Nonparaxial elliptic waves and solitary waves in coupled nonlinear Helmholtz equations

Abstract

We obtain a class of elliptic wave solutions of coupled nonlinear Helmholtz (CNLH) equations describing nonparaxial ultra-broad beam propagation in nonlinear Kerr-like media, in terms of the Jacobi elliptic functions and also discuss their limiting forms (hyperbolic solutions). Especially, we show the existence of non-trivial solitary wave profiles in the CNLH system. The effect of nonparaxiality on the speed, pulse width and amplitude of the nonlinear waves is analysed in detail. Particularly a mechanism for tuning the speed by altering the nonparaxial parameter is proposed. We also identify a novel phase-unlocking behaviour due to the presence of nonparaxial parameter.