Codimension 2 and 3 situations in a ring cavity with elliptically polarized electromagnetic waves

TL;DR

This paper investigates pattern formation in a Kerr-like medium within a ring cavity with elliptically polarized light, analyzing codimension 2 and 3 instabilities using coupled equations and numerical simulations.

Contribution

It introduces a method to identify parameters leading to codimension 2 or 3 instabilities in a polarized Kerr cavity model, considering various material properties.

Findings

Instabilities cannot exceed codimension 3.

A systematic method to find parameters for codimension 2 or 3.

Numerical simulations show coexistence and competition of instabilities.

Abstract

We study pattern formation on the plane transverse to propagation direction, in a ring cavity filled with a Kerr-like medium, subject to an elliptically polarized incoming field, by means of two coupled Lugiato-Lefever equations. We consider a wide range of possible values for the coupling parameter between different polarizations, *B*, as may happen in composite materials. Positive and also negative refraction index materials are considered. Examples of marginal instability diagrams are shown. It is shown that, within the model, instabilities cannot be of codimension higher than 3. A method for finding parameters for which codimension 2 or 3 takes place is given. The method allows us to choose parameters for which unstable wavenumbers fulfill different relations. Numerical integration results where different instabilities coexist and compete are shown.