Pulse repetition-frequency multiplication in a passively mode-locked semiconductor laser coupled to an external passive cavity

Using a delay differential equation model with two time delays, we investigate the dynamics of a semiconductor laser with an active cavity coupled to an external passive cavity. Our numerical simulations indicate that when the coupling between the two cavities is strong enough and the round-trip time of the active cavity is an integer multiple of the round-trip time of the external passive cavity, a harmonic mode-locking regime can develop in the laser with the pulse repetition period close to the passive cavity round trip time. We also demonstrate that the output field intensity sensitively depends on the relative phase between the electric fields in the two cavities giving rise to a resonant behavior. The period and width of the resonances depend on the ratio of the round-trip times and the coupling between the two cavities. We show that the coupled cavity system under consideration can demonstrate a bistability between different regimes of generation