Locking Phenomena in Semiconductor Lasers near Threshold with Optical Feedback and Sinusoidal Current Modulation

The dynamics of semiconductor lasers with optical feedback and current modulation has been extensively studied, and it is, by now, well known that the interplay of modulation and feedback can produce a rich variety of nonlinear phenomena. Near threshold, in the so-called low frequency fluctuations regime, the intensity emitted by the laser, without modulation, exhibits feedback-induced spikes, which occur at irregular times. When the laser current is sinusoidally modulated, under appropriate conditions, the spikes lock to the modulation and become periodic. In previous works, we studied experimentally the locked behavior and found sub-harmonic locking (regular spike timing such that a spike is emitted every two or three modulation cycles), but we did not find spikes with regular timing, emitted every modulation cycle. To understand why 1:1 regular locking was not observed, here, we perform simulations of the well-known Lang–Kobayashi model. We find a good qualitative agreement with the experiments: with small modulation amplitudes, we find wide parameter regions in which the spikes are sub-harmonically locked to the modulation, while 1:1 locking occurs at much higher modulation amplitudes.