Fluctuations and correlations in hexagonal optical patterns.

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.