Frontiers of Optoelectronics, Volume. 17, Issue 2, 12200(2024)
Information-entropy enabled identifying topological photonic phase in real space
[2] [2] Wang, Z., Wang, X., Hu, Z., Bongiovanni, D., Juki-, D., Tang, L.,Song, D., Morandotti, R., Chen, Z., Buljan, H.: Sub-symmetryprotected topological states. Nat. Phys. 19(7), 992–998 (2023)
[3] [3] Parto, M., Leefmans, C., Williams, J., Nori, F., Marandi, A.: Non-Abelian effects in dissipative photonic topological lattices. Nat.Commun. 14(1), 1440 (2023)
[4] [4] Li, Y.Z., Xu, S., Zhang, Z.J., Yang, Y.M., Xie, X.R., Ye, W.Z.,Liu, F., Xue, H.R., Jing, L.Q., Wang, Z.J., Chen, Q.D., Sun, H.B.,Li, E.P., Chen, H.S., Gao, F.: Polarization-orthogonal nondegenerate plasmonic higher-order topological states. Phys. Rev. Lett.130(21), 213603 (2023)
[5] [5] El Hassan, A., Kunst, F.K., Moritz, A., Andler, G., Bergholtz, E.J.,Bourennane, M.: Corner states of light in photonic waveguides.Nat. Photonics 13(10), 697–700 (2019)
[6] [6] Yan, Q., Cao, E., Sun, Q., Ao, Y.T., Hu, X.Y., Shi, X., Gong, Q.H.,Misawa, H.: Near-field imaging and time-domain dynamics of photonic topological edge states in plasmonic nanochains. Nano Lett. 21(21), 9270–9278 (2021)
[7] [7] Cheng, Q.Q., Pan, Y.M., Wang, Q.J., Li, T., Zhu, S.N.: Topologically protected interface mode in plasmonic waveguide arrays.Laser Photonics Rev. 9(4), 392–398 (2015)
[8] [8] Harder, T.H., Egorov, O.A., Krause, C., Beierlein, J., Gagel, P.,Emmerling, M., Schneider, C., Peschel, U., H-fling, S., Klembt,S.: Kagome flatbands for coherent exciton-polariton lasing. ACS Photonics 8(11), 3193–3200 (2021)
[9] [9] Zhong, H., Kartashov, Y.V., Szameit, A., Li, Y.D., Liu, C.L.,Zhang, Y.Q.: Theory of topological corner state laser in Kagome waveguide arrays. APL Photonics 6(4), 040802 (2021)
[10] [10] Liu, P.F., Zeng, H.F., Czaplewski, D.A., Stern, N.P.: Low index contrast valley hall topological photonics for robust transport in the visible spectrum. ACS Photonics 9(3), 922–928 (2022)
[11] [11] Yu, Z., Lin, H., Zhou, R., Li, Z., Mao, Z., Peng, K., Liu, Y., Shi,X.: Topological valley crystals in a photonic Su–Schrieffer–Heeger (SSH) variant. J. Appl. Phys. 132(16), 163101 (2022)
[12] [12] Amrani, F., Osório, J.H., Delahaye, F., Giovanardi, F., Vincetti,L., Debord, B., Gér-me, F., Benabid, F.: Low-loss single-mode hybrid-lattice hollow-core photonic-crystal fibre. Light Sci.Appl. 10(1), 7 (2021)
[13] [13] Noh, J., Huang, S., Chen, K.P., Rechtsman, M.C.: Observation of photonic topological valley Hall edge states. Phys. Rev. Lett.120(6), 063902 (2018)
[14] [14] Aidelsburger, M., Lohse, M., Schweizer, C., Atala, M., Barreiro,J.T., Nascimbène, S., Cooper, N.R., Bloch, I., Goldman, N.:Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms. Nat. Phys. 11(2), 162–166 (2015)
[15] [15] Wintersperger, K., Braun, C., ünal, F.N., Eckardt, A., Liberto,M.D., Goldman, N., Bloch, I., Aidelsburger, M.: Realization of an anomalous Floquet topological system with ultracold atoms.Nat. Phys. 16(10), 1058–1063 (2020)
