state. Optica 6, 786–789 (2019). doi: 10.1364/OPTICA.6.000786 |
| [42] | Zhang, X. J. et al. Second-order topology and multidimensional topological transitions in sonic crystals. Nat. Phys. 15, 582–588 (2019). doi: 10.1038/s41567-019-0472-1 |
| [43] | Noh, J. et al. Topological protection of photonic mid-gap defect modes. Nat. Photonics 12, 408–415 (2018). doi: 10.1038/s41566-018-0179-3 |
| [44] | Liu, T. et al. Second-order topological phases in non-hermitian systems. Phys. Rev. Lett. 122, 076801 (2019). doi: 10.1103/PhysRevLett.122.076801 |
| [45] | Akahane, Y. et al. High-Q photonic nanocavity in a two-dimensional photonic crystal. Nature 425, 944–947 (2003). doi: 10.1038/nature02063 |
| [46] | Zak, J. Berry's phase for energy bands in solids. Phys. Rev. Lett. 62, 2747–2750 (1989). doi: 10.1103/PhysRevLett.62.2747 |
| [47] | Liu, F. & Wakabayashi, K. Novel topological phase with a zero berry curvature. Phys. Rev. Lett. 118, 076803 (2017). doi: 10.1103/PhysRevLett.118.076803 |
| [48] | Qian, C. J. et al. Two-photon rabi splitting in a coupled system of a nanocavity and exciton complexes. Phys. Rev. Lett. 120, 213901 (2018). doi: 10.1103/PhysRevLett.120.213901 |
| [49] | Yang, J. N. et al. Diabolical points in coupled active cavities with quantum emitters. Light 9, 6 (2020). doi: 10.1038/s41377-020-0244-9 |
| [50] | Bjork, G. & Yamamoto, Y. Analysis of semiconductor microcavity lasers using rate equations. IEEE J. Quantum Electron. 27, 2386–2396 (1991). doi: 10.1109/3.100877 |