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Coupled waveguide–cavity system based on higher-order topological states in square lattice photonic crystals

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Abstract

Recently, higher-order topological states have been widely researched due to its unique properties in manipulating the propagation of light. In this paper, we propose a square lattice photonic crystal composed of rhombic dielectric columns, and realize topological phase transition by lattice transformation without breaking the C4 symmetry. The topological edge states and topological corner states are demonstrated in the combination structures of two photonic crystals with different Zak phases. We also present a new method to make four nearly degenerate topological corner states having larger frequency difference and construct a waveguide–cavity coupling system based on topological photonic crystals to realize the multifunction of topological optical switch and controllable optical storage. Our research paves a new way for the design of optical communication devices.

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Data availability

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. X.-W. Luo, C. Zhang, Higher-order topological corner states induced by gain and loss. Phys. Rev. Lett. (2019). https://doi.org/10.1103/PhysRevLett.123.073601

    Article  MathSciNet  Google Scholar 

  2. W. Zhang, D. Zou, Q. Pei, W. He, J. Bao, H. Sun, X. Zhang, Experimental observation of higher-order topological anderson insulators. Phys. Rev. Lett. (2021). https://doi.org/10.1103/PhysRevLett.126.146802

    Article  Google Scholar 

  3. X.-D. Chen, W.-M. Deng, F.-L. Zhao, J.-W. Dong, Accidental double dirac cones and robust edge states in topological anisotropic photonic crystals. Laser Photon. Rev. (2018). https://doi.org/10.1002/lpor.201800073

    Article  Google Scholar 

  4. M.-C. Jin, Y.-F. Gao, H.-Z. Lin, Y.-H. He, M.-Y. Chen, Corner states in second-order two-dimensional topological photonic crystals with reversed materials. Phys. Rev. A. (2022). https://doi.org/10.1103/PhysRevA.106.013510

    Article  Google Scholar 

  5. F. Liu, H.-Y. Deng, K. Wakabayashi, Topological photonic crystals with zero Berry curvature. Phys. Rev. B. (2018). https://doi.org/10.1103/PhysRevB.97.035442

    Article  Google Scholar 

  6. 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. (2019). https://doi.org/10.1103/PhysRevLett.122.233902

    Article  Google Scholar 

  7. F. Gao, Z. Gao, X. Shi, Z. Yang, X. Lin, H. Xu, J.D. Joannopoulos, M. Soljacic, H. Chen, L. Lu, Y. Chong, B. Zhang, Probing topological protection using a designer surface plasmon structure. Nat. Commun. (2016). https://doi.org/10.1038/ncomms11619

    Article  Google Scholar 

  8. S. Mukherjee, A. Spracklen, M. Valiente, E. Andersson, P. Ohberg, N. Goldman, R.R. Thomson, Experimental observation of anomalous topological edge modes in a slowly driven photonic lattice. Nat. Commun. (2017). https://doi.org/10.1038/ncomms13918

    Article  Google Scholar 

  9. N. Parappurath, F. Alpeggiani, L. Kuipers, E. Verhagen, Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing, Sci. Adv. 6, eaaw4137 (2020).

  10. H. Fan, B. Xia, L. Tong, S. Meng, D. Yu, Elastic Higher-Order Topological insulator with topologically protected corner states. Phys. Rev. Lett. (2019). https://doi.org/10.1103/PhysRevLett.122.204301

    Article  Google Scholar 

  11. Y.-F. Gao, Y.-H. He, A. Maimaiti, M.-C. Jin, Y. He, X.-F. Qi, Manipulation of coupling between topological edge state and corner state in photonic crystals. Opt. Laser Technol. 155, 108387 (2022)

    Article  Google Scholar 

  12. Z.G. Geng, Y.G. Peng, P.Q. Li, Y.X. Shen, D.G. Zhao, X.F. Zhu, Mirror-symmetry induced topological valley transport along programmable boundaries in a hexagonal sonic crystal. J. Phys. Condens. Matter 31, 245403 (2019)

    Article  ADS  Google Scholar 

  13. J. Vila, R.K. Pal, M. Ruzzene, Observation of topological valley modes in an elastic hexagonal lattice. Phys. Rev. B. (2017). https://doi.org/10.1103/PhysRevB.96.134307

    Article  Google Scholar 

  14. Y.-H. He, Y.-F. Gao, Y. He, X.-F. Qi, J.-Q. Si, M. Yang, S.-Y. Zhou, Realization of edge and corner states in photonic crystals with kagome lattices through topological insulator generators. Opt. Laser Technol. 161, 109196 (2023)

