Interaction of modulational instabilities in semiconductor resonators

In our communication we study analytically the interaction between two modulational instabilities in a coherently driven semiconductor cavity. A normal form description is derived in the limit where thresholds associated with these instabilities are close to one other. We show that an infinity of branches of periodic solutions emerge from the unstable portion of the homogeneous steady state. These branches have a nontrivial envelope in the bifurcation diagram that can smoothly join the two instabilities. The important issue of our analysis is to predict the occurrence of an isolated structures which are not connected to any homogeneous branch of solutions. Interestingly, thresholdless appearance of periodic patterns was observed. This experimental observation was interpreted as a result of device imperfection. Here, we show an alternative, dynamical, mechanism for the thresholdless appearance of patterns.