Transition from unidirectional to delayed bidirectional coupling in optically coupled semiconductor lasers

We investigate the transition from unidirectional to delayed bidirectional coupling of semiconductor lasers. By tuning the coupling strength in one direction we show how the locking region evolves as a function of the detuning and coupling strength. We consider two representative values of the relaxation oscillation damping: one where the relaxation oscillations are very underdamped and one where they are very overdamped. Qualitatively different dynamical scenarios are shown to emerge for each case. Several features of the delayed bidirectional system can be seen as remaining from the unidirectional system while others clearly arise due to the delayed coupling and are similar to effects seen in delayed feedback configurations.