G.K. Harkness

Dynamical properties of two-dimensional Kerr cavity solitons

We present the results of our study of the dynamics of two-dimensional Kerr cavity solitons. The solitons are absolutely stable over a substantial parameter domain. We analyze their dynamics beyond the instability boundary, finding regions of stable oscillation and of fivefold or sixfold azimuthal instability. The Hopf oscillation is surprisingly robust, owing to the influence of a lower-amplitude unstable soliton.

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. We demonstrate by means of computer simulation, the effect of the control in two different optical systems.

Measuring disorder with correlation functions of averaged patterns

Abstract We propose an indicator of disorder which can be measured on averaged intensity images of a weakly turbulent complex field.

Correlation functions in the presence of optical vortices

Abstract We evaluate two-dimensional field and intensity correlation functions for the optical Ginzburg-Landau and laser equations in the presence of optical vortices. Configurations of rotating vortices, vortices superimposed on travelling waves and defect mediated turbulance are analysed and compared. Intensity correlations provide a qualitative indicator for the degree of disorder of spatio-temporal evolutions. For example, patterns with few rotating vortices have correlation lengths comparable to or larger than the transverse size of the system, while few vortices superimposed on travelling waves can generate weak turbulance.

Existence, Stability, and Properties of Cavity Solitons

The history, theory, and physical interpretation of cavity solitons are reviewed. These are bright, stable, nondiffracting spots of light in a driven optical cavity. The cavity must contain a nonlinear medium, which need not, however, support ordinary (propagating) spatial solitons. We use the Kerr cavity as an example to describe methods to find them and analyze their stability, demonstrating a sizeable domain of stability of two-dimensional cavity solitons in a Kerr cavity. Cavity solitons in semiconductor microresonators may have properties interesting for applications to optical information processing, and we outline some results from models of such systems.

Traveling Wave Patterns in Lasers with Curved Mirrors

the Maxwcll-l3locli cqiititioiis (.LIl<E) [2], the ineclianisms hcliiiid tlie waves and cavity modcs arc analagous [3]. In fact, numerical siiniilatioiis show that. for large enough input energ)(pump). iptteriis of a travclling-wavc nature arr rccovcred rveri wiicii the mirrors are curved. The threshold for tlie transition from patterns made up of empty cavity iiiodcs to ones of a travelling, wave nature i s shown i n panel 2 of the figure. As the radius of curvature of the mirrors, R, decreases the threshold values of the pump increase. In the shadcd region therr is bistability between target and Gauss-Laguerre pattern types. Above the threshold, the patterns lake the form of the cylindrically syiiimctric travelling waves shown in panel 3 of the figure. The waves are generated at the edge and travel inwards. We have analysed these structures using amplitude equations derived in the Gauss-Laguerre basis, and a numerical shooting method. This method allows us to study the stability of these target patterns: complex spatio-temporal behaviour is predicted for specific parameter ranges. In particular we have found an instability of the source of travelling waves which leads to a weak turbulence characterised by the erratic emission of vortices. These and other fascinating laser spatio-temporal structures will be presented with the aid of video displays. This work is, in part, supported by EPSRC grant GR/.1/30998.

Cracking of optical patterns

This work characterizes the process of cracking of optical patterns by studying the evolution of the homogeneous islands for different values of the parameters, the initial wave-vector and the amplitude of an additive noise. In particular, an initial hexagonal structure is considered with wave-vector smaller than the critical wave-vector of the incoming modulational instability.

Localized structures and circular domain walls in a vectorial Kerr cavity

Two kinds of localized structures, dark cavity solitons and circular domain walls, are found in different regimes in self-defocusing vectorial Kerr cavities. In the former (later) regime droplets shrink (grow) as R(t) ≈ t−1/2 (R(t) ≈ t1/3).

Computer-aided determination of existence and stability of optical patterns

Summary form only given. In recent years, studies into transverse effects in nonlinear optical systems have revealed a wealth of spatial complexity, ranging from periodic patterns to localised structures. We present here a computer-assisted technique, valid for arbitrary values of the system parameters, which can find the stationary solutions of a model. It uses a Newton-type method and a Fourier transform to evaluate the spatial derivatives. The Newton method automatically gives the linearisation around the solutions found and therefore can be extended to find their eigenspectrum and hence stability. We will demonstrate the method by finding exact hexagonal, roll and square solutions for a model of a saturable absorber in a cavity. We will show these pattern solutions as a function of their wavenumber and of the intensity of the input pump.

Removal of defects in broad area optical systems

Summary form only given. Control techniques based on optical feedback of filtered Fourier components have been applied successfully to a wide range of experimental configurations in order to both manipulate stable and unstable spatial structures and to eliminate optical turbulence.