    Article  Google Scholar 

  15. M. Ezawa, Higher-order topological insulators and semimetals on the breathing kagome and pyrochlore lattices. Phys. Rev. Lett. (2018). https://doi.org/10.1103/PhysRevLett.120.026801

    Article  Google Scholar 

  16. B.Y. Xie, H.F. Wang, H.X. Wang, X.Y. Zhu, J.H. Jiang, M.H. Lu, Y.F. Chen, Second-order photonic topological insulator with corner states. Phys. Rev. B. (2018). https://doi.org/10.1103/PhysRevB.98.205147

    Article  Google Scholar 

  17. L. Jin, Z. Song, Bulk-boundary correspondence in a non-hermitian system in one dimension with chiral inversion symmetry. Phys. Rev. B (2019). https://doi.org/10.1103/PhysRevB.99.081103

    Article  Google Scholar 

  18. S. Longhi, Topological phase transition in non-hermitian quasicrystals. Phys. Rev. Lett. (2019). https://doi.org/10.1103/PhysRevLett.122.237601

    Article  Google Scholar 

  19. M. Verbin, O. Zilberberg, Y.E. Kraus, Y. Lahini, Y. Silberberg, Observation of topological phase transitions in photonic quasicrystals. Phys. Rev. Lett. (2013). https://doi.org/10.1103/PhysRevLett.110.076403

    Article  Google Scholar 

  20. S. Weidemann, M. Kremer, S. Longhi, A. Szameit, Topological triple phase transition in non-hermitian floquet quasicrystals. Nature 601(7893), 345–359 (2022)

    Article  ADS  Google Scholar 

  21. M. Atala, M. Aidelsburger, J.T. Barreiro, D. Abanin, T. Kitagawa, E. Demler, I. Bloch, Direct measurement of the zak phase in topological bloch bands. Nat. Phys. 9, 795–800 (2013)

    Article  Google Scholar 

  22. 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. (2015). https://doi.org/10.1103/PhysRevLett.115.040402

    Article  Google Scholar 

  23. A. Shi, B. Yan, R. Ge, J. Xie, Y. Peng, H. Li, W.E.I. Sha, J. Liu, Coupled cavity-waveguide based on topological corner state and edge state. Opt. Lett. 46(5), 1089 (2021)

    Article  ADS  Google Scholar 

  24. F. Liu, K. Wakabayashi, Novel topological phase with a zero berry curvature. Phys. Rev. Lett. (2017). https://doi.org/10.1103/PhysRevLett.118.076803

    Article  Google Scholar 

  25. B.-Y. Xie, H.-F. Wang, H.-X. Wang, X.-Y. Zhu, J.-H. Jiang, M.-H. Lu, Y.-F. Chen, Second-order photonic topological insulator with corner states. Phys. Rev. B (2018). https://doi.org/10.1103/PhysRevB.98.205147

    Article  Google Scholar 

  26. Y. Peng, B. Yan, J. Xie, E. Liu, H. Li, R. Ge, F. Gao, J. Liu, Variation of topological edge states of 2d honeycomb lattice photonic crystals. Physica Status Solidi-Rapid Res. Lett. (2020). https://doi.org/10.1002/pssr.202000202

    Article  Google Scholar 

  27. X.D. Zhang, Z.Q. Zhang, Creating a gap without symmetry breaking in two-dimensional photonic crystals. Phys. Rev. B 61, 9847–9850 (2000)

    Article  ADS  Google Scholar 

  28. X. Xie, W. Zhang, X. He, S. Wu, J. Dang, K. Peng, F. Song, L. Yang, H. Ni, Z. Niu, C. Wang, K. Jin, X. Zhang, X. Xu, Cavity quantum electrodynamics with second-order topological corner state. Laser Photon. Rev. (2020). https://doi.org/10.1103/PhysRevB.61.9847

    Article  Google Scholar 

  29. H.-R. Kim, M.-S. Hwang, D. Smirnova, K.-Y. Jeong, Y. Kivshar, H.-G. Park, Ieee, Lasing from multipolar modes of topological corner states, 2021 Conference on Lasers and Electro-Optics (CLEO) 2021.

