Theoretical Model for Nonlinear Photonic Topological Insulators

Abstract

Over the past few years, nonlinear topological photonics have garnered significant attention due to their intriguing properties and potential applications. Research in nonlinear topological photonics has revealed a variety of interesting phenomena, including nonlinearity-induced topological phase transitions, the formation of edge solitons, and the influence of the Kerr effect on the emergence of edge modes. This thesis focuses on investigating the spontaneous symmetry breaking of counter-propagating light, specifically between clockwise (CW) and counterclockwise (CCW) modes, within the framework of a one-dimensional Su-Schrieffer-Heeger (SSH) model consisting of optical ring resonators with Kerr nonlinearity. The approach in this thesis is based on the Lugiato-Lefever equation, which we extended to describe the field amplitudes in each ring resonator for both CW and CCW modes, considering small and large cross-phase modulation (XPM) strength. With a small XPM strength, one can demonstrate the optical bistability of the edge mode. However, with large XPM strength, when the coupling between CW and CCW modes becomes stronger, we observed complex dynamics in light propagation as well as optical bistability. Strong nonlinearity via XPM with the associated high pump intensity leads to excitation of the bulk modes for large detuning values, showing periodic and chaotic oscillations. As there are many parameters that can affect the spontaneous symmetry breaking of counter-propagating light through nonlinear SSH lattice, we will present phase diagrams depending on variant parameters: input intensity, XPM strength, coupling with sources, and intercell coupling coefficient. Then, we will compare the dynamic of the nonlinear SSH lattice with identical coupling coefficients. Further, to investigate the system in depth, we will apply a data-driven method called dynamical mode decomposition, which extracts spatial modes. The study of nonlinear topological photonics and spontaneous symmetry breaking in optical SSH lattices paves the way for applications such as robust optical isolators and circulators, all-optical memory and switching devices.