Please wait a minute...
Shopping Cart Email List Chinese
Advanced Search Fig/Tab
Frontiers of Optoelectronics

ISSN 2095-2759

ISSN 2095-2767(Online)

CN 10-1029/TN

Postal Subscription Code 80-976

Featured Articles  |  Most Downloaded  |  Most Reading
Online Submission Subscribe to Our RSS Content Feed
Front. Optoelectron.    2023, Vol. 16 Issue (4) : 38    https://doi.org/10.1007/s12200-023-00094-z
RESEARCH ARTICLE
A scheme for realizing nonreciprocal interlayer coupling in bilayer topological systems
Xiaoxiao Wang1, Ruizhe Gu1, Yandong Li1, Huixin Qi1, Xiaoyong Hu1,2,3,4(), Xingyuan Wang5(), Qihuang Gong1,2,3,4
1. State Key Laboratory for Mesoscopic Physics and Department of Physics, Collaborative Innovation Center of Quantum Matter & Frontiers Science Center for Nano-Optoelectronics, Beijing Academy of Quantum Information Sciences, Peking University, Beijing 100871, China
2. Peking University Yangtze Delta Institute of Optoelectronics, Nantong 226010, China
3. Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
4. Hefei National Laboratory, Hefei 230088, China
5. College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China
 Download: PDF(3678 KB)  
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

Nonreciprocal interlayer coupling is difficult to practically implement in bilayer non-Hermitian topological photonic systems. In this work, we identify a similarity transformation between the Hamiltonians of systems with nonreciprocal interlayer coupling and on-site gain/loss. The similarity transformation is widely applicable, and we show its application in one- and two-dimensional bilayer topological systems as examples. The bilayer non-Hermitian system with nonreciprocal interlayer coupling, whose topological number can be defined using the gauge-smoothed Wilson loop, is topologically equivalent to the bilayer system with on-site gain/loss. We also show that the topological number of bilayer non-Hermitian C6v-typed domain-induced topological interface states can be defined in the same way as in the case of the bilayer non-Hermitian Su–Schrieffer–Heeger model. Our results show the relations between two microscopic provenances of the non-Hermiticity and provide a universal and convenient scheme for constructing and studying nonreciprocal interlayer coupling in bilayer non-Hermitian topological systems. This scheme is useful for observation of non-Hermitian skin effect in three-dimensional systems.
Keywords Nonreciprocal      Bilayer      Interlayer coupling      Topological photonics     
Corresponding Author(s): Xiaoyong Hu,Xingyuan Wang   
Issue Date: 13 December 2023
 Cite this article:   
Xiaoxiao Wang,Ruizhe Gu,Yandong Li, et al. A scheme for realizing nonreciprocal interlayer coupling in bilayer topological systems[J]. Front. Optoelectron., 2023, 16(4): 38.
 URL:  
https://academic.hep.com.cn/foe/EN/10.1007/s12200-023-00094-z
https://academic.hep.com.cn/foe/EN/Y2023/V16/I4/38
1 K. Zhang,, X. Zhang,, L. Wang,, D. Zhao,, F. Wu,, Y. Yao,, M. Xia,, Y. Guo,: Observation of topological properties of non-Hermitian crystal systems with diversified coupled resonators chains. J. Appl. Phys. 130, 064502 (2021)
https://doi.org/10.1063/5.0058245
2 Y.T. Ao,, X.Y. Hu,, Y.L. You,, C.C. Lu,, Y.L. Fu,, X.Y. Wang,, Q.H. Gong,: Topological phase transition in the non-Hermitian coupled resonator array. Phys. Rev. Lett. 125(1), 013902 (2020)
