Photonics Research, Volume. 9, Issue 4, 574(2021)
Sensitivity of topological edge states in a non-Hermitian dimer chain
[1] D. Xiao, M. C. Chang, Q. Niu. Berry phase effects on electronic properties. Rev. Mod. Phys., 82, 1959-2007(2010).
[2] M. Z. Hasan, C. L. Kane. Topological insulators. Rev. Mod. Phys., 82, 3045-3067(2010).
[3] X. L. Qi, S. C. Zhang. Topological insulators and superconductors. Rev. Mod. Phys., 83, 1057-1110(2011).
[4] M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, A. Szameit. Photonic Floquet topological insulators. Nature, 496, 196-200(2013).
[5] A. B. Khanikaev, S. H. Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, G. Shvets. Photonic topological insulators. Nat. Mater., 12, 233-239(2013).
[6] L. Lu, J. D. Joannopoulos, M. Soljačić. Topological photonics. Nat. Photonics, 8, 821-829(2014).
[7] Y. E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, O. Zilberberg. Topological states and adiabatic pumping in quasicrystals. Phys. Rev. Lett., 109, 106402(2012).
[8] M. A. Bandres, M. C. Rechtsman, M. Segev. Topological photonic quasicrystals: fractal topological spectrum and protected transport. Phys. Rev. X, 6, 011016(2016).
[9] Z. W. Guo, H. T. Jiang, Y. Sun, Y. H. Li, H. Chen. Asymmetric topological edge states in a quasiperiodic Harper chain composed of split-ring resonators. Opt. Lett., 43, 5142-5145(2018).
[10] S. Longhi. Topological phase transition in non-Hermitian quasicrystals. Phys. Rev. Lett., 122, 237601(2019).
[11] D. Varjas, A. Lau, K. Pöyhönen, A. R. Akhmerov, D. I. Pikulin, I. C. Fulga. Topological phases without crystalline counterparts. Phys. Rev. Lett., 123, 196401(2019).
[12] W. P. Su, J. R. Schrieffer, A. J. Heeger. Solitons in polyacetylene. Phys. Rev. Lett., 42, 1698-1701(1979).
[13] N. Malkova, I. Hromada, X. Wang, G. Bryant, Z. Chen. Observation of optical Shockley-like surface states in photonic superlattices. Opt. Lett., 34, 1633-1635(2009).
[14] J. Jiang, Z. W. Guo, Y. Q. Ding, Y. Sun, Y. H. Li, H. T. Jiang, H. Chen. Experimental demonstration of the robust edge states in a split-ring-resonator chain. Opt. Express, 26, 12891-12902(2018).
[15] J. Jiang, J. Ren, Z. W. Guo, W. W. Zhu, Y. Long, H. T. Jiang, H. Chen. Seeing topological winding number and band inversion in photonic dimer chain of split-ring resonators. Phys. Rev. B, 101, 165427(2020).
[16] Y. Hadad, J. C. Soric, A. B. Khanikaev, A. Alù. Self-induced topological protection in nonlinear circuit arrays. Nat. Electron., 1, 178-182(2018).
[17] D. A. Dobrykh, A. V. Yulin, A. P. Slobozhanyuk, A. N. Poddubny, Y. S. Kivshar. Nonlinear control of electromagnetic topological edge states. Phys. Rev. Lett., 121, 163901(2018).
[18] Y. Wang, L. J. Lang, C. H. Lee, B. L. Zhang, Y. D. Chong. Topologically enhanced harmonic generation in a nonlinear transmission line metamaterial. Nat. Commun., 10, 1102(2019).
[19] S. Kruk, A. Poddubny, D. Smirnova, L. Wang, A. Slobozhanyuk, A. Shorokhov, I. Kravchenko, B. Luther-Davies, Y. Kivshar. Nonlinear light generation in topological nanostructures. Nat. Nanotechnol., 14, 126-130(2019).
[20] D. Smirnova, D. Leykam, Y. D. Chong, Y. Kivshar. Nonlinear topological photonics. Appl. Phys. Rev., 7, 021306(2020).
[21] S. Xia, D. Jukić, N. Wang, D. Smirnova, L. Smirnov, L. Tang, D. Song, A. Szameit, D. Leykam, J. Xu, Z. Chen, H. Buljan. Nontrivial coupling of light into a defect: the interplay of nonlinearity and topology. Light Sci. Appl., 9, 147(2020).
[22] Y. Ota, K. Takata, T. Ozawa, A. Amo, Z. Jia, B. Kante, M. Notomi, Y. Arakawa, S. Iwamoto. Active topological photonics. Nanophotonics, 9, 547-567(2020).
[23] H. Zhao, P. Miao, M. H. Teimourpour, S. Malzard, R. El-Ganainy, H. Schomerus, L. Feng. Topological hybrid silicon microlasers. Nat. Commun., 9, 981(2018).
[24] M. Parto, S. Wittek, H. Hodaei, G. Harari, M. A. Bandres, J. Ren, M. C. Rechtsman, M. Segev, D. N. Christodoulides, M. Khajavikhan. Edge-mode lasing in 1D topological active arrays. Phys. Rev. Lett., 120, 113901(2018).
[25] Y. Ota, R. Katsumi, K. Watanabe, S. Iwamoto, Y. Arakawa. Topological photonic crystal nanocavity laser. Commun. Phys., 1, 86(2018).
[26] 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).
[27] L. Feng, R. El-Ganainy, L. Ge. Non-Hermitian photonics based on parity–time symmetry. Nat. Photonics, 11, 752-762(2017).
[28] K. Özdemir, S. Rotter, F. Nori, L. Yang. Parity–time symmetry and exceptional points in photonics. Nat. Mater., 18, 783-798(2019).
[29] M. A. Miri, A. Alù. Exceptional points in optics and photonics. Science, 363, 7709(2019).
[30] A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, D. N. Christodoulides. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett., 103, 093902(2009).
[31] 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).
[32] H. Xu, D. Mason, L. Jiang, J. G. E. Harris. Topological energy transfer in an optomechanical system with exceptional points. Nature, 537, 80-83(2016).
[33] S. Assawaworrarit, X. F. Yu, S. H. Fan. Robust wireless power transfer using a nonlinear parity–time-symmetric circuit. Nature, 546, 387-390(2017).
[34] 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).
[35] J. Doppler, A. A. Mailybaev, J. Böhm, U. Kuhl, A. Girschik, F. Libisch, T. J. Milburn, P. Rabl, N. Moiseyev, S. Rotter. Dynamically encircling an exceptional point for asymmetric mode switching. Nature, 537, 76-79(2016).
[36] A. U. Hassan, B. Zhen, M. Soljačić, M. Khajavikhan, D. N. Christodoulides. Dynamically encircling exceptional points: exact evolution and polarization state conversion. Phys. Rev. Lett., 118, 093002(2017).
[37] X. L. Zhang, S. B. Wang, B. Hou, C. T. Chan. Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point. Phys. Rev. X, 8, 021066(2018).
[38] Q. J. Liu, S. Y. Li, B. Wang, S. L. Ke, C. Z. Qin, K. Wang, W. W. Liu, D. S. Gao, P. Berini, P. X. Lu. Efficient mode transfer on a compact silicon chip by encircling moving exceptional points. Phys. Rev. Lett., 124, 153903(2020).
[39] J. Wiersig. Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: application to microcavity sensors for single-particle detection. Phys. Rev. Lett., 112, 203901(2014).
[40] H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia-Gracia, R. El-ganainy, D. N. Christodoulides, M. Khajavikhan. Enhanced sensitivity at higher-order exceptional points. Nature, 548, 187-191(2017).
[41] W. J. Chen, K. Özdemir, G. M. Zhao, J. Wiersig, L. Yang. Exceptional points enhance sensing in an optical microcavity. Nature, 548, 192-196(2017).
[42] P. Y. Chen, M. Sakhdari, M. Hajizadegan, Q. S. Cui, M.-C. Cheng, R. El-Ganainy, A. Alù. Generalized parity–time symmetry condition for enhanced sensor telemetry. Nat. Electron., 1, 297-304(2018).
[43] S. B. Wang, B. Hou, W. X. Lu, Y. T. Chen, Z. Q. Zhang, C. T. Chan. Arbitrary order exceptional point induced by photonic spin-orbit interaction in coupled resonators. Nat. Commun., 10, 832(2018).
[44] K. Ding, G. C. Ma, Z. Q. Zhang, C. T. Chan. Exceptional demonstration of an anisotropic exceptional point. Phys. Rev. Lett., 121, 085702(2018).
[45] Z. Dong, Z. P. Li, F. Yang, C.-W. Qiu, J. S. Ho. Sensitive readout of implantable microsensors using a wireless system locked to an exceptional point. Nat. Electron., 2, 335-342(2019).
[46] Q. Zhong, J. Ren, M. Khajavikhan, D. N. Christodoulides, K. Özdemir, R. El-Ganainy. Sensing with exceptional surfaces in order to combine sensitivity with robustness. Phys. Rev. Lett., 122, 153902(2019).
[47] Z. C. Xiao, H. N. Li, T. Kottos, A. Alù. Enhanced sensing and nondegraded thermal noise performance based on PT-symmetric electronic circuits with a sixth-order exceptional point. Phys. Rev. Lett., 123, 213901(2019).
[48] Y. J. Zhang, H. Kwon, M.-A. Miri, E. Kallos, H. Cano-Garcia, M. S. Tong, A. Alù. Noninvasive glucose sensor based on parity-time symmetry. Phys. Rev. Appl., 11, 044049(2019).
[49] J.-H. Park, A. Ndao, W. Cai, L. Hsu, A. Kodigala, T. Lepetit, Y.-H. Lo, B. Kanté. Symmetry-breaking-induced plasmonic exceptional points and nanoscale sensing. Nat. Phys., 16, 462-468(2020).
[50] J. M. Zeuner, M. C. Rechtsman, Y. Plotnik, Y. Lumer, S. Nolte, M. S. Rudner, M. Segev, A. Szameit. Observation of a topological transition in the bulk of a non-Hermitian system. Phys. Rev. Lett., 115, 040402(2015).
[51] C. Poli, M. Bellec, U. Kuhl, F. Mortessagne, H. Schomerus. Selective enhancement of topologically induced interface states in a dielectric resonator chain. Nat. Commun., 6, 6710(2015).
[52] S. Weimann, M. Kremer, Y. Plotnik, Y. Lumer, S. Nolte, K. G. Makris, M. Segev, M. C. Rechtsman, A. Szameit. Topologically protected bound states in photonic parity–time-symmetric crystals. Nat. Mater., 16, 433-438(2017).
[53] S. Y. Yao, Z. Wang. Edge states and topological invariants of non-Hermitian systems. Phys. Rev. Lett., 121, 086803(2018).
[54] B. K. Qi, L. X. Zhang, L. Ge. “Defect states emerging from a non-Hermitian flatband of photonic zero modes. Phys. Rev. Lett., 120, 093901(2018).
[55] K. Takata, M. Notomi. Photonic topological insulating phase induced solely by gain and loss. Phys. Rev. Lett., 121, 213902(2018).
[56] S. Longhi, L. Feng. Non-Hermitian multimode interference. Opt. Lett., 45, 1962-1965(2020).
[57] S. Lieu. Topological phases in the non-Hermitian Su–Schrieffer–Heeger model. Phys. Rev. B, 97, 045106(2018).
[58] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, M. Ueda. Topological phases of non-Hermitian systems. Phys. Rev. X, 8, 031079(2018).
[59] A. Cerjan, M. Xiao, L. Yuan, S. Fan. Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges. Phys. Rev. B, 97, 075128(2018).
[60] S. Liu, S. J. Ma, C. Yang, L. Zhang, W. L. Gao, Y. J. Xiang, T. J. Cui, S. Zhang. Gain- and loss-induced topological insulating phase in a non-Hermitian electrical circuit. Phys. Rev. Appl., 13, 014047(2020).
[61] Z. W. Guo, H. T. Jiang, Y. H. Li, H. Chen, G. S. Agarwal. Enhancement of electromagnetically induced transparency in metamaterials using long range coupling mediated by a hyperbolic material. Opt. Express, 26, 627-641(2018).
[62] Z. W. Guo, H. T. Jiang, H. Chen. Hyperbolic metamaterials: from dispersion manipulation to applications. J. Appl. Phys., 127, 071101(2020).
[63] W. Gao, X. Y. Hu, C. Li, J. H. Yang, Z. Chai, J. Y. Xie, Q. H. Gong. Fano-resonance in one-dimensional topological photonic crystal heterostructure. Opt. Express, 26, 8634-8644(2018).
[64] F. Zangeneh-Nejad, R. Fleury. Topological Fano resonances. Phys. Rev. Lett., 122, 014301(2019).
[65] Q. S. Huang, Z. W. Guo, J. T. Feng, C. Y. Yu, H. T. Jiang, Z. Zhang, Z. S. Wang, H. Chen. Observation of a topological edge state in the X-ray band. Laser Photon. Rev., 13, 1800339(2019).
[66] W. Song, W. Z. Sun, C. Chen, Q. H. Song, S. M. Xiao, S. N. Zhu, T. Li. Breakup and recovery of topological zero modes in finite non-Hermitian optical lattices. Phys. Rev. Lett., 123, 165701(2019).
[67] W. G. Song, W. Z. Sun, C. Chen, Q. H. Song, S. M. Xiao, S. N. Zhu, T. Li. Robust and broadband optical coupling by topological waveguide arrays. Laser Photon. Rev., 14, 1900193(2020).
[68] J. Ningyuan, C. Owens, A. Sommer, D. Schuster, J. Simon. Time- and site-resolved dynamics in a topological circuit. Phys. Rev. X, 5, 021031(2015).
[69] V. V. Albert, L. I. Glazman, L. Jiang. Topological properties of linear circuit lattices. Phys. Rev. Lett., 114, 173902(2015).
[70] S. Imhof, C. Berger, F. Bayer, J. Brehm, L. W. Molenkamp, T. Kiessling, F. Schindler, C. H. Lee, M. Greiter, T. Neupert, R. Thomale. Topolectrical-circuit realization of topological corner modes. Nat. Phys., 14, 925-929(2018).
[71] Y. Li, Y. Sun, W. W. Zhu, Z. W. Guo, J. Jiang, T. Kariyado, H. Chen, X. Hu. Topological LC-circuits based on microstrips and observation of electromagnetic modes with orbital angular momentum. Nat. Commun., 9, 4598(2018).
[72] T. Helbig, T. Hofmann, S. Imhof, M. Abdelghany, T. Kiessling, L. W. Molenkamp, C. H. Lee, A. Szameit, M. Greiter, R. Thomale. Generalized bulk-boundary correspondence in non-Hermitian topolectrical circuits. Nat. Phys., 16, 747-750(2020).
[73] X. F. Zhang, K. Ding, X. J. Zhou, J. Xu, D. F. Jin. Experimental observation of an exceptional surface in synthetic dimension with magnon polaritons. Phys. Rev. Lett., 123, 237202(2019).
[74] F. X. Zhang, Y. M. Feng, X. F. Chen, L. Ge, W. J. Wan. Synthetic anti-PT symmetry in a single microcavity. Phys. Rev. Lett., 124, 053901(2020).
[75] J. Feis, C. J. Stevens, E. Shamonina. Wireless power transfer through asymmetric topological edge states in diatomic chains of coupled meta-atoms. Appl. Phys. Lett., 117, 134106(2020).
[76] L. Zhang, Y. H. Yang, Z. Jiang, Q. L. Chen, Q. H. Yan, Z. Y. Wu, B. L. Zhang, J. T. Huangfu, H. S. Chen. Topological wireless power transfer(2020).
[77] J. Song, F. Q. Yang, Z. W. Guo, Y. Q. Chen, H. T. Jiang, Y. H. Li, H. Chen. One-dimensional topological quasiperiodic chain for directional wireless power transfer(2020).
[78] J. Song, F. Q. Yang, Z. W. Guo, X. Wu, K. J. Zhu, J. Jiang, Y. Sun, Y. H. Li, H. T. Jiang, H. Chen. Wireless power transfer via topological modes in dimer chains. Phys. Rev. Appl., 15, 014009(2021).
[79] T. Hofmann, T. Helbig, F. Schindler, N. Salgo, M. Brzezińska, M. Greiter, T. Kiessling, D. Wolf, A. Vollhardt, A. Kabaši, C. H. Lee, A. Bilušić, R. Thomale, T. Neupert. Reciprocal skin effect and its realization in a topolectrical circuit. Phys. Rev. Res., 2, 023265(2020).
[80] S. Weidemann, P. Kremer, T. Helbig, T. Hofmann, A. Stegmaier, M. Greiter, R. Thomale, A. Szameit. Topological funneling of light. Science, 368, 311-314(2020).
[81] V. Peano, M. Houde, F. Marquardt, A. A. Clerk. Topological quantum fluctuations and traveling wave amplifiers. Phys. Rev. X, 6, 041026(2016).
[82] J. Ran, Y. W. Zhang, X. D. Chen, H. Chen. Frequency mixer based on Doppler effect. IEEE Microw. Wireless Compon. Lett., 28, 43-45(2018).
[83] Y. Sun, W. Tan, H. Q. Li, J. Li, H. Chen. Experimental demonstration of a coherent perfect absorber with PT phase transition. Phys. Rev. Lett., 112, 143903(2014).
Get Citation
Copy Citation Text
Zhiwei Guo, Tengzhou Zhang, Juan Song, Haitao Jiang, Hong Chen. Sensitivity of topological edge states in a non-Hermitian dimer chain[J]. Photonics Research, 2021, 9(4): 574
Category: Physical Optics
Received: Oct. 30, 2020
Accepted: Feb. 3, 2021
Published Online: Apr. 6, 2021
The Author Email: Zhiwei Guo (2014guozhiwei@tongji.edu.cn), Hong Chen (hongchen@tongji.edu.cn)