Theory and application of cavity solitons in photonic devices.

Driven optical cavities containing a nonlinear medium support stable dissipative solitons, cavity solitons, in the form of bright or dark spots of light on a uniformly-lit background. Broadening effects due to diffraction or group velocity dispersion are balanced by the nonlinear interaction with the medium while cavity losses balance the input energy. The history, properties, physical interpretation and wide application of cavity solitons are reviewed.

Observation of Mode-Locked Spatial Laser Solitons.

A stable nonlinear wave packet, self-localized in all three dimensions, is an intriguing and much sought after object in nonlinear science in general and in nonlinear photonics in particular. We report on the experimental observation of mode-locked spatial laser solitons in a vertical-cavity surface-emitting laser with frequency-selective feedback from an external cavity. These spontaneously emerging and long-term stable spatiotemporal structures have a pulse length shorter than the cavity round-trip time and may pave the way to completely independent cavity light bullets.

Quantum threshold for optomechanical self-structuring in a Bose-Einstein condensate.

Theoretical analysis of the optomechanics of degenerate bosonic atoms with a single feedback mirror shows that self-structuring occurs only above an input threshold that is quantum mechanical in origin. This threshold also implies a lower limit to the size (period) of patterns that can be produced in a condensate for a given pump intensity. These thresholds are interpreted as due to the quantum rigidity of Bose-Einstein condensates, which has no classical counterpart.

Self-organization in cold atomic gases: a synchronization perspective.

We study non-equilibrium spatial self-organization in cold atomic gases, where long-range spatial order spontaneously emerges from fluctuations in the plane transverse to the propagation axis of a single optical beam. The self-organization process can be interpreted as a synchronization transition in a fully connected network of fictitious oscillators, and described in terms of the Kuramoto model.

Kinetic theory for transverse optomechanical instabilities.

We investigate transverse symmetry-breaking instabilities emerging from the optomechanical coupling between light and the translational degrees of freedom of a collisionless, damping-free gas of cold, two-level atoms. We develop a kinetic theory that can also be mapped on to the case of an electron plasma under ponderomotive forces. A general criterion for the existence and spatial scale of transverse instabilities is identified; in particular, we demonstrate that monotonically decreasing velocity distribution functions are always unstable.

Dissipative solitons in the coupled dynamics of light and cold atoms.

We investigate the coupled dynamics of light and cold atoms in a unidirectional ring cavity, in the regime of low saturation and linear single-atom response. As the dispersive opto-mechanical coupling between light and the motional degrees of freedom of the atoms makes the dynamics nonlinear, we find that localized, nonlinearity-sustained and bistable structures can be encoded in the atomic density by means of appropriate control beams.

Adler synchronization of spatial laser solitons pinned by defects.

Defects due to growth fluctuations in broad-area semiconductor lasers induce pinning and frequency shifts of spatial laser solitons. The effects of defects on the interaction of two solitons are considered in lasers with frequency-selective feedback both theoretically and experimentally. We demonstrate frequency and phase synchronization of paired laser solitons as their detuning is varied.

Vortex solitons in lasers with feedback.

We report on the existence, stability and dynamical properties of two-dimensional self-localized vortices with azimuthal numbers up to 4 in a simple model for lasers with frequency-selective feedback.We build the full bifurcation diagram for vortex solutions and characterize the different dynamical regimes. The mathematical model used, which consists of a laser rate equation coupled to a linear equation for the feedback field, can describe the spatiotemporal dynamics of broad area vertical cavity surface emitting lasers with external frequency selective feedback in the limit of zero delay.

Self-localized structures in vertical-cavity surface-emitting lasers with external feedback.

In this paper, we analyze a model of broad area vertical-cavity surface-emitting lasers subjected to frequency-selective optical feedback. In particular, we analyze the spatio-temporal regimes arising above threshold and the existence and dynamical properties of cavity solitons. We build the bifurcation diagram of stationary self-localized states, finding that branches of cavity solitons emerge from the degenerate Hopf bifurcations marking the homogeneous solutions with maximal and minimal gain.

Collective atomic recoil lasing with a partially coherent pump.

We investigate the effect of pump phase noise on the collective backscattering of light by a cold, collisionless atomic gas. We show that for a partially coherent pump field, the growth rate of the backscattered field is reduced relative to that for a coherent pump, but the backscattered intensity can be increased. Our results demonstrate that fluctuations and noise can play a counterintuitive role in nonlocally coupled many-body systems.

Realization of a semiconductor-based cavity soliton laser.

The realization of a cavity soliton laser using a vertical-cavity surface-emitting semiconductor gain structure coupled to an external cavity with a frequency-selective element is reported. All-optical control of bistable solitonic emission states representing small microlasers is demonstrated by injection of an external beam. The control scheme is phase insensitive and hence expected to be robust for all-optical processing applications.

Two-dimensional front dynamics and spatial solitons in a nonlinear optical system.

Two-dimensional fronts and coarsening dynamics with a t{1/2} power law are analyzed experimentally and theoretically in a nonlinear optical system of a sodium vapor cell with single-mirror feedback. Modifications of the t{1/2} power law are observed in the vicinity of a modulational instability leading to the formation of spatial solitons of different sizes. The experimental and numerical observations give direct evidence for the locking of fronts as the mechanism of soliton formation.

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.

On homoclinic snaking in optical systems.

The existence of localized structures, including so-called cavity solitons, in driven optical systems is discussed. In theory, they should exist only below the threshold of a subcritical modulational instability, but in experiment they often appear spontaneously on parameter variation. The addition of a nonlocal nonlinearity may 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.

Giant excess noise and transient gain in misaligned laser cavities.

The excess noise factor is calculated analytically for a very general class of optical cavities, and is shown to have a superexponential dependence on cavity misalignment, easily attaining values of order 10(10). The physical basis is shown to be "ransient gain" associated with amplified spontaneous emission. Similarly dramatic effects of symmetry breaking can be expected in other physical systems with non-normal modes.

Stability of spiralling solitary waves in Hamiltonian systems.

We present a rigorous criterion for stability of spiralling solitary structures in Hamiltonian systems incorporating the angular momentum integral and demonstrate its applicability to the spiralling of two mutually incoherent optical beams propagating in a photorefractive material.

Computationally determined existence and stability of transverse structures. II. Multipeaked cavity solitons.

We apply quasi-exact numerical techniques to the calculation of stationary one- and two-dimensional, bound multipeaked cavity soliton solutions of a model describing a saturable absorber in a driven optical cavity. We calculate the existence and stability domains of a wide range of such states and determine the perturbative eigenmodes that cause loss of stability. We relate the existence of N-peaked states to the locking range between patterned and homogeneous solutions, as a function of two parameters.

Computationally determined existence and stability of transverse structures. I. Periodic optical patterns.

We present a Fourier-transform based, computer-assisted, technique to find the stationary solutions of a model describing a saturable absorber in a driven optical cavity. We illustrate the method by finding essentially exact hexagonal and roll solutions as a function of wave number and of the input pump. The method, which is widely applicable, also allows the determination of the domain of stability (Busse balloon) of the pattern, and sheds light on the mechanisms responsible for any instability.

Polarization dynamics of Bragg solitons.

The families of vectorial Bragg solitons existing in transversely periodic media and their stability properties are studied in detail. Two qualitatively distinct types of polarization instabilities have been found. One leads to the significant radiation transfer into nonsolitonic forms, while the other mainly redistributes energy between two soliton components.

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.

Two-dimensional clusters of solitary structures in driven optical cavities.

Using analytical and numerical approaches we study clusters of the two-dimensional localized structures of light excited in the externally driven optical cavities. Stability and instability properties of clusters of two, three, and four structures are analyzed in detail. We develop a technique for calculation of the expression for the interaction potential through modified Bessel functions that has applicability going beyond the model under consideration.

Modulational instability of bright solitary waves in incoherently coupled nonlinear Schrödinger equations.

We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schrödinger equations. Varying the relative strength of cross-phase and self-phase effects we show the existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical interpretation of our results in terms of the group-velocity-dispersion- (GVD-) induced polarization dynamics of spatial solitary waves.

Perturbation theory for domain walls in the parametric Ginzburg-Landau equation.

We demonstrate that in the parametrically driven Ginzburg-Landau equation arbitrarily small nongradient corrections lead to qualitative differences in the dynamical properties of domain walls in the vicinity of the transition from rest to motion. These differences originate from singular rotation of the eigenvector governing the transition. We present analytical results on the stability of Ising walls, deriving explicit expressions for the critical eigenvalue responsible for the transition from rest to motion.