[16] [16] Zhang, P.F., Shen, H.T., Zhai, H.: Machine learning topological invariants with neural networks. Phys. Rev. Lett. 120(6), 066401 (2018)
[17] [17] Lang, T.C., Essin, A.M., Gurarie, V., Wessel, S.: Z2 topological invariants in two dimensions from quantum Monte Carlo. Phys Rev B Condens Matter Mater Phys. 87(20), 205101 (2013)
[18] [18] Grusdt, F., Abanin, D., Demler, E.: Measuring Z2 topological invariants in optical lattices using interferometry. Phys. Rev. A89(4), 043621 (2014)
[19] [19] Sun, Z., Zhou, H., Wang, C., Kumar, S., Geng, D., Yue, S.,Han, X., Haraguchi, Y., Shimada, K., Cheng, P., Chen, L., Shi,Y., Wu, K., Meng, S., Feng, B.: Observation of topological flat bands in the Kagome semiconductor Nb3Cl8.Nano Lett. 22(11),4596–4602 (2022)
[20] [20] Duan, S.S., You, J.Y., Gou, J., Chen, J., Huang, Y.L., Liu, M.Z.,Sun, S., Wang, Y.H., Yu, X.J., Wang, L., Feng, Y.P., Sun, Y.Y.,Wee, T.S., Chen, W.: Epitaxial growth of single-layer Kagome nanoflakes with topological band inversion. ACS Nano 16(12),21079–21086 (2022)
[21] [21] Xiong, L.L., Liu, Y.F., Zhang, Y., Zheng, Y.X., Jiang, X.Y.:Topological properties of a two-dimensional photonic square lattice without C4 and Mx(y) symmetries. ACS Photonics 9(7),2448–2454 (2022)
[22] [22] Chen, Y.F., Lan, Z.H., Zhu, J.: Second-order topological phases in C4V-symmetric photonic crystals beyond the two-dimensional Su- Schrieffer–Heeger model. Nanophotonics 11(7), 1345–1354 (2022)
[23] [23] Zhang, W.X., Xie, X., Hao, H.M., Dang, J.C., Xiao, S., Shi,S.S., Ni, H.Q., Niu, Z.C., Wang, C., Jin, K.J., Zhang, X.D.,Xu, X.L.: Low-threshold topological nanolasers based on the second-order corner state. Light Sci. Appl. 9(1), 109 (2020)
[24] [24] Padavi-, K., Hegde, S.S., DeGottardi, W., Vishveshwara, S.:Topological phases, edge modes, and the Hofstadter butterfly in coupled Su-Schrieffer-Heeger systems. Phys. Rev. B 98(2),024205 (2018)
[25] [25] Wang, Y.H., Liu, W.J., Ji, Z.R., Modi, G., Hwang, M., Agarwal,R.: Coherent interactions in one-dimensional topological photonic systems and their applications in all-optical logic operation.Nano Lett. 20(12), 8796–8802 (2020)
[26] [26] Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379–423 (1948)
[27] [27] Machta, J.: Entropy, information, and computation. Am. J. Phys.67(12), 1074–1077 (1999)
[28] [28] Di Crescenzo, A., Longobardi, M.: On cumulative entropies. J.Stat. Plan. Inference 139(12), 4072–4087 (2009)
[29] [29] Cui, T.J., Liu, S., Li, L.L.: Information entropy of coding metasurface.Light Sci. Appl. 5(11), e16172 (2016)
[30] [30] Zhang, Y.Q., Ren, B.Q., Li, Y.D., Ye, F.W.: Topological states in the super-SSH model. Opt. Express 29(26), 42827–42836 (2021)
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Rui Ma, Qiuchen Yan, Yihao Luo, Yandong Li, Xingyuan Wang, Cuicui Lu, Xiaoyong Hu, Qihuang Gong. Information-entropy enabled identifying topological photonic phase in real space[J]. Frontiers of Optoelectronics, 2024, 17(2): 12200
Category: RESEARCH ARTICLE
Received: Jan. 25, 2024
Accepted: Mar. 20, 2024
Published Online: Aug. 21, 2024
The Author Email: Yan Qiuchen (qiuchenyan@pku.edu.cn)