https://doi.org/10.1103/PhysRevLett.125.013902
3 S. Weidemann,, M. Kremer,, T. Helbig,, T. Hofmann,, A. Stegmaier,, M. Greiter,, R. Thomale,, A. Szameit,: Topological funneling of light. Science 368(6488), 311–314 (2020)
https://doi.org/10.1126/science.aaz8727
4 C.H. Lee,, L.H. Li,, J.B. Gong,: Hybrid higher-order skin-top-ological modes in nonreciprocal systems. Phys. Rev. Lett. 123, 016805 (2019)
https://doi.org/10.1103/PhysRevLett.123.016805
5 E.J. Bergholtz,, J.C. Budich,, F.K. Kunst,: Exceptional topology of non-Hermitian systems. Rev. Mod. Phys. 93(1), 015005 (2021)
https://doi.org/10.1103/RevModPhys.93.015005
6 X.P. Zhou,, S.K. Gupta,, Z. Huang,, Z.D. Yan,, P. Zhan,, Z. Chen,, M.H. Lu,, Z.L. Wang,: Optical lattices with higher-order exceptional points by non-Hermitian coupling. Appl. Phys. Lett. 113, 101108 (2018)
https://doi.org/10.1063/1.5043279
7 D. Leykam,, S. Flach,, Y.D. Chong,: Flat bands in lattices with non-Hermitian coupling. Phys. Rev. B 96(6), 064305 (2017)
https://doi.org/10.1103/PhysRevB.96.064305
8 D. Jalas,, A. Petrov,, M. Eich,, W. Freude,, S.H. Fan,, Z.F. Yu,, R. Baets,, M. Popovic,, A. Melloni,, J.D. Joannopoulos,, M. Vanwolleghem,, C.R. Doerr,, H. Renner,: What is—and what is not—an optical isolator. Nat. Photonics 7(8), 579–582 (2013)
https://doi.org/10.1038/nphoton.2013.185
9 V.S. Asadchy,, M.S. Mirmoosa,, A. Diaz-Rubio,, S.H. Fan,, S.A. Tretyakov,: Tutorial on electromagnetic nonreciprocity and its origins. Proc. IEEE 108(10), 1684–1727 (2020)
https://doi.org/10.1109/JPROC.2020.3012381
10 Z. Wang,, Y.D. Chong,, J.D. Joannopoulos,, M. Soljacic,: Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461(7265), 772–775 (2009)
https://doi.org/10.1038/nature08293
11 K.Y. Bliokh,, D. Smirnova,, F. Nori,: Quantum spin Hall effect of light. Science 348(6242), 1448–1451 (2015)
https://doi.org/10.1126/science.aaa9519
12 X.J. Zhang,, T. Zhang,, M.H. Lu,, Y.F. Chen,: A review on non-Hermitian skin effect. Adv. Phys. X 7:1, 2109431, (2022).
https://doi.org/10.1080/23746149.2022.2109431
13 Y.L. Song,, W.W. Liu,, L.Z. Zheng,, Y.C. Zhang,, B. Wang,, P.X. Lu,: Two-dimensional non-Hermitian Skin Effect in a Synthetic Photonic Lattice. Phys. Rev. Appl. 14, 064076 (2020)
https://doi.org/10.1103/PhysRevApplied.14.064076
14 F.K. Kunst,, E. Edvardsson,, J.C. Budich,, E.J. Bergholtz,: Biorthogonal bulk-boundary correspondence in non-Hermitian systems. Phys. Rev. Lett. 121(2), 026808 (2018)
https://doi.org/10.1103/PhysRevLett.121.026808
15 F. Song,, S.Y. Yao,, Z. Wang,: Non-Hermitian topological invariants in real space. Phys. Rev. Lett. 123, 246801 (2019)
https://doi.org/10.1103/PhysRevLett.123.246801
16 C. Caloz,, A. Alu,, S. Tretyakov,, D. Sounas,, K. Achouri,, Z.L. Deck-Leger,: Electromagnetic nonreciprocity. Phys. Rev. Appl. 10(4), 047001 (2018)
https://doi.org/10.1103/PhysRevApplied.10.047001
17 B. Peng,, S.K. Ozdemir,, F.C. Lei,, F. Monifi,, M. Gianfreda,, G.L. Long,, S.H. Fan,, F. Nori,, C.M. Bender,, L. Yang,: Parity–time-symmetric whispering-gallery microcavities. Nat. Phys. 10(5), 394–398 (2014)
https://doi.org/10.1038/nphys2927
18 X.Y. Huang,, C.C. Lu,, C. Liang,, H.G. Tao,, Y.C. Liu,: Loss-induced nonreciprocity. Light Sci. Appl. 10, 30 (2021)
https://doi.org/10.1038/s41377-021-00464-2
