Theory of dynamical relaxation oscillations and frequency locking in a synchronously-pumped laser diode

It is shown that the rate equations for the plasma density and the light intensity, together with a delayed feedback of the light in the external resonator, can be used to describe the nonlinear dynamics of actively mode-locked laser diodes. In particular, the relaxation oscillations of the laser intensity and the plasma density around the stationary pulse solutions are calculated for a laser diode in a long resonator with a periodically pulsed pump current. For small negative detuning between the round-trip period and the pump period, slow dynamical relaxation oscillations that give rise to megahertz-sