Order parameter fragmentation after a symmetry-breaking transition

As a nonlinear optical system consisting of a Kerr medium inserted in a feedback loop is exposed to a light intensity growing linearly from below to above the threshold for pattern formation, the critical slowing down around threshold freezes the defect population. The measured number of defects immediately after the transition scales with the quench time as predicted by Zurek for a two-dimensional Ginzburg-Landau model. The further temporal evolution of the defect number is in agreement with a simple annihilation model, once the drift of defects specific for our system is taken into account

Domain segregation in a two-dimensional system in the presence of drift

Motivated by experiments on optical patterns we analyze two-dimensional extended bistable systems with drift after a quench above threshold. The evolution can be separated into successive stages: linear growth and diffusion, coarsening, and transport, leading finally to a quasi-one-dimensional kink-antikink state. The phenomenon is general and occurs when the bistability relates to uniform phases or two different patterns

The birth of defects in pattern formation: testing of the Kibble-Zurek mechanism

Abstract. The extension of the cosmological mechanism of Kibble to second order phase transitions in condensed matter systems by Zurek, can be further generalized to bifurcations of out-of-equilibrium systems in continuum media, since the argument used in the derivation of the Kibble–Zurek scaling law is general. Here we review the validity of such scaling comparing several bifurcations where the test has been checked. Also, new experimental results of a nonlinear optical system are reported

Quantum properties of transverse pattern formation in second-harmonic generation

We investigate the spatial quantum noise properties of the one dimensional transverse pattern formation instability in intra-cavity second-harmonic generation. The Q representation of a quasi-probability distribution is implemented in terms of nonlinear stochastic Langevin equations. We study these equations through extensive numerical simulations and analytically in the linearized limit. Our study, made below and above the threshold of pattern formation, is guided by a microscopic scheme of photon interaction underlying pattern formation in second-harmonic generation. Close to the threshold for pattern formation, beams with opposite direction of the off-axis critical wave numbers are shown to be highly correlated. This is observed for the fundamental field, for the second harmonic field and also for the cross-correlation between the two fields. Nonlinear correlations involving the homogeneous transverse wave number, which are not identified in a linearized analysis, are also described. The intensity differences between opposite points of the far fields are shown to exhibit sub-Poissonian statistics, revealing the quantum nature of the correlations. We observe twin beam correlations in both the fundamental and second-harmonic fields, and also nonclassical correlations between them.Comment: 18 pages, 17 figures, submitted to Phys. Rev.

Temporal fluctuations of waves in weakly nonlinear disordered media

We consider the multiple scattering of a scalar wave in a disordered medium with a weak nonlinearity of Kerr type. The perturbation theory, developed to calculate the temporal autocorrelation function of scattered wave, fails at short correlation times. A self-consistent calculation shows that for nonlinearities exceeding a certain threshold value, the multiple-scattering speckle pattern becomes unstable and exhibits spontaneous fluctuations even in the absence of scatterer motion. The instability is due to a distributed feedback in the system "coherent wave + nonlinear disordered medium". The feedback is provided by the multiple scattering. The development of instability is independent of the sign of nonlinearity.Comment: RevTeX, 15 pages (including 5 figures), accepted for publication in Phys. Rev.

Pinning control of chaos in the LCLV device

We study the feasibility of transferring data in an optical device by using a limited number of parallel channels. By applying a spatially localized correcting term to the evolution of a liquid crystal light valve in its spatio{ temporal chaotic regime, we are able to restore the dynamics to a speci ed target pattern. The system is controlled in a nite time. The number and position of pinning points needed to attain control is also investigated

Pinning control of chaos in the LCLV device

We study the feasibility of transferring data in an optical device by using a limited number of parallel channels. By applying a spatially localized correcting term to the evolution of a liquid crystal light valve in its spatio{ temporal chaotic regime, we are able to restore the dynamics to a speci ed target pattern. The system is controlled in a nite time. The number and position of pinning points needed to attain control is also investigated

Boundary-induced localized structures in a nonlinear optical feedback experiment

Experimental and numerical evidence of symmetry-breaking bifurcations of a circular dissipative soliton with additional boundary conditions in the feedback of a liquid crystal light valve are reported. By tuning the strength of the nonlinearity or the size of the additional boundaries, the circular structure breaks up into polygonal symmetries and the system exhibits multistability. The experimental results are confirmed by numerical simulations with different configurations of the polarizers thus demonstrating the universality of the phenomenon