Thermal effects and cavity solitons in passive semiconductor microresonators

We formulate a model including the thermal dynamics in the time evolution of a passive semiconductor microresonator, containing a bulk medium, driven by a coherent holding beam. Thermal effects are taken into account via a dynamical equation for the lattice temperature, describing heat dissipation toward the environment, heating due to carrier generation, and thermal diffusion. The temperature dynamics is coupled to the carrier and field dynamics via the material susceptibility, a red-shift of the band-gap energy of the semiconductor upon an increase of temperature and a linear shift of the cavity resonance. The presence of thermal effects introduces a Hopf instability which, in certain regions of the parameter space, dominates the dynamics of the system. In this case our numerical simulations show that the output intensity may oscillate for constant holding beam intensity (regenerative oscillations), and if the input intensity grows slowly enough the hysteresis cycle may be inverted (switching point inversion). Oscillatory instabilities can also develop a modulational character, meaning that travelling patterns can be found. These phenomena develop over the slow timescale (microseconds) characterizing thermal effects in these devices. In other parameter regimes, the well-known Turing instability giving rise to stationary modulated patterns prevails, and the system displays the usual scenario of stable patterns and cavity solitons. Thermal effects seem not to play any relevant role in these regimes