Existence, stability and control of transverse optical structures

Summary form only given. We present a computer-assisted technique, valid for arbitrary values of the system parameters, which allows us to find the model equations´ stable and unstable stationary solutions, including periodic patterns and localised structures. It can be extended to find their eigenspectrum, and hence their stability and can also find their response to perturbations. The technique uses a Fourier transform to compute the spatial derivatives in a discretised set of model equations and then a Newton method to solve the resulting set of algebraic equations for the stationary solutions. The Jacobian matrix, implicit in the application of the Newton method, gives the linearisation around the solutions found and, as such, its eigenvalues give the solutions´ stability. The projection of perturbations onto the eigenvectors of the corresponding adjoint problem give the system´s response to that perturbation. We have applied the technique to a wide variety of pattern forming systems and we present results for a system based on a liquid crystal light valve with diffractive feedback. We computed hexagon, roll and square solutions and their stability as a function of the input intensity and the pattern wave vector. We have also studied stable and unstable branches of localised solutions (optical bulletholes or cavity solitons). As an example, we present results from a theoretical model for multi-quantum-well and bulk semiconductors in microcavities.