Patterns arising from the interaction between scalar and vectorial instabilities in two-photon resonant Kerr cavities

TL;DR

This paper investigates how scalar and vectorial instabilities interact to produce complex polarization patterns in a Kerr cavity near two-photon resonance, revealing the role of bifurcations and competing instabilities in pattern formation.

Contribution

It introduces a mean field model analyzing the interaction of scalar and vectorial instabilities, highlighting the emergence of diverse polarization patterns through bifurcation analysis.

Findings

Pattern arises from a codimension two bifurcation at negative detunings.

Two wave numbers become unstable simultaneously, leading to Turing-like instabilities.

Competition between instabilities results in various polarization structures, influenced by detuning.

Abstract

We study pattern formation associated with the polarization degree of freedom of the electric field amplitude in a mean field model describing a nonlinear Kerr medium close to a two-photon resonance, placed inside a ring cavity with flat mirrors and driven by a coherent $\hat x$-polarized plane-wave field. In the self-focusing case, for negative detunings the pattern arises naturally from a codimension two bifurcation. For a critical value of the field intensity there are two wave numbers that become unstable simultaneously, corresponding to two Turing-like instabilities. Considered alone, one of the instabilities would originate a linearly polarized hexagonal pattern whereas the other instability is of pure vectorial origin and would give rise to an elliptically polarized stripe pattern. We show that the competition between the two wavenumbers can originate different structures, being the detuning a natural selection parameter.