Cavity soliton inhibition of extreme events in lasers with injection.

Vortex mediated turbulence can be the key element in the generation of extreme events in spatially extended lasers with optical injection. Here, we study the interplay of vortex mediated turbulence and cavity solitons on the onset of extreme events in semiconductor lasers with injection. We first analyze and characterize these two features separately, spatiotemporal chaotic optical vortices for low values of the injection intensity and cavity solitons above the locking regime. In regimes where vortex mediated turbulence and cavity solitons coexist, localized peaks of light inhibit instead of enhancing the generation of rogue waves by locally regularizing the otherwise chaotic phase of the optical field. Cavity solitons can then be used to manipulate and control extreme events in systems displaying vortex mediated turbulence.

A Kerr polarization controller.

Kerr-effect-induced changes of the polarization state of light are well known in pulsed laser systems. An example is nonlinear polarization rotation, which is critical to the operation of many types of mode-locked lasers. Here, we demonstrate that the Kerr effect in a high-finesse Fabry-Pérot resonator can be utilized to control the polarization of a continuous wave laser. It is shown that a linearly-polarized input field is converted into a left- or right-circularly-polarized field, controlled via the optical power. The observations are explained by Kerr-nonlinearity induced symmetry breaking, which splits the resonance frequencies of degenerate modes with opposite polarization handedness in an otherwise symmetric resonator. The all-optical polarization control is demonstrated at threshold powers down to 7 mW. The physical principle of such Kerr effect-based polarization controllers is generic to high-Q Kerr-nonlinear resonators and could also be implemented in photonic integrated circuits. Beyond polarization control, the spontaneous symmetry breaking of polarization states could be used for polarization filters or highly sensitive polarization sensors when operating close to the symmetry-breaking point.

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. Above the threshold, the condensate self-organizes into an ordered supersolid state with a spatial period self-selected by optical diffraction.

A simple but precise method for quantitative measurement of the quality of the laser focus in a scanning optical microscope.

We report a method for characterizing the focussing laser beam exiting the objective in a laser scanning microscope. This method provides the size of the optical focus, the divergence of the beam, the ellipticity and the astigmatism. We use a microscopic-scale knife edge in the form of a simple transmission electron microscopy grid attached to a glass microscope slide, and a light-collecting optical fibre and photodiode underneath the specimen. By scanning the laser spot from a reflective to a transmitting part of the grid, a beam profile in the form of an error function can be obtained and by repeating this with the knife edge at different axial positions relative to the beam waist, the divergence and astigmatism of the postobjective laser beam can be obtained. The measured divergence can be used to quantify how much of the full numerical aperture of the lens is used in practice. We present data of the beam radius, beam divergence, ellipticity and astigmatism obtained with low (0.15, 0.7) and high (1.3) numerical aperture lenses and lasers commonly used in confocal and multiphoton laser scanning microscopy. Our knife-edge method has several advantages over alternative knife-edge methods used in microscopy including that the knife edge is easy to prepare, that the beam can be characterized also directly under a cover slip, as necessary to reduce spherical aberrations for objectives designed to be used with a cover slip, and it is suitable for use with commercial laser scanning microscopes where access to the laser beam can be limited.

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.

Energy shedding during nonlinear self-focusing of optical beams.

Self-focusing of intense laser beams and pulses of light in real nonlinear media is in general accompanied by material losses that require corrections to the conservative Nonlinear Schrödinger equations describing their propagation. Here we examine loss mechanisms that exist even in lossless media and are caused by shedding of energy away from the self-trapping beam making it to relax to an exact solution of lower energy. Using the conservative NLS equations with absorbing boundary conditions we show that energy shedding not only occurs during the initial reshaping process but also during oscillatory propagation induced by saturation of the nonlinear effect. For pulsed input we also show that, depending on the sign and magnitude of dispersion, pulse splitting, energy shedding, collapse or stable self-focusing may result.

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. In both theory and experiment the locking behavior is well described by the Adler model for the synchronization of coupled oscillators.

State dependent pseudoresonances and excess noise.

We show that strong response to nonresonant modulations and excess noise are state dependent in generic nonlinear systems; i.e., they affect some output states but are absent from others. This is demonstrated in complex Swift-Hohenberg models relevant to optics, where it is caused by the non-normality of the linearized stability operators around selected output states, even though the cavity modes are orthogonal. In particular, we find the effective parameters that control excess noise and the response to modulations and show cases where these phenomena are enhanced by an order of magnitude.

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. A phenomenological equation for the dynamics of the domain radius explains the observed behavior.

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.

Manipulation and removal of defects in spontaneous optical patterns.

Defects play an important role in a number of fields dealing with ordered structures. We demonstrate theoretically and experimentally the possibility of an active manipulation of defects in terms of an externally induced motion. We focus on the spontaneous formation of two-dimensional spatial structures in a nonlinear-optical system, a liquid crystal light valve under single optical feedback. For a particular parameter setting, a spontaneously formed hexagonal intensity pattern contains several dislocation-type defects. A scheme based on Fourier filtering allows us to restore spatial order in a selectable part of the pattern. Starting without control, the controlled area is progressively expanded, such that defects are swept out of the pattern.

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.

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. To show the usefulness of our numerical technique, we describe cracking and shrinking patches of patterns in a particular region of parameter space.

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.

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. We find that traveling waves are the predominant solutions and that the defects are vectorial dislocations that appear at the boundaries of the regions where traveling waves of different phase or wave-vector orientation are formed. A dislocation is defined by two topological charges, one associated with the phase and another with the wave-vector orientation. We also show how to stabilize a single defect in a realistic experimental situation. The effects of phase mismatch of nonlinear interaction are finally considered.

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. We then develop a weakly nonlinear theory to characterize the singular character of the transition and analyze the dynamical effects of spatial inhomogeneities.

Stable droplets and growth laws close to the modulational instability of a domain wall.

We consider the curvature driven dynamics of a domain wall separating two equivalent states in systems displaying a modulational instability of a flat front. An amplitude equation for the dynamics of the curvature close to the bifurcation point from growing to shrinking circular droplets is derived. We predict the existence of stable droplets with a radius R that diverges at the bifurcation point, where a curvature driven growth law R(t) approximately t(1/4) is obtained. Our general analytical predictions, which are valid for a wide variety of systems including models of nonlinear optical cavities and reaction-diffusion systems, are illustrated in the parametrically driven complex Ginzburg-Landau equation.