Coexistence of in-phase and out-of-phase dynamics in a multimode external cavity laser diode operating in the low-frequency fluctuations regime

We study the dynamics of a multimode laser diode with delayed optical feedback operating in the low-frequency fluctuations regime. We show that a multimode extension of the Lang-Kobayashi equations that takes into account spontaneous emission noise predicts two qualitatively different behaviors of the laser on the picosecond time scale. Individual modes of the laser can emit pulses in-phase or oscillate out-of-phase, depending on the operating parameters. The corresponding statistical distributions are in good agreement with two recent experiments.