Phase equations for periodically driven injected lasers

Summary form only given. Recent experiments using diode lasers subject to strong external injection have shown that adding a small reference current modulation to the DC-bias current can easily lock the oscillations frequency of the laser to the reference frequency. Tunable outputs oscillating at stable frequencies from 9.5 to 13.1 GHz have been obtained. These remarkable performances result from the fact that the laser relaxation oscillation frequency depends on the injection strength at high injection rates. A first analysis of the laser rate equations gives expressions for the locking domain in terms of the modulation amplitude /spl delta/, the modulation frequency /spl omega/, and the injection strength /spl eta/. Our determination of the locking domain does not reveal the time dependent transition from locking to unlocking as the injection strength is changed. This transition is, however, observed in the experiments. If the modulation amplitude is sufficiently weak, the main effect of the time-periodic forcing is on the phase of the unperturbed limit-cycle oscillations.