Cavity solitons in semiconductor microresonators: existence, stability, and dynamical properties

We apply a versatile numerical technique to establishing the existence of cavity solitons (CS) in a semiconductor microresonator with bulk GaAs or multiple quantum well GaAs/AlGaAs as its active layer. Based on a Newton method, our approach implies the evaluation of the linearized operator describing deviations from the exact stationary state. The eigenvalues of this operator determine the dynamical stability of the CS. A typical eigenspectrum contains a zero eigenvalue with which a "neutral mode" of the CS is associated. Such neutral modes are characteristic of models with translational symmetry. All other eigenvalues typically have negative real parts large enough to cause any excitations to die out in a few medium response times. The neutral mode thus dominates the response to external random or deterministic perturbations, and its excitation induces a simple translation of the CS, which are thus stable and robust. We show how to relate the speed with which a CS moves under external perturbations to the projection of the perturbations on to the neutral mode, and give some examples, including weak gradients on the driving field and interaction with other CS. Finally, we show that the separatrix between two stable coexisting solutions: the homogeneous solution and the CS is the intervening unstable CS solution. Our results are important with a view to future applications of CS to optical information processing.