Comparison of two types of synchronization of external-cavity semiconductor lasers

We study numerically the synchronization of external-cavity semiconductor lasers in a master-slave configuration, based on a Lang-Kobayashi-type model. Depending on the feedback and coupling strengths, the slave laser synchronizes with the injected optical field or with the injected field but lags in time. We show that these two types of synchronization present different robustness with respect to the noise, frequency detuning, and current modulation of the master laser.