Dipole and quadrupole nonparaxial solitary waves

TL;DR

This paper investigates nonparaxial ultrashort pulse solitary waves in optical media, revealing how their structure, speed, and stability depend on system parameters, with new solutions including dipole and quadrupole elliptic waves.

Contribution

It introduces new analytical solutions for dipole and quadrupole solitary waves in a nonparaxial cubic nonlinear Helmholtz model with higher-order effects.

Findings

Existence of periodic elliptic solitary waves with dipole and quadrupole structures.

The nonparaxial parameter influences wave speed, allowing deceleration.

Numerical stability analysis confirms robustness of the solitary waves.

Abstract

The cubic nonlinear Helmholtz equation with third and fourth order dispersion and non-Kerr nonlinearity like the self steepening and the self frequency shift is considered. This model describes nonparaxial ultrashort pulse propagation in an optical medium in the presence of spatial dispersion originating from the failure of slowly varying envelope approximation. We show that this system admits periodic (elliptic) solitary waves with dipole structure within a period and also transition from dipole to quadrupole structure within a period depending on the value of the modulus parameter of Jacobi elliptic function. The parametric conditions to be satisfied for the existence of these solutions are given. The effect of the nonparaxial parameter on physical quantities like amplitude, pulse-width and speed of the solitary waves are examined. It is found that by adjusting the nonparaxial parameter, the speed of solitary waves can be decelerated. The stability and robustness of the solitary waves are discussed numerically.