19 C. Shen,, X.H. Zhu,, J.F. Li,, S.A. Cummer,: Nonreciprocal acoustic transmission in space-time modulated coupled resonators. Phys. Rev. B 100, 054302 (2019)
https://doi.org/10.1103/PhysRevB.100.054302
20 Z.F. Yu,, S.H. Fan,: Complete optical isolation created by indirect interband photonic transitions. Nat. Photonics 3, 91–94 (2009)
https://doi.org/10.1038/nphoton.2008.273
21 D.L. Sounas,, C. Caloz,, A. Alu,: Giant non-reciprocity at the subwavelength scale using angular momentum-biased metamaterials. Nat. Commun. 4(1), 2407 (2013)
https://doi.org/10.1038/ncomms3407
22 C. Yuce,: Anomalous features of non-Hermitian topological states. Ann. Phys. 415, 168098 (2020)
https://doi.org/10.1016/j.aop.2020.168098
23 W. Wang,, X. Wang,, G. Ma,: Non-Hermitian morphing of topological modes. Nature 608(7921), 50–55 (2022)
https://doi.org/10.1038/s41586-022-04929-1
24 X. Zhang,, Y. Tian,, J.H. Jiang,, M.H. Lu,, Y.F. Chen,: Observation of higher-order non-Hermitian skin effect. Nat. Commun. 12(1), 5377 (2021)
https://doi.org/10.1038/s41467-021-25716-y
25 L. Qi,, G.L. Wang,, S. Liu,, S. Zhang,, H.F. Wang,: Robust interface-state laser in non-Hermitian microresonator arrays. Phys. Rev. Appl. 13(6), 064015 (2020)
https://doi.org/10.1103/PhysRevApplied.13.064015
26 K. Wang,, A. Dutt,, C.C. Wojcik,, S. Fan,: Topological complexenergy braiding of non-Hermitian bands. Nature 598(7879), 59–64 (2021)
https://doi.org/10.1038/s41586-021-03848-x
27 Z. Gao,, X. Qiao,, M. Pan,, S. Wu,, J. Yim,, K. Chen,, B. Midya,, L. Ge,, L. Feng,: Two-dimensional reconfigurable non-Hermitian gauged laser array. Phys. Rev. Lett. 130(26), 263801 (2023)
https://doi.org/10.1103/PhysRevLett.130.263801
28 W.P. Su,, J.R. Schrieffer,, A.J. Heeger,: Solitons in polyacetylene. Phys. Rev. Lett. 42(25), 1698–1701 (1979)
https://doi.org/10.1103/PhysRevLett.42.1698
29 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(4), 433–438 (2017)
https://doi.org/10.1038/nmat4811
30 W.G. 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)
https://doi.org/10.1103/PhysRevLett.123.165701
31 H.C. Wu,, L. Jin,, Z. Song,: Topology of an anti-parity-time symmetric non-Hermitian Su-Schrieffer-Heeger model. Phys. Rev. B 103, 235110 (2021)
https://doi.org/10.1103/PhysRevB.103.235110
32 S.D. Liang,, G.Y. Huang,: Topological invariance and global Berry phase in non-Hermitian systems. Phys. Rev. A 87(1), 012118 (2013)
https://doi.org/10.1103/PhysRevA.87.012118
33 K. Takata,, M. Notomi,: Photonic topological insulating phase induced solely by gain and loss. Phys. Rev. Lett. 121(21), 213902 (2018)
https://doi.org/10.1103/PhysRevLett.121.213902
34 Z. Xing,, Y. Li,, Y. Ao,, X. Hu,: Winding number and bulk-boundary correspondence in a one-dimensional non-Hermitian photonic lattice. Phys. Rev. A (Coll. Park) 107(1), 013515 (2023)
https://doi.org/10.1103/PhysRevA.107.013515
35 C.M. Othon,, A. Laracuente,, H.D. Ladouceur,, B.R. Ringeisen,: Sub-micron parallel laser direct-write. Appl. Surf. Sci. 255(5), 3407–3413 (2008)
https://doi.org/10.1016/j.apsusc.2008.09.058
36 E. Lustig,, L.J. Maczewsky,, J. Beck,, T. Biesenthal,, M. Heinrich,, Z. Yang,, Y. Plotnik,, A. Szameit,, M. Segev,: Photonic topological insulator induced by a dislocation in three dimensions. Nature 609(7929), 931–935 (2022)
https://doi.org/10.1038/s41586-022-05129-7
37 L.J. Maczewsky,, M. Heinrich,, M. Kremer,, S.K. Ivanov,, M. Ehrhardt,, F. Martinez,, Y.V. Kartashov,, V.V. Konotop,, L. Torner,, D. Bauer,, A. Szameit,: Nonlinearity-induced photonic topological insulator. Science 370(6517), 701–704 (2020)
https://doi.org/10.1126/science.abd2033
38 F. Yu,, X.L. Zhang,, Z.N. Tian,, Q.D. Chen,, H.B. Sun,: General rules governing the dynamical encircling of an arbitrary number of exceptional points. Phys. Rev. Lett. 127(25), 253901 (2021)
https://doi.org/10.1103/PhysRevLett.127.253901
39 L.H. Wu,, X. Hu,: Scheme for achieving a topological photonic crystal by using dielectric material. Phys. Rev. Lett. 114, 223901 (2015)
https://doi.org/10.1103/PhysRevLett.114.223901
40 W.J. Liu,, Z.R. Ji,, Y.H. Wang,, G. Modi,, M. Hwang,, B.Y. Zheng,, V.J. Sorger,, A.L. Pan,, R. Agarwal,: Generation of helical topological exciton-polaritons. Science 370(6516), 600–604 (2020)
https://doi.org/10.1126/science.abc4975
41 H. Zhao,, X.D. Qiao,, T.W. Wu,, B. Midya,, S. Longhi,, L. Feng,: Non-Hermitian topological light steering. Science 365(6458), 1163–1166 (2019)
https://doi.org/10.1126/science.aay1064
42 Y.D. Li,, C.X. Fan,, X.Y. Hu,, Y.T. Ao,, C.C. Lu,, C.T. Chan,, D.M. Kennes,, Q.H. Gong,: Effective hamiltonian for photonic topological insulator with non-Hermitian domain walls. Phys. Rev. Lett. 129, 053903 (2022)
https://doi.org/10.1103/PhysRevLett.129.053903
43 X.X. Wang,, Y.D. Li,, X.Y. Hu,, R.Z. Gu,, Y.T. Ao,, P. Jiang,, Q.H. Gong,: Non-Hermitian high-quality-factor topological photonic crystal cavity. Phys. Rev. A (Coll Park) 105(2), 023531 (2022)
https://doi.org/10.1103/PhysRevA.105.023531
44 X.D. Chen,, X.T. He,, J.W. Dong,: All-dielectric layered photonic topological insulators. Laser Photonics Rev. 13, 1900091 (2019)
https://doi.org/10.1002/lpor.201900091
45 Y.T. Yang,, Y.F. Xu,, T. Xu,, H.X. Wang,, J.H. Jiang,, X. Hu,, Z.H. Hang,: Visualization of a unidirectional electromagnetic waveguide using topological photonic crystals made of dielectric materials. Phys. Rev. Lett. 120, 217401 (2018)
https://doi.org/10.1103/PhysRevLett.120.217401
46 X.D. Chen,, W.M. Deng,, F.L. Shi,, F.L. Zhao,, M. Chen,, J.W. Dong,: Direct observation of corner states in second-order topological photonic crystal slabs. Phys. Rev. Lett. 122(23), 233902 (2019).
https://doi.org/10.1103/PhysRevLett.122.233902
47 Y. Liu,, S. Leung,, F.F. Li,, Z.K. Lin,, X. Tao,, Y. Poo,, J.H. Jiang,: Bulk–disclination correspondence in topological crystalline insulators. Nature 589(7842), 381–385 (2021)
https://doi.org/10.1038/s41586-020-03125-3
48 A. Guo,, G.J. Salamo,, D. Duchesne,, R. Morandotti,, M. Volatier-Ravat,, V. Aimez,, G.A. Siviloglou,, D.N. Christodoulides,: Observation of P T-symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103(9), 093902 (2009).
https://doi.org/10.1103/PhysRevLett.103.093902
49 W. Zhu,, J. Gong,: Photonic corner skin modes in non-Hermitian photonic crystals. Phys. Rev. B 108(3), 035406 (2023)
https://doi.org/10.1103/PhysRevB.108.035406
50 N.R. Bernier,, L.D. Tóth,, A. Koottandavida,, M.A. Ioannou,, D. Malz,, A. Nunnenkamp,, A.K. Feofanov,, T.J. Kippenberg,: Nonreciprocal reconfigurable microwave optomechanical circuit. Nat. Commun. 8(1), 604 (2017)
https://doi.org/10.1038/s41467-017-00447-1
[1] Yu BI, Lingling HUANG, Xiaowei LI, Yongtian WANG. Magnetically controllable metasurface and its application[J]. Front. Optoelectron., 2021, 14(2): 154-169.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed