Topological Edge States and Gap Solitons in the Nonlinear Dirac Model

Abstract

Topological photonics has emerged recently as a novel approach for realizingrobust optical circuitry, and the study of nonlinear effects in topologicalphotonics is expected to open the door for tunability of photonic structureswith topological properties. Here, the topological edge states and topologicalgap solitons which reside in the same band gaps described by the nonlinearDirac model are studied, in both one and two dimensions. Strong nonlinearinteractions between these dissimilar topological modes, manifested in theefficient excitation of topological edge states by scattered traveling gapsolitons are revealed. Nonlinear tunability of localized states is explicated withexact analytical solutions for the two-component spinor wave function. Ourstudies are complemented by spatiotemporal numerical modeling of thenonlinear scattering in 1D and 2D photonic lattices. Show more