Gap solitons in dual-core Bragg gratings with dispersive reflectivity

Abstract

We investigate the existence and stability of gap solitons in a system of two linearly coupled Bragg gratings with dispersive reflectivity. It is found that families of symmetric and asymmetric solitons fill the entire bandgap and that above a certain value of the dispersive reflectivity parameter the solitons develop sidelobes. Exact analytical expressions for the tails of symmetric and asymmetric solitons are presented and found to be in excellent agreement with the numerical results. We also derive analytical conditions for the appearance of the sidelobes. The stability of symmetric and asymmetric solitons is investigated numerically. A key finding is that dispersive reflectivity has a stabilizing effect and results in the expansion of the stability region for the asymmetric solitons. It is also shown that the stabilization effect due to dispersive reflectivity is more pronounced for smaller coupling coefficients.