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  • Letter
  • Open Access

Evolution of topological edge modes from honeycomb photonic crystals to triangular-lattice photonic crystals

Jin-Kyu Yang1,2,*, Yongsop Hwang2, and Sang Soon Oh3,†

  • 1Department of Optical Engineering, Kongju National University, Cheonan 31080, South Korea
  • 2Institute of Application and Fusion for Light, Kongju National University, Cheonan 31080, South Korea
  • 3School of Physics and Astronomy, Cardiff University, Cardiff CF24 3AA, United Kingdom

  • *jinkyuyang@kongju.ac.kr
  • †OhS2@cardiff.ac.uk
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Phys. Rev. Research 3, L022025 – Published 21 June, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L022025

Abstract

The presence of edge modes at the interface of two perturbed honeycomb photonic crystals with C6 symmetry is often attributed to the different signs of Berry curvature at the K and K′ valleys. In contrast to the electronic counterpart, the Chern number defined in photonic valley Hall effect is not a quantized quantity but can be tuned to a finite value including zero simply by changing geometrical perturbations. Here, we argue that the edge modes in photonic valley Hall effect can exist even when Berry curvature vanishes. We numerically demonstrate the presence of the zero-Berry-curvature edge modes in triangular-lattice photonic crystal slab structures in which C3 symmetry is maintained but the inversion symmetry is broken. We investigate the evolution of the Berry curvature from the honeycomb-lattice slab structure to the triangular-lattice photonic crystal slab and show that the triangular-lattice photonic crystals still support edge modes in a very wide photonic band gap. We find that the edge modes with zero Berry curvature can propagate with extremely low bending loss along the interface formed by the triangular-lattice photonic crystals.

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References (31)

  1. C. L. Kane and E. J. Mele, Quantum Spin Hall Effect in Graphene, Phys. Rev. Lett. 95, 226801 (2005).
  2. B. A. Bernevig, T. L. Hughes, and S.-C. Zhang,Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science 314, 1757 (2006).
  3. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  4. F. D. M. Haldane and S. Raghu, Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry, Phys. Rev. Lett. 100, 013904 (2008).
  5. Z. Wang, Y. D. Chong, J. D. Joannopoulos, and M. Soljacic, Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal, Phys. Rev. Lett. 100, 013905 (2008).
  6. A. B. Khanikaev, S. H. Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, Photonic topological insulators, Nat. Mater. 12, 233 (2013).
  7. M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Photonic Floquet topological insulators Nature (London) 496, 196 (2013)
  8. X. Cheng, C. Jouvaud, X. Ni, S. H. Mousavi, A. Z. Genack, and A. B. Khanikaev, Robust reconfigurable electromagnetic pathways within a photonic topological insulator, Nat. Mater. 15, 542 (2016).
  9. W.-J. Chen, S.-J. Jiang, X.-D. Chen, J.-W. Dong, and C. T. Chan, Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide, Nat. Commun. 5, 5782 (2014).
  10. X.-D. Chen, F.-L. Zhao, M. Chen, and J.-W. Dong, Valley-contrasting physics in all-dielectric photonic crystals: Orbital angular momentum and topological propagation, Phys. Rev. B 96, 020202(R) (2017).
  11. T. Ma and G. Shvets, All-Si valley-Hall photonic topological insulator, New J. Phys. 18, 025012 (2016).
  12. M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, and N. M. Litchinitser, Robust topologically protected transport in photonic crystals at telecommunication wavelengths, Nat. Nanotechnol. 14, 31 (2019).
  13. S. Arora, T. Bauer, R. Barczyk et al., Direct quantification of topological protection in symmetry-protected photonic edge states at telecom wavelengths, Light: Sci. Appl. 10, 9 (2021).
  14. L.-H. Wu and X. Hu, Scheme for Achieving a Topological Photonic Crystal by Using Dielectric Material, Phys. Rev. Lett. 114, 223901 (2015).
  15. Y. Yang, Y. F. Xu, T. Xu, H. X. Wang, J. H. Jiang, X. Hu, and Z. H. Hang, Visualization of a Unidirectional Electromagnetic Waveguide Using Topological Photonic Crystals Made of Dielectric Materials, Phys. Rev. Lett. 120, 217401 (2018).
  16. N. Parappurath, F. Alpeggiani, L. Kuipers, and E. Verhagen, Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing, Sci. Adv. 6, eaaw4137 (2020).
  17. M. Proctor, P. A. Huidobro, B. Bradlyn, M. B. de Paz, M. G. Vergniory, D. Bercioux, and A. Garcia-Etxarri, Robustness of topological corner modes in photonic crystals, Phys. Rev. Research 2, 042038(R) (2020).
  18. X. T. He, E. T. Liang, J. J. Yuan, H. Y. Qiu, X. D. Chen, F. L. Zhao, and J. W. Dong, A silicon-on-insulator slab for topological valley transport, Nat. Commun. 10, 872 (2019).
  19. M. J. Mehrabad, A. P. Foster, R. Dost, E. Clarke, P. K. Patil, A. M. Fox, M. S. Skolnick, and L. R. Wilson, Chiral topological photonics with an embedded quantum emitter, Optica 7, 1690 (2020)
  20. S. Wong, M. Saba, O. Hess, and S. S. Oh, Gapless unidirectional photonic transport using all-dielectric kagome lattices, Phys. Rev. Research 2, 012011(R) (2020).
  21. The MATLAB codes used to calculate Berry curvature and Chern numbers are available on https://github.com/PTIcode/ChernCalc.
  22. M. Saba, S. Wong, M. Elman, S. S. Oh, and O. Hess, Nature of topological protection in photonic spin and valley Hall insulators, Phys. Rev. B 101, 054307 (2020).
  23. S. G. Johnson and J. D. Joannopoulos, Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis, Opt. Express 8, 173 (2001).
  24. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L022025 for band analysis and field analysis of photonic topological edge modes.
  25. COMSOL Multiphysics v. 5.4. www.comsol.com. COMSOL AB, Stockholm, Sweden.
  26. J. L. Liu, W. M. Ye, and S. Zhang, Pseudospin-induced chirality with staggered optical graphene, Light: Sci. Appl. 5, e16094 (2016).
  27. F. Liu and K. Wakabayashi, Novel Topological Phase with a Zero Berry Curvature, Phys. Rev. Lett. 118, 076803 (2017).
  28. F. Liu, H. Y. Deng, and K. Wakabayashi, Topological photonic crystals with zero Berry curvature, Phys. Rev. B 97, 035442 (2018).
  29. D. J. Bisharat and D. F. Sievenpiper, Topological local-valley interface in ordinary photonic crystal waveguide, Proc. SPIE 11290, 112900N (2020).
  30. A. Taflove and S. G. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 2005).
  31. I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, Deterministic photon-emitter coupling in chiral photonic circuits, Nat. Nanotechnol. 10, 775 (2015).

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Phys. Rev. Research 3, L022025– Published 21 June, 2021
  • Received 13 January 2021
  • Revised 5 April 2021
  • Accepted 5 May 2021
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