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

We apply a versatile numerical technique to establishing the existence of c avity solitons (CS) in a semiconductor microresonator with bulk GaAs or mul tiple quantum well GaAs/AlGaAs as its active layer. Based on a Newton metho d, our approach implies the evaluation of the linearized operator describin g deviations from the exact stationary state. The eigenvalues of this opera tor determine the dynamical stability of the CS. A typical eigenspectrum co ntains a zero eigenvalue With which a ''neutral mode" of the CS is associat ed. Such neutral modes are characteristic of models with translational symm etry. All other eigenvalues typically have negative real parts large enough to cause any excitations to die out in a few medium response times. The ne utral mode thus dominates the response to external random or deterministic perturbations, and its excitation induces a simple translation of the CS, w hich 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 perturbat ions on to the neutral mode, and give some examples, including weak gradien ts on the driving field and interaction with other CS. Finally, we show tha t the separatrix between two stable coexisting solutions: the homogeneous s olution 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.