Abstract

Transverse optical patterns are capable of allowing noteworthy aspects linked to quantum fluctuations. These issues have been mainly studied in stripes patterns, which present only two modes in the far-field. Here we address the study of the fluctuations and correlations in an hexagonal pattern in a ring cavity filled with a self-focusing Kerr medium. The dynamics of the electric field can be described, in the mean-field approximation, by a Langevin equation for the scaled slowly varying amplitude of the field E: where E_o is the pump field, θ the cavity detuning, a the strength of diffraction, the transverse Laplacian and $\xi \left(\overrightarrow{x},t\right)$ a Gaussian white complex noise.

© 2000 IEEE