  30. M.S. Rudner, N.H. Lindner, E. Berg, M. Levin, Anomalous edge states and the bulk-edge correspondence for periodically driven two-dimensional systems. Phys. Rev. X (2013). https://doi.org/10.1103/PhysRevX.3.031005

    Article  Google Scholar 

  31. Z. Song, Z. Fang, C. Fang, (d-2)-Dimensional edge states of rotation symmetry protected topological states. Phys. Rev. Lett. (2017). https://doi.org/10.1103/PhysRevLett.119.246402

    Article  Google Scholar 

  32. X. Wu, Y. Meng, J. Tian, Y. Huang, H. Xiang, D. Han, W. Wen, Direct observation of valley-polarized topological edge states in designer surface plasmon crystals. Nat. Commun. (2017). https://doi.org/10.1038/s41467-017-01515-2

    Article  Google Scholar 

  33. B.-Y. Xie, G.-X. Su, H.-F. Wang, H. Su, X.-P. Shen, P. Zhan, M.-H. Lu, Z.-L. Wang, Y.-F. Chen, Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals. Phys. Rev. Lett. (2019). https://doi.org/10.1103/PhysRevLett.122.233903

    Article  Google Scholar 

  34. X.-L. Sheng, C. Chen, H. Liu, Z. Chen, Z.-M. Yu, Y.X. Zhao, S.A. Yang, Two-dimensional second-order topological insulator in graphdiyne. Phys. Rev. Lett. (2019). https://doi.org/10.1103/PhysRevLett.123.256402

    Article  Google Scholar 

  35. Z. Wang, S. Fan, Magneto-optical defects in two-dimensional photonic crystals. Appl. Phys. B-Lasers Opt. 81, 369–375 (2005)

    Article  ADS  Google Scholar 

  36. Y. Chen, J. Zhu, Z. Su, Topology optimization of a second-order phononic topological insulator with dual-band corner states. J Sound Vibr 544, 117410 (2023)

    Article  Google Scholar 

  37. S.K. Ivanov, Y.V. Kartashov, L. Torner, Light bullets in Su-Schrieffer-Heeger photonic topological insulators. Phys. Rev. A (2023). https://doi.org/10.1103/PhysRevA.107.033514

    Article  Google Scholar 

  38. P. Markos, V. Kuzmiak, Coupling between Fano and Bragg bands in the photonic band structure of two- dimensional metallic photonic structures. Phys. Rev. A (2016). https://doi.org/10.1103/PhysRevA.94.033845

    Article  Google Scholar 

  39. S.-L. Shen, J.-L. Li, J.-F. Wu, C. Li, All-optical analog to electromagnetically induced transparency based on higher-order topological states. Eur. Phys. J. Plus (2022). https://doi.org/10.1140/epjp/s13360-021-02313-y

    Article  Google Scholar 

  40. T. Hai, G. Xie, J. Ma, H. Shao, Z. Qiao, Z. Qin, Y. Sun, F. Wang, P. Yuan, J. Ma, L. Qian, Pushing optical switch into deep mid-Infrared region: band theory, characterization, and performance of topological semimetal antimonene. ACS Nano 15, 7430–7438 (2021).

  41. J.-Q. Zhao, H.-S. Shi, L.-R. Zeng, H. Ge, Y.-H. Hou, X.-M. Wu, C.-Y. Yue, X.-W. Lei, Highly emissive zero-dimensional antimony halide for anti-counterfeiting and confidential information encryption-decryption. Chem. Eng. J (2022). https://doi.org/10.1016/j.cej.2021.134336

    Article  Google Scholar 

  42. C. Wu, F. Feng, Y. Xie, Design of vanadium oxide structures with controllable electrical properties for energy applications. Chem. Soc. Rev. 42(12), 5157 (2013)

    Article  Google Scholar 

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Acknowledgements

This work was supported by the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX23_3628), the Industrial Center’s Innovation & Practice Program of Jiangsu University, China (Grant Nos. ZXJG2022036 and ZXJG2022037), the Practice and Innovation Training Project of College Students of Jiangsu University (Grant No. 202310299206Y).

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Authors and Affiliations

  1. School of Mechanical Engineering, Jiangsu University, Zhenjiang, 212013, Jiangsu, China

    Yong-Feng Gao, Xiao-Fei Qi, Subinuer Rouzi, Meng-Cheng Jin, Yue He, Yi-Han He & Ming-Yang Sun

  2. School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, 212013, Jiangsu, China

    Zhi-Guo Yan

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Contributions

Yong-Feng Gao: Project administration, Conceptualization, Writing – review & editing. Xiao-Fei Qi: Methodology, Investigation, Writing – original draft. Zhi-Guo Yan: Investigation. Subinuer Rrouzi: Data curation. Meng-Cheng Jin: Software. Yue He: Formal analysis. Yi-Han He: Investigation, Validation. Ming-Yang Sun: Visualization. All authors reviewed the manuscript.

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Correspondence to Yong-Feng Gao.

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Gao, YF., Qi, XF., Yan, ZG. et al. Coupled waveguide–cavity system based on higher-order topological states in square lattice photonic crystals. Appl. Phys. B 129, 156 (2023). https://doi.org/10.1007/s00340-023-08101-z

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