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-dime nsional model derived from the infinite-dimensional Lang-Kobayashi (LK) equ ations. The simplified model preserves the dynamical properties of the exte rnal-cavity modes (ECMs) and antimodes which play a fundamental role in the generation of LFFs. This model yields a clear picture of the dynamical ori gin 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. I n particular, we show that, in the absence of noise, LFFs are a consequence of the dynamical interactions among different ECMs and antimodes. When a s mall 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, wh ich has been observed recently in experiments, is explained, and a scaling relation is obtained between the average switching time and the noise stren gth.