Proposed resolution of theory-experiment discrepancy in homoclinic snaking.

In spatially extended Turing-unstable systems, parameter variation should, in theory, produce only fully developed patterns. In experiment, however, localized patterns or solitons sitting on a smooth background often appear. Addition of a nonlocal nonlinearity can resolve this discrepancy by tilting the "snaking" bifurcation diagram characteristic of such problems.

Localized traveling waves in vertical-cavity surface-emitting lasers with frequency-selective optical feedback.

Spatially self-localized states have been found in a model of vertical-cavity surface-emitting lasers with frequency-selective optical feedback. The structures obtained differ from most known dissipative solitons in optics in that they are localized traveling waves. The results suggest a route to realization of a cavity soliton laser using standard semiconductor laser designs.

Reversible soliton motion.

We show that spatial solitons on either phase- or amplitude-modulated backgrounds can change their direction of motion according to the modulation frequency. A soliton may, therefore, move up or down phase gradients or remain motionless regardless of where it is in relation to the background modulation. The general theory is in good agreement with numerical results in a variety of nonlinear systems.

Stochastic resonance in the presence of spatially localized structures.

Stable spatially localized structures exist in a wide variety of spatially extended nonlinear systems, including nonlinear optical devices. We study stochastic resonance (SR) in models of optical parametric oscillators in the presence of a spatially uniform time-periodic driving and in a regime where two equivalent states with equal intensity but opposite phase exist. Diffraction and nonlinearity enable the existence of localized states, formed by the locking of kinks and antikinks and displaying spatially damped oscillatory tails (in one dimension) or the stabilization of dark ring cavity solitons (in two dimensions).

Suppression of spatial chaos via noise-induced growth of arrays of spatial solitons.

Domain walls with oscillatory tails are commonplace in models of spatially extended nonlinear optical devices. Their interaction and locking at discrete distances lead to asymptotically stable spatial disorder. We show that noise in the presence of domain walls with oscillatory tails can suppress spatial disorder by privileging highly correlated dynamical states consisting of arrays of spatial solitons.

Self-propelled cavity solitons in semiconductor microcavities.

We demonstrate the existence of both bright and dark spontaneously moving spatial solitons in a model of a semiconductor microcavity. The motion is caused by temperature-induced changes in the cavity detuning and arises through an instability of the stationary soliton solution above some threshold. An order parameter equation is derived for the moving solitons and is used to explain their behavior in the presence of externally imposed parameter modulations.

Polarization patterns and vectorial defects in type-II optical parametric oscillators.

Previous studies of lasers and nonlinear resonators have revealed that the polarization degree of freedom allows for the formation of polarization patterns and novel localized structures, such as vectorial defects. Type- II optical parametric oscillators are characterized by the fact that the down-converted beams are emitted in orthogonal polarizations. In this paper we show the results of the study of pattern and defect formation and dynamics in a type-II degenerate optical parametric oscillator, for which the pump field is not resonated in the cavity.

Characterization, dynamics and stabilization of diffractive domain walls and dark ring cavity solitons in parametric oscillators.

Mean field models of spatially extended degenerate optical parametric oscillators possess one-dimensional stable domain wall solutions in the presence of diffraction. We characterize these structures as spiral heteroclinic connections and study the spatial frequency of the local oscillations of the signal intensity which distinguish them from diffusion kinks. Close to threshold, at resonance or with positive detunings, the dynamics of two-dimensional diffractive domain walls is ruled by curvature effects with a t(1/2) growth law, and coalescence of domains is observed.

Controlling pattern formation and spatio-temporal disorder in nonlinear optics.

We present a feedback control method for the stabiliza- tion of unstable patterns and for the control of spatio-temporal disor- der. The control takes the form of a spatial modulation to the input pump, which is obtained via filtering in Fourier space of the output electric field. The control is powerful, exible and non-invasive: the feedback vanishes once control is achieved.