Thermal effects and transverse structures in semiconductor microcavities

We formulate a model to describe the spatio-temporal dynamics of a semiconductor microcavity driven by an external coherent field, including the diffusive dynamics of the lattice thermal field. This allows us to describe the spatio-temporal effects due to the thermal dynamics with regard to pattern formation and especially cavity solitons. We consider both the case of a bulk medium in a passive configuration, following a previously introduced modelisation, and the case of a multiple quantum well (MQW) medium in an active configuration, that is, the device is electrically pumped, behaving as an amplifier, following another previously introduced model. We analyse the instabilities affecting the system by performing the linear stability analysis of the homogeneous steady state, and we perform the numerical integration of the equations describing the electric field, carrier and temperature dynamics, and we show the main numerical results. The inclusion of thermal effects introduces a Hopf instability which, in certain region of the parameter space, dominates the behaviour of the system.