"Exact" solutions for circularly polarized Kerr solitons

TL;DR

This paper derives exact solutions for circularly polarized Kerr solitons by reducing the nonlinear vector curl-curl equation to a system of four first-order ODEs, revealing detailed internal structures of stationary optical beams.

Contribution

It introduces an exact reduction method for the nonlinear vector curl-curl equation, enabling detailed numerical analysis of Kerr solitons with complex polarization and vortex structures.

Findings

Revealed internal vortex structures of Kerr solitons.

Demonstrated the existence of a small opposite polarization component.

Provided a numerical framework for analyzing stationary optical beams.

Abstract

For the nonlinear vector curl-curl equation describing a monochromatic light wave in a Kerr medium, an exact reduction is suggested which results in a system of four ordinary differential equations, of the first order each, for functions of the transverse radial coordinate. Numerical solutions of this system, with appropriate boundary conditions, give full information about internal structure of a strongly nonlinear, stationary optical beam consisting mainly of a definite circular polarization, but with a small portion of the opposite polarization containing a double vortex, as well as with the parallel component of the electric field containing an ordinary vortex.