Small-scale light structures in a Kerr medium

TL;DR

This paper introduces a new, numerically efficient system of equations for modeling small-scale light structures in Kerr media, demonstrating stable solitons, vortex interactions, and polarization effects through simulations.

Contribution

The paper presents a new set of equations for Kerr media that simplifies numerical simulations of small-scale optical structures, enabling detailed analysis of solitons and vortex interactions.

Findings

Stable 2D vector solitons can exist without nonlinearity modification.

Inelastic collisions between narrow beams with opposite polarizations were simulated.

Examples of vortex interactions and polarization separation were demonstrated.

Abstract

A system of equations has been proposed for a monochromatic weakly nonlinear light wave in a Kerr medium. This system is equivalent up to the third order in electric field to the known equation $\mbox{curl}\,\mbox{curl}\, {\bf E}=k_0^2[{\bf E} +\alpha |{\bf E}|^2{\bf E}+\beta({\bf E}\cdot{\bf E}){\bf E}^*]$, but the new equations are much more convenient for numerical computation. Optical fields with small structures of two or three wavelengths have been simulated using this system. It has been found that a stable self-focused light beam (a 2D vector soliton) in some parametric domain is possible even without modification of nonlinearity. ``Inelastic'' collisions between two such narrow beams with opposite circular polarizations have been computed. Furthermore, examples of interacting optical vortices, spatial separation of the circular polarizations, and the Kelvin--Helmholtz instability have been given for defocusing nonlinearity.