Topological Edge States and Gap Solitons in the Nonlinear Dirac Model

Topological photonics has emerged recently as a novel approach for realizing robust optical circuitry, and the study of nonlinear effects in topological photonics is expected to open the door for tunability of photonic structures with topological properties. Here, the topological edge states and topological gap solitons which reside in the same band gaps described by the nonlinear Dirac model are studied, in both one and two dimensions. Strong nonlinear interactions between these dissimilar topological modes, manifested in the efficient excitation of topological edge states by scattered traveling gap solitons are revealed. Nonlinear tunability of localized states is explicated with exact analytical solutions for the two-component spinor wave function. Our studies are complemented by spatiotemporal numerical modeling of the nonlinear scattering in 1D and 2D photonic lattices.