Vortex Structures in Optical Fibers Under the Influence of Third-Order Dispersion and Self-Steepening Effect

Abstract

In this paper, we investigate for the first time the generation and formation of amplitude-type vortices propagating in single-mode optical fibers with a step-index profile under the influence of third-order dispersion and the self-steepening effect, also known as the dispersion of nonlinearity in the medium. The main model is based on the vector nonlinear amplitude equation, from which a system of two scalar partial differential equations is derived. These equations describe the evolution of the x- and y-components of the vector amplitude function  of an optical pulse under the influence of higher-order nonlinear and dispersive effects. Exact analytical solutions of the resulting system of equations are obtained in the form of optical vortices. They exhibit amplitude-type singularities and appear as ring-like structures in the components of the laser pulses. Numerical simulations of the obtained solutions are performed. It is shown that the vortex parameter m is related to the number of these ring structures. Significant depolarization of the electric field is observed in the focal region of the laser radiation.