Fluctuations and correlations in hexagonal optical patterns

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• is larger than between pairs forming 180• , contrary to what a naive interpretation of emission in terms of twin photons would suggest. PACS number(s): 05.40.-a, 47.54.+r, 42.65.sf

Theory of quantum fluctuations of optical dissipative structures and its application to the squeezing properties of bright cavity solitons

“…We refer the reader to existing reviews for a resume of the main researches in the field [16,17]. For our purposes, which concern the analysis of the squeezing in dissipative structures, the work carried out by Gatti and Lugiato [20,21] on the squeezing of extended degenerate optical parametric oscillators (DOPO) below threshold, is particularly close (see also [22]), as well as the analysis of the role played by the Goldstone mode in [23,24].…”

Non-classical behavior in multimode and disordered transverse structures in OPO

“…Moments involving such big fluctuations cannot be correctly described within a linearized treatment in the fields amplitudes. In particular, such an approach leads to unphysically divergent quadrature correlations, although correct results can be obtained for the intensity correlations [18].…”

“…Some results have been obtained in the context of multimode interaction in linear approximations in other systems [16,17,18]. However, a full multimode nonlinear description is needed well above threshold where the emission of the critical modes necessarily stimulates spatial harmonics in both the pump and the signal, and undamped modes associated to spatial broken symmetries play an important role.…”

Quantum squeezing of optical dissipative structures

“…(11) we consider its projections onto the eigenvectors w 1x(1y) and w 2x(2y) introduced above: [20]. We further notice that the equation for c 2x is analogous to that derived in [21] for the hexagonal mode stationary phase in a Kerr cavity, which is later interpreted as the hexagonal pattern transverse momentum in [22].…”