Characterization of stationary patterns and their link with cavity solitons in semiconductor microresonators

We study the periodic structures that emerge beyond the instability threshold point in a semiconductor microcavity driven by a coherent stationary holding beam; the active layer of the microresonator is bulk GaAs or multiple quantum-well GaAs-AlGaAs. We apply a numerical technique to directly establish stationary solutions of the dynamical equations governing the electric field inside the cavity and the carrier density of the active material. To overcome the heavy computational requirements in the case of twodimensional patterns, we consider small nonorthogonal integration grids, whose geometrical properties are those of the pattern elementary cell. We investigate the mechanism of pattern formation in connection with the modulational instability threshold, and we study, both in one and two dimensions, the bifurcation structure of various branches of patterns. We show how cavity solitons are related to periodic structures and we study the behavior that cavity soliton branches may exhibit in two dimensions.