2022/06/12 by Mark J. Ablowitz, Ablowitz, Mark, Justin T. Cole +3
Physics and Astronomy · #14D21 #35F20 #35F50 #78A60 #78M34 #78M35 #FOS: Physical sciences #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS) #Quantum chaos and dynamical systems #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2206.05832
openalex publication_date 2022/06/12 · openalex created_date 2022/06/16 · openalex updated_date 2026/08/01
A unified method to analyze the dynamics and topological structure associated with a class of Floquet topological insulators is presented. The method is applied to a system that describes the propagation of electromagnetic waves through the bulk of a two-dimensional lattice that is helically-driven in the direction of propagation. Tight-binding approximations are employed to derive reduced dynamical systems. Further asymptotic approximations, valid in the high-frequency driving regime, yield a time-averaged system which governs the leading order behavior of the wave. From this follows an analytic calculation of the Berry connection, curvature and Chern number by analyzing the local behavior of the eigenfunctions near the critical points of the spectrum. Examples include honeycomb, Lieb and kagome lattices. In the nonlinear regime novel equations governing slowly varying wave envelopes are derived. For the honeycomb lattice, numerical simulations show that for relatively small nonlinear effects a striking spiral patterns occurs; as nonlinearity increases localized structures emerge and for somewhat higher nonlinearity the waves collapse.