- Letter
- Open Access
Asymmetrical temporal dynamics of edge modes in Su-Schrieffer-Heeger lattice with Kerr nonlinearity
Phys. Rev. Research 6, L042013 – Published 15 October, 2024
DOI: https://doi.org/10.1103/PhysRevResearch.6.L042013
Abstract
Optical bistability and oscillating phases exist in a Sagnac interferometer and a single ring resonator made of a nonlinear medium where the refractive indices are modulated by the light intensity due to the Kerr nonlinearity. An array of coupled nonlinear ring resonators behave similarly but with more complexity due to the presence of the additional couplings. Here we theoretically demonstrate the bifurcation of edge modes, which leads to optical bistability in the Su-Schrieffer-Heeger lattice with the Kerr nonlinearity. We also demonstrate periodic and chaotic switching behaviors in an oscillating phase resulting from the coupling between the edge mode and bulk modes with different chiralities, i.e., clockwise and counterclockwise circulations.
Physics Subject Headings (PhySH)
Article Text
References (45)
- R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic Press, London, 2008).
- A. Kaplan and P. Meystre, Directionally asymmetrical bistability in a symmetrically pumped nonlinear ring interferometer, Opt. Commun. 40, 229 (1982).
- L. Del Bino, J. M. Silver, S. L. Stebbings, and P. Del'Haye, Symmetry breaking of counter-propagating light in a nonlinear resonator, Sci. Rep. 7, 43142 (2017).
- L. Del Bino, J. M. Silver, M. T. M. Woodley, S. L. Stebbings, X. Zhao, and P. Del'Haye, Microresonator isolators and circulators based on the intrinsic nonreciprocity of the Kerr effect, Optica 5, 279 (2018).
- J.-B. Shim, P. Schlagheck, M. Hentschel, and J. Wiersig, Nonlinear dynamical tunneling of optical whispering gallery modes in the presence of a Kerr nonlinearity, Phys. Rev. A 94, 053849 (2016).
- G. Xu, A. U. Nielsen, B. Garbin, L. Hill, G. L. Oppo, J. Fatome, S. G. Murdoch, S. Coen, and M. Erkintalo, Spontaneous symmetry breaking of dissipative optical solitons in a two-component Kerr resonator, Nat. Commun. 12, 4023 (2021).
- S. Coen, B. Garbin, G. Xu, L. Quinn, N. Goldman, G.-L. Oppo, M. Erkintalo, S. G. Murdoch, and J. Fatome, Nonlinear topological symmetry protection in a dissipative system, Nat. Commun. 15, 1398 (2024).
- A. Ghosh, A. Pal, L. Hill, G. N. Campbell, T. Bi, Y. Zhang, A. Alabbadi, S. Zhang, G.-L. Oppo, and P. Del'Haye, Controlled light distribution with coupled microresonator chains via Kerr symmetry breaking, arXiv:2402.10673.
- L. Hill, G.-L. Oppo, M. T. M. Woodley, and P. Del'Haye, Effects of self- and cross-phase modulation on the spontaneous symmetry breaking of light in ring resonators, Phys. Rev. A 101, 013823 (2020).
- J. C. Y. Teo and C. L. Kane, Topological defects and gapless modes in insulators and superconductors, Phys. Rev. B 82, 115120 (2010).
- R.-J. Slager, The translational side of topological band insulators, J. Phys. Chem. Solids 128, 24 (2019).
- R.-J. Slager, A. Mesaros, V. Juričić, and J. Zaanen, Interplay between electronic topology and crystal symmetry: Dislocation-line modes in topological band insulators, Phys. Rev. B 90, 241403(R) (2014).
- T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys. 91, 015006 (2019).
- A. B. Khanikaev, S. Hossein Mousavi, W.-K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, Photonic topological insulators, Nat. Mater. 12, 233 (2013).
- J. Noh, S. Huang, K. P. Chen, and M. C. Rechtsman, Observation of photonic topological valley Hall edge states, Phys. Rev. Lett. 120, 063902 (2018).
- C. Han, M. Lee, S. Callard, C. Seassal, and H. Jeon, Lasing at topological edge states in a photonic crystal L3 nanocavity dimer array, Light: Sci. Appl. 8, 40 (2019).
- G. Harari, M. A. Bandres, Y. Lumer, M. C. Rechtsman, Y. D. Chong, M. Khajavikhan, D. N. Christodoulides, and M. Segev, Topological insulator laser: Theory, Science 359, eaar4003 (2018).
- M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Topological insulator laser: Experiments, Science 359, eaar4005 (2018).
- Y. Gong, S. Wong, A. J. Bennett, D. L. Huffaker, and S. S. Oh, Topological insulator laser using valley-Hall photonic crystals, ACS Photon. 7, 2089 (2020).
- S. Wong, J. Olthaus, T. K. Bracht, D. E. Reiter, and S. S. Oh, A machine learning approach to drawing phase diagrams of topological lasing modes, Commun. Phys. 6, 104 (2023).
- D. Leykam and Y. D. Chong, Edge solitons in nonlinear-photonic topological insulators, Phys. Rev. Lett. 117, 143901 (2016).
- X. Zhou, Y. Wang, D. Leykam, and Y. Chong, Optical isolation with nonlinear topological photonics, New J. Phys. 19, 095002 (2017).
- L. J. Maczewsky, M. Heinrich, M. Kremer, S. K. Ivanov, M. Ehrhardt, F. Martinez, Y. V. Kartashov, V. V. Konotop, L. Torner, D. Bauer, and A. Szameit, Nonlinearity-induced photonic topological insulator, Science 370, 701 (2020).
- S. K. Ivanov, Y. V. Kartashov, and L. Torner, Light bullets in Su-Schrieffer-Heeger photonic topological insulators, Phys. Rev. A 107, 033514 (2023).
- Y. V. Kartashov and D. V. Skryabin, Bistable topological insulator with exciton-polaritons, Phys. Rev. Lett. 119, 253904 (2017).
- W. Zhang, X. Chen, Y. V. Kartashov, D. V. Skryabin, and F. Ye, Finite-dimensional bistable topological insulators: From small to large, Laser Photon. Rev. 13, 1900198 (2019).
- Y. Hadad, A. B. Khanikaev, and A. Alù, Self-induced topological transitions and edge states supported by nonlinear staggered potentials, Phys. Rev. B 93, 155112 (2016).
- D. A. Dobrykh, A. V. Yulin, A. P. Slobozhanyuk, A. N. Poddubny, and Y. S. Kivshar, Nonlinear control of electromagnetic topological edge states, Phys. Rev. Lett. 121, 163901 (2018).
- D. Leykam and L. Yuan, Topological phases in ring resonators: Recent progress and future prospects, Nanophotonics 9, 4473 (2020).
- A. Roy, M. Parto, R. Nehra, C. Leefmans, and A. Marandi, Topological optical parametric oscillation, Nanophotonics 11, 1611 (2022).
- M. Ezawa, Nonlinearity-induced transition in the nonlinear Su-Schrieffer-Heeger model and a nonlinear higher-order topological system, Phys. Rev. B 104, 235420 (2021).
- M. Ezawa, Nonlinear non-Hermitian higher-order topological laser, Phys. Rev. Res. 4, 013195 (2022).
- M.-S. Wei, M.-J. Liao, C. Wang, C. Zhu, J. Xu, and Y. Yang, Phase transition and dynamics of qubits in coupled-cavity arrays with nonlinear topological photonics, Results Phys. 45, 106232 (2023).
- Y.-P. Ma and H. Susanto, Topological edge solitons and their stability in a nonlinear Su-Schrieffer-Heeger model, Phys. Rev. E 104, 054206 (2021).
- L. A. Lugiato and R. Lefever, Spatial dissipative structures in passive optical systems, Phys. Rev. Lett. 58, 2209 (1987).
- H. H. Haus, Waves and Fields in Optoelectronics (Prentice Hall, New Jersey, 1984).
- W. Suh, Z. Wang, and S. Fan, Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities, IEEE J. Quantum Electron. 40, 1511 (2004).
- G. Agrawal, Nonlinear Fiber Optics, 6th ed. (Academic Press, London, 2019).
- A. E. Kaplan and P. Meystre, Enhancement of the Sagnac effect due to nonlinearly induced nonreciprocity, Opt. Lett. 6, 590 (1981).
- Q.-T. Cao, R. Liu, H. Wang, Y.-K. Lu, C.-W. Qiu, S. Rotter, Q. Gong, and Y.-F. Xiao, Reconfigurable symmetry-broken laser in a symmetric microcavity, Nat. Commun. 11, 1136 (2020).
- S. Longhi, Y. Kominis, and V. Kovanis, Presence of temporal dynamical instabilities in topological insulator lasers, Europhys. Lett. 122, 14004 (2018).
- W. Bogaerts, P. De Heyn, T. Van Vaerenbergh, K. De Vos, S. Kumar Selvaraja, T. Claes, P. Dumon, P. Bienstman, D. Van Thourhout, and R. Baets, Silicon microring resonators, Laser Photon. Rev. 6, 47 (2012).
- L. D. Bino, N. Moroney, and P. Del'Haye, Optical memories and switching dynamics of counterpropagating light states in microresonators, Opt. Express 29, 2193 (2021).
- M. T. M. Woodley, L. Hill, L. Del Bino, G.-L. Oppo, and P. Del'Haye, Self-switching Kerr oscillations of counterpropagating light in microresonators, Phys. Rev. Lett. 126, 043901 (2021).
- S. S. Oh, G. Alharbi, S. Wong, and Y. Gong, Research data supporting “Asymmetrical temporal dynamics of edge modes in Su-Schrieffer-Heeger lattice with Kerr nonlinearity” (2024), doi:10.17035/cardiff.26565526.v1.