Fluctuations and correlations in hexagonal optical patterns

TL;DR

This paper investigates the role of noise in hexagonal optical patterns within nonlinear Kerr cavities, revealing how different modes influence fluctuations and correlations in the pattern's intensity.

Contribution

It provides a detailed analysis of fluctuation sources and correlation structures in hexagonal patterns, highlighting the dominance of damped modes in far field fluctuations and unexpected correlation patterns.

Findings

Far field intensity fluctuations are dominated by damped modes.

Strong correlations exist between wave vector pairs, especially at 120 degrees.

Correlations between 120-degree pairs are larger than between 180-degree pairs.

Abstract

We analyze the influence of noise in transverse hexagonal patterns in nonlinear Kerr cavities. The near field fluctuations are determined by the neutrally stable Goldstone modes associated to translational invariance and by the weakly damped soft modes. However these modes do not contribute to the far field intensity fluctuations which are dominated by damped perturbations with the same wave vectors than the pattern. We find strong correlations between the intensity fluctuations of any arbitrary pair of wave vectors of the pattern. Correlation between pairs forming 120 degrees is larger than between pairs forming 180 degrees, contrary to what a naive interpretation of emission in terms of twin photons would suggest.