RESEARCH ARTICLE

A scheme for realizing nonreciprocal interlayer coupling in bilayer topological systems

  • Xiaoxiao Wang 1 ,
  • Ruizhe Gu 1 ,
  • Yandong Li 1 ,
  • Huixin Qi 1 ,
  • Xiaoyong Hu , 1,2,3,4 ,
  • Xingyuan Wang , 5 ,
  • Qihuang Gong 1,2,3,4
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  • 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
xiaoyonghu@pku.edu.cn
wang_xingyuan@mail.buct.edu.cn

Received date: 21 Aug 2023

Accepted date: 29 Oct 2023

Copyright

2023 The Author(s) 2023

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.

Cite this article

Xiaoxiao Wang , Ruizhe Gu , Yandong Li , Huixin Qi , Xiaoyong Hu , Xingyuan Wang , Qihuang Gong . A scheme for realizing nonreciprocal interlayer coupling in bilayer topological systems[J]. Frontiers of Optoelectronics, 2023 , 16(4) : 38 . DOI: 10.1007/s12200-023-00094-z

1
Zhang, K., Zhang, X., Wang, L., Zhao, D., Wu, F., Yao, Y., Xia, M., Guo, Y.: Observation of topological properties of non-Hermitian crystal systems with diversified coupled resonators chains. J. Appl. Phys. 130, 064502 (2021)

DOI

2
Ao, Y.T., Hu, X.Y., You, Y.L., Lu, C.C., Fu, Y.L., Wang, X.Y., Gong, Q.H.: Topological phase transition in the non-Hermitian coupled resonator array. Phys. Rev. Lett. 125(1), 013902 (2020)

DOI

3
Weidemann, S., Kremer, M., Helbig, T., Hofmann, T., Stegmaier, A., Greiter, M., Thomale, R., Szameit, A.: Topological funneling of light. Science 368(6488), 311–314 (2020)

DOI

4
Lee, C.H., Li, L.H., Gong, J.B.: Hybrid higher-order skin-top-ological modes in nonreciprocal systems. Phys. Rev. Lett. 123, 016805 (2019)

DOI

5
Bergholtz, E.J., Budich, J.C., Kunst, F.K.: Exceptional topology of non-Hermitian systems. Rev. Mod. Phys. 93(1), 015005 (2021)

DOI

6
Zhou, X.P., Gupta, S.K., Huang, Z., Yan, Z.D., Zhan, P., Chen, Z., Lu, M.H., Wang, Z.L.: Optical lattices with higher-order exceptional points by non-Hermitian coupling. Appl. Phys. Lett. 113, 101108 (2018)

DOI

7
Leykam, D., Flach, S., Chong, Y.D.: Flat bands in lattices with non-Hermitian coupling. Phys. Rev. B 96(6), 064305 (2017)

DOI

8
Jalas, D., Petrov, A., Eich, M., Freude, W., Fan, S.H., Yu, Z.F., Baets, R., Popovic, M., Melloni, A., Joannopoulos, J.D., Vanwolleghem, M., Doerr, C.R., Renner, H.: What is—and what is not—an optical isolator. Nat. Photonics 7(8), 579–582 (2013)

DOI

9
Asadchy, V.S., Mirmoosa, M.S., Diaz-Rubio, A., Fan, S.H., Tretyakov, S.A.: Tutorial on electromagnetic nonreciprocity and its origins. Proc. IEEE 108(10), 1684–1727 (2020)

DOI

10
Wang, Z., Chong, Y.D., Joannopoulos, J.D., Soljacic, M.: Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461(7265), 772–775 (2009)

DOI

11
Bliokh, K.Y., Smirnova, D., Nori, F.: Quantum spin Hall effect of light. Science 348(6242), 1448–1451 (2015)

DOI

12
Zhang, X.J., Zhang, T., Lu, M.H., Chen, Y.F.: A review on non-Hermitian skin effect. Adv. Phys. X 7:1, 2109431, (2022).

DOI

13
Song, Y.L., Liu, W.W., Zheng, L.Z., Zhang, Y.C., Wang, B., Lu, P.X.: Two-dimensional non-Hermitian Skin Effect in a Synthetic Photonic Lattice. Phys. Rev. Appl. 14, 064076 (2020)

DOI

14
Kunst, F.K., Edvardsson, E., Budich, J.C., Bergholtz, E.J.: Biorthogonal bulk-boundary correspondence in non-Hermitian systems. Phys. Rev. Lett. 121(2), 026808 (2018)

DOI

15
Song, F., Yao, S.Y., Wang, Z.: Non-Hermitian topological invariants in real space. Phys. Rev. Lett. 123, 246801 (2019)

DOI

16
Caloz, C., Alu, A., Tretyakov, S., Sounas, D., Achouri, K., Deck-Leger, Z.L.: Electromagnetic nonreciprocity. Phys. Rev. Appl. 10(4), 047001 (2018)

DOI

17
Peng, B., Ozdemir, S.K., Lei, F.C., Monifi, F., Gianfreda, M., Long, G.L., Fan, S.H., Nori, F., Bender, C.M., Yang, L.: Parity–time-symmetric whispering-gallery microcavities. Nat. Phys. 10(5), 394–398 (2014)

DOI

18
Huang, X.Y., Lu, C.C., Liang, C., Tao, H.G., Liu, Y.C.: Loss-induced nonreciprocity. Light Sci. Appl. 10, 30 (2021)

DOI

19
Shen, C., Zhu, X.H., Li, J.F., Cummer, S.A.: Nonreciprocal acoustic transmission in space-time modulated coupled resonators. Phys. Rev. B 100, 054302 (2019)

DOI

20
Yu, Z.F., Fan, S.H.: Complete optical isolation created by indirect interband photonic transitions. Nat. Photonics 3, 91–94 (2009)

DOI

21
Sounas, D.L., Caloz, C., Alu, A.: Giant non-reciprocity at the subwavelength scale using angular momentum-biased metamaterials. Nat. Commun. 4(1), 2407 (2013)

DOI

22
Yuce, C.: Anomalous features of non-Hermitian topological states. Ann. Phys. 415, 168098 (2020)

DOI

23
Wang, W., Wang, X., Ma, G.: Non-Hermitian morphing of topological modes. Nature 608(7921), 50–55 (2022)

DOI

24
Zhang, X., Tian, Y., Jiang, J.H., Lu, M.H., Chen, Y.F.: Observation of higher-order non-Hermitian skin effect. Nat. Commun. 12(1), 5377 (2021)

DOI

25
Qi, L., Wang, G.L., Liu, S., Zhang, S., Wang, H.F.: Robust interface-state laser in non-Hermitian microresonator arrays. Phys. Rev. Appl. 13(6), 064015 (2020)

DOI

26
Wang, K., Dutt, A., Wojcik, C.C., Fan, S.: Topological complexenergy braiding of non-Hermitian bands. Nature 598(7879), 59–64 (2021)

DOI

27
Gao, Z., Qiao, X., Pan, M., Wu, S., Yim, J., Chen, K., Midya, B., Ge, L., Feng, L.: Two-dimensional reconfigurable non-Hermitian gauged laser array. Phys. Rev. Lett. 130(26), 263801 (2023)

DOI

28
Su, W.P., Schrieffer, J.R., Heeger, A.J.: Solitons in polyacetylene. Phys. Rev. Lett. 42(25), 1698–1701 (1979)

DOI

29
Weimann, S., Kremer, M., Plotnik, Y., Lumer, Y., Nolte, S., Makris, K.G., Segev, M., Rechtsman, M.C., Szameit, A.: Topologically protected bound states in photonic parity–time-symmetric crystals. Nat. Mater. 16(4), 433–438 (2017)

DOI

30
Song, W.G., Sun, W.Z., Chen, C., Song, Q.H., Xiao, S.M., Zhu, S.N., Li, T.: Breakup and recovery of topological zero modes in finite non-Hermitian optical lattices. Phys. Rev. Lett. 123, 165701 (2019)

DOI

31
Wu, H.C., Jin, L., Song, Z.: Topology of an anti-parity-time symmetric non-Hermitian Su-Schrieffer-Heeger model. Phys. Rev. B 103, 235110 (2021)

DOI

32
Liang, S.D., Huang, G.Y.: Topological invariance and global Berry phase in non-Hermitian systems. Phys. Rev. A 87(1), 012118 (2013)

DOI

33
Takata, K., Notomi, M.: Photonic topological insulating phase induced solely by gain and loss. Phys. Rev. Lett. 121(21), 213902 (2018)

DOI

34
Xing, Z., Li, Y., Ao, Y., Hu, X.: Winding number and bulk-boundary correspondence in a one-dimensional non-Hermitian photonic lattice. Phys. Rev. A (Coll. Park) 107(1), 013515 (2023)

DOI

35
Othon, C.M., Laracuente, A., Ladouceur, H.D., Ringeisen, B.R.: Sub-micron parallel laser direct-write. Appl. Surf. Sci. 255(5), 3407–3413 (2008)

DOI

36
Lustig, E., Maczewsky, L.J., Beck, J., Biesenthal, T., Heinrich, M., Yang, Z., Plotnik, Y., Szameit, A., Segev, M.: Photonic topological insulator induced by a dislocation in three dimensions. Nature 609(7929), 931–935 (2022)

DOI

37
Maczewsky, L.J., Heinrich, M., Kremer, M., Ivanov, S.K., Ehrhardt, M., Martinez, F., Kartashov, Y.V., Konotop, V.V., Torner, L., Bauer, D., Szameit, A.: Nonlinearity-induced photonic topological insulator. Science 370(6517), 701–704 (2020)

DOI

38
Yu, F., Zhang, X.L., Tian, Z.N., Chen, Q.D., Sun, H.B.: General rules governing the dynamical encircling of an arbitrary number of exceptional points. Phys. Rev. Lett. 127(25), 253901 (2021)

DOI

39
Wu, L.H., Hu, X.: Scheme for achieving a topological photonic crystal by using dielectric material. Phys. Rev. Lett. 114, 223901 (2015)

DOI

40
Liu, W.J., Ji, Z.R., Wang, Y.H., Modi, G., Hwang, M., Zheng, B.Y., Sorger, V.J., Pan, A.L., Agarwal, R.: Generation of helical topological exciton-polaritons. Science 370(6516), 600–604 (2020)

DOI

41
Zhao, H., Qiao, X.D., Wu, T.W., Midya, B., Longhi, S., Feng, L.: Non-Hermitian topological light steering. Science 365(6458), 1163–1166 (2019)

DOI

42
Li, Y.D., Fan, C.X., Hu, X.Y., Ao, Y.T., Lu, C.C., Chan, C.T., Kennes, D.M., Gong, Q.H.: Effective hamiltonian for photonic topological insulator with non-Hermitian domain walls. Phys. Rev. Lett. 129, 053903 (2022)

DOI

43
Wang, X.X., Li, Y.D., Hu, X.Y., Gu, R.Z., Ao, Y.T., Jiang, P., Gong, Q.H.: Non-Hermitian high-quality-factor topological photonic crystal cavity. Phys. Rev. A (Coll Park) 105(2), 023531 (2022)

DOI

44
Chen, X.D., He, X.T., Dong, J.W.: All-dielectric layered photonic topological insulators. Laser Photonics Rev. 13, 1900091 (2019)

DOI

45
Yang, Y.T., Xu, Y.F., Xu, T., Wang, H.X., Jiang, J.H., Hu, X., Hang, Z.H.: Visualization of a unidirectional electromagnetic waveguide using topological photonic crystals made of dielectric materials. Phys. Rev. Lett. 120, 217401 (2018)

DOI

46
Chen, X.D., Deng, W.M., Shi, F.L., Zhao, F.L., Chen, M., Dong, J.W.: Direct observation of corner states in second-order topological photonic crystal slabs. Phys. Rev. Lett. 122(23), 233902 (2019).

DOI

47
Liu, Y., Leung, S., Li, F.F., Lin, Z.K., Tao, X., Poo, Y., Jiang, J.H.: Bulk–disclination correspondence in topological crystalline insulators. Nature 589(7842), 381–385 (2021)

DOI

48
Guo, A., Salamo, G.J., Duchesne, D., Morandotti, R., Volatier-Ravat, M., Aimez, V., Siviloglou, G.A., Christodoulides, D.N.: Observation of P T-symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103(9), 093902 (2009).

DOI

49
Zhu, W., Gong, J.: Photonic corner skin modes in non-Hermitian photonic crystals. Phys. Rev. B 108(3), 035406 (2023)

DOI

50
Bernier, N.R., Tóth, L.D., Koottandavida, A., Ioannou, M.A., Malz, D., Nunnenkamp, A., Feofanov, A.K., Kippenberg, T.J.: Nonreciprocal reconfigurable microwave optomechanical circuit. Nat. Commun. 8(1), 604 (2017)

DOI

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