Synchronization properties of coupled semiconductor lasers subject to filtered optical feedback

We study numerically the synchronization properties of two unidirectionally coupled semiconductor lasers subject to filtered optical feedback. By adding a perturbation (a message) to the output of the master laser, we show that mutual information allows distinguishing between chaotic synchronization (at low to moderate coupling strengths) and injection locking (at large coupling strength). We find that a receiver subject to a feedback similar to that of the emitter (closed-loop receiver) shows better synchronization with the master laser when compared with a receiver without feedback (open-loop receiver). Closed-loop receivers also show better capability to recover weak messages. The filter in the feedback loop allows reducing the bandwidth of the chaotic carrier, improves the synchronization with respect to the conventional feedback case, and requires less coupling strength with a minor loss in complexity.