Thermally-induced and guided motion of semiconductor cavity solitons

We describe here the spatio-temporal dynamics of a semiconductor microresonator driven by an external coherent field, including the diffusive dynamics of the lattice thermal field. This allows us to describe the thermal effects with particular regard to pattern formation and cavity solitons (CS). We consider both the case of a bulk medium in a passive configuration, 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). Thermal effects are taken into account through a temperature dependence of the band-gap energy of the semiconductor, a linear shift of the cavity resonance, and a rate equation for the temperature field dominated by lattice-carrier heat exchange. We formulate a set of dynamical equations which are characterised by three very different time scales. The system can eventually be affected by a thermally-induced dynamical instability of the Hopf type, giving rise to different dynamical regimes. In the passive case, it turns out that the Hopf instability, when present, has often a global character: it leads the system to oscillations of the whole beam, called regenerative oscillations, where the system displays an oscillatory homogeneous output intensity, for a constant homogeneous input intensity. There are also conditions in which the system is dominated by a stationary modulational instability (Turing); in this regime pattern formation seems to be unaffected by the presence of thermal effects, and stable CS can be obtained in wide parametric ranges. In other regimes, both in the active and in the passive case, we found that the Hopf instability is a dynamical modulational instability, and travelling spatial patterns develop. Under the same conditions, bright CS are possible in the active case, but after their excitation, they start travelling on the thermal time-scale (microseconds), but they can be guided or trapped using gradients in the holding beam.