We propose a delay-differential equation to model dynamical instabilities in a quantum dot laser. We focus on a laser with a small gain section and a long empty section. A long cavity reduces the strong damping of the relaxation oscillation frequency. It leads to the appearance of dropouts at the delay period, which evolve to chaos. © 2007 Optical Society of America OCIS codes: 190.3100, 140.5960. Delay-induced instabilities are well known in semiconductor laser physics. The most famous example is the occurrence of low-frequency fluctuations that are observed near the lasing threshold when a semiconductor laser is subjected to an optical feedback. The output is characterized by intensity dropouts with an average time between consecutive dropouts much longer than either relaxation oscillation periods or mode beating characteristic times. This phenomenon has been extensively studied experimentally and numerically. Although some experiments demonstrate the importance of the multimode character of the laser emission, 1 the quite simple delay-differential equation model derived by Lang and Kobayashi 2 (LK) gives a good qualitative explanation for most of the experimental observations. The first experiments with semiconductor lasers based on quantum dot (QD) materials have shown that these lasers do not exhibit similar instabilities.3 This low sensitivity to optical feedback is a plus for some applications and was attributed to the strong damping of the relaxation oscillations and relatively low linewidth enhancement factor in QD lasers. 4,5 The linewidth enhancement factor in QD lasers depends strongly on the device temperature. A strong optical feedback induces an instability range at high temperature. 6 These instabilities are very different from those commonly observed in quantum well lasers and cannot be explained in the frame of the conventional LK approach because experimental conditions include high pumping current, strong optical feedback, and a relatively long external cavity. The observations include periodic oscillations at the delay period, which evolve to chaos. There is a bistability between these oscillations and a stable steady-state regime of operation.Our goal in this Letter is to introduce a model for QD lasers that accounts for most of the experimental observations in Ref. 6. We propose a system of delaydifferential equations that predicts the appearance of the periodic dropouts, intermittency, and chaos in the QD laser output and is not limited by the assumption of low pumping current and weak optical feedback.Let us briefly explain the essential ingredients derived from the experiments for the model construction. The experiments done at high pumping current and with strong optical feedback ͑ϳ5-10 dB͒ with a large delay were essential for the observation of instabilities. In lasers, the damping rate of the relaxation oscillation is proportional to the frequency itself. The increase of the cavity length decreases the relaxation oscillation frequency and, therefore, its damping rate. This effec...