Low-frequency fluctuations in external cavity semiconductor lasers: understanding based on a simple dynamical model

We investigate the dynamical origin of low-frequency fluctuations (LFFs) in external cavity semiconductor lasers by utilizing a simplified, three-dimensional model derived from the infinite-dimensional Lang-Kobayashi (LK) equations. The simplified model preserves the dynamical properties of the external-cavity modes (ECMs) and antimodes which play a fundamental role in the generation of LFFs. This model yields a clear picture of the dynamical origin of the LFFs. Two distinct regions are observed in parameter space, one with the presence of the maximum-gain mode (MGM), and another without it. In particular, we show that, in the absence of noise, LFFs are a consequence of the dynamical interactions among different ECMs and antimodes. When a small amount of noise is present, LFFs result from an intermittent switching of trajectories among different coexisting attractors in the phase space. The presence of double peaks in the distribution of power dropout times, which has been observed recently in experiments, is explained, and a scaling relation is obtained between the average switching time and the noise strength.