Transient growth and generalised stability analysis in semiconductor lasers

In this work we show that there can be transient growth of perturbations of a lasing state even for laser systems with orthogonal cavity modes. We show that whenever the background state is a lasing state, the linear stability operator has, in general, non-orthogonal modes. This means that the short term dynamics and the spectrum of the perturbations are always different from those predicted by a standard stability analysis. It does not, however, guarantee the presence of transient gain in the region where the background state is stable. We show the universality of this phenomenon by proving that the linear stability operator of the complex Swift-Hohenberg equations (CSH) for semiconductor lasers (Mercier, 2002) always presents non-orthogonal eigenvectors when the background state is a lasing state.