Experimental synchronization of spatiotemporal chaos in nonlinear optics.

We demonstrate that a unidirectional coupling between a pattern forming system and its replica induces complete synchronization of the slave to the master system onto a spatiotemporal chaotic state.

Pattern stabilization through parameter alternation in a nonlinear optical system.

We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are used for both numerical simulations and a weakly nonlinear analysis of the patterned states. The simulations show excellent agreement with the experiment. The nonlinear analysis provides an explanation of the patterning under alternation and accurately predicts both the observed dependence of the patterning on the frequency of alternation and the measured spatial frequencies of the patterns.

Dissipative solitons driving and bound state control via parameter gradients.

The effect of phase and intensity gradients on the motion of dissipative solitons in a nonlinear interferometer is investigated. We show how the forces exerted by parameter gradients on the solitons alter their interactions. Consequently, it is possible to tune the spectrum of soliton bound states via the introduction of proper spatial distribution of the system parameters. Furthermore, we show how the use of properly shaped parameter distributions can lead to a relevant reduction of the cross-talk between close by solitons in applications.

Experimental targeting and control of spatiotemporal chaos in nonlinear optics.

We demonstrate targeting and control over spatiotemporal chaos in an optical feedback loop experiment. Different stationary target patterns are stabilized in real time by means of a two dimensional space extended perturbation field driven by an interfaced computer and applied in real space to a liquid crystal display device inserted within a control optical loop. The flexibility of the system in switching between different target patterns is also demonstrated.

Detecting local synchronization in coupled chaotic systems.

We introduce a technique to detect and quantify local functional dependencies between coupled chaotic systems. The method estimates the fraction of locally synchronized configurations, in a pair of signals with an arbitrary state of global synchronization. Application to a pair of interacting Rössler oscillators shows that our method is able to quantify the number of dynamical configurations where a local prediction task is possible, as well as in the absence of global synchronization features.

Transition to space-time chaos in an optical loop with translational transport.

We describe the transition from regular patterns to space-time chaos in an optical system with nonlocal feedback. The nonlocality introduced breaks the rotational symmetry of the system, resulting in a scenario for the transition from regular patterns to a disordered dynamics. The different regimes are characterized both in terms of spatial and temporal correlation functions, and by means of a Kahrunen-Loeve decomposition. This allows the determination of the structures participating in the dynamics, and an estimation of the active degrees of freedom versus the control parameter.

Bistability between different localized structures in nonlinear optics.

We report the observation of different localized structures coexisting for the same parameter values in an extended system. The experimental findings are carried out in a nonlinear optical interferometer and are fully confirmed by numerical simulations. The existence of each kind of localized structure is put in relation to a corresponding delocalized pattern observed. A quantitative evaluation of the range of pump parameter allowing bistability between localized structures is given. The phenomenon reported results to be robust in parameter space.

Control of localized structures in an optical feedback interferometer.

We report a detailed experimental investigation of the dependence of localized structures, observed in a nonlinear optical device, on several control parameters. A first step of the study consists in the determination of the region of existence of localized states as a function of the system variables. Subsequently, we show how different control parameters can be used to the aim of tuning several localized structures properties; among these, of particular relevance are the contrast and the amplitude and frequency of the oscillations appearing on the tails of the structures. A discussion of the relation between the localized states here studied and the one predicted by general model for pattern forming systems is also given.

Tailoring the profile and interactions of optical localized structures.

We experimentally demonstrate the broad tunability of the main features of optical localized structures (LS's) in a nonlinear interferometer. By discussing how a single LS depends on the system spatial frequency bandwidth, we show that a modification of its tail leads to the possibility of tuning the interactions between LS pairs, and thus the equilibrium distances at which LS bound states form. This is in agreement with a general theoretical model describing weak interactions of LS in nonlinear dissipative systems.

Experimental evidence for detuning induced pattern selection in nonlinear optics.

We give quantitative experimental evidence of the influence of cavity detuning in determining the pattern selection in a one-dimensional large Fresnel number optical oscillator. The issues of the selection of the transverse mode close to threshold and the value of the pump parameter at threshold are addressed. Competition between right and left traveling waves, resulting in a winner takes all dynamics, is also reported. Experimental results are in quantitative agreement with the theoretical predictions formulated for a broad class of systems comparable to the one here considered.

Pattern formation and competition in photorefractive oscillators.

We introduce a general model of pattern formation in optical systems made of a cavity with an active medium as a photorefractive crystal fed by a pump. The model is based on the interplay of a diffractive equation for the optical field and a diffusive equation for the medium refractivity. The aim of the model is to describe a series of experiments which have shown mode competition (periodic or chaotic alternation) for low Fresnel numbers (F) and mode coexistence, leading to short range space correlations, for high F. For low F, a linear stability analysis provides the set of modes above threshold as a function of the transverse wave number. Due to the interplay of the optical and the diffusive interactions, different behaviors result depending on the thickness of the medium as compared to the optical absorption length and diffusion length. Including the leading nonlinearities compatible with the symmetry constraints, we introduce normal form equations which describe the time-dependent mode competition. In the case of a large number of modes (high F), nonlinear mode-mode interaction is equivalent to a self-induced noise. In this limit, the relevant feature to be compared with the experiment is the power spectrum.