Nonparaxial elliptic waves and solitary waves in coupled nonlinear Helmholtz equations

TL;DR

This paper derives elliptic and solitary wave solutions for coupled nonlinear Helmholtz equations, analyzing how nonparaxial effects influence wave properties and revealing a new phase-unlocking phenomenon.

Contribution

It introduces explicit elliptic and solitary wave solutions for CNLH equations and explores the impact of nonparaxiality on wave characteristics and phase behavior.

Findings

Existence of elliptic and solitary wave solutions in CNLH equations

Nonparaxiality affects wave speed, width, and amplitude

Discovery of phase-unlocking behavior due to nonparaxial effects

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.