Pere Colet | PubMed Health

PubMed2002

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 that 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.

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PubMed2002

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

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 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 wave numbers can originate different structures, the detuning being a natural selection parameter.

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