Stability of nonparaxial gap-soliton bullets in waveguide gratings

We investigate the formation and propagation of gap-soliton bullets in nonlinear periodic waveguides at frequencies close to the gap for Bragg reflection beyond the paraxial approximation. Using a multiple-scales analysis, we derive a two-dimensional (2D) nonlinear Schrödinger equation with higher-order correction terms that consider the nonparaxial regimes in the slowly-varying envelope approximation. In addition, a fully numerical simulation of the newly derived model equation demonstrates that the mutual balancing between Kerr, dimensionality, higher-order dispersions and nonparaxiality allows shape-preserving propagation of gap-soliton bullets in a grating waveguide.