Chirped Elliptic Waves: Coupled Helmholtz Equations

TL;DR

This paper derives exact chirped elliptic wave solutions in coupled Helmholtz equations with non-Kerr nonlinearities, analyzing how parameters influence wave chirp, speed, and stability for potential applications in nonlinear optics.

Contribution

It presents new exact solutions for chirped elliptic waves in coupled Helmholtz equations considering non-Kerr effects, including self steepening and frequency shift.

Findings

Chirp reversal occurs for specific parameter combinations.

Wave speed can be tuned via nonparaxial parameter.

Stable propagation achieved with appropriate parameter choices.

Abstract

Exact chirped elliptic wave solutions are obtained within the framework of coupled cubic nonlinear Helmholtz equations in the presence of non-Kerr nonlinearity like self steepening and self frequency shift. It is shown that, for a particular combination of the self steepening and the self frequency shift parameters, the associated nontrivial phase gives rise to chirp reversal across the solitary wave profile. But a different combination of non-Kerr terms leads to chirping but no chirp reversal. The effect of nonparaxial parameter on physical quantities such as intensity, speed and pulse-width of the elliptic waves is studied too. It is found that the speed of the solitary wave can be tuned by altering the nonparaxial parameter. Stable propagation of these nonparaxial elliptic waves is achieved by an appropriate choice of parameters.