Low frequency fluctuations in a multimode semiconductor laser with optical feedback

Summary form only given. We study a multimode semiconductor laser subject to a moderate optical feedback with a time delay comparable to the relaxation oscillation periods. The laser total output exhibits low frequency fluctuations (LFF). This phenomenon is characterized by intensity dropouts with an average time between the dropouts much longer than the relaxation oscillation periods and mode beating characteristic times. We propose a model of external cavity semiconductor laser, which is a multimode extension of the Lang-Kobayashi model and show that some important experimental effects can be explained as a general property of multimode operation. Our model takes into account the grating associated with a Fabry-Perot configuration and is able to describe both in-phase and out-of-phase multimode dynamics. We consider the influence of the delay on the LFF period and find a non-monotonic dependence. This is directly related to two types of relaxation oscillation frequencies in the model which predicts two possible instabilities for the steady states: a self-pulsing instability where all modes are in phase, and a new instability which leads to LFF with antiphased modal intensities. The first instability is a standard Hopf bifurcation while the second is an (N-1)-fold degenerate Hopf bifurcation where N is the number of lasing modes. Depending on the experimental conditions, either of these two bifurcations can be the first to destabilize the steady state.