Instabilities and solitons in systems with spatio-temporal dispersions and non paraxial approximations

Abstract

We consider the evolution of light beams in nonlinear Kerr media wherein the beam propagation is governed by the coupled non-paraxial (2+1) dimensional nonlinear Schrödinger equation. In the advent of system failing to obey the slowly varying envelope approximation, the usual paraxial approximation cannot be adopted. Our model equation could potentially serve as a governing model for nano-waveguides and on-chip silicon photonic devices. Using the trial solution method, we derive the different combinations of soliton solutions such as bright–bright, dark–dark, and bright–dark soliton and briefly discuss the characteristics of the soliton. Following the initial discussion on the soliton solution, we extend the study to investigate the modulational instability of the system of equations. We examine the role of the dispersion/diffraction in the instability spectra and demonstrate the different characteristics of the instability bands as a function of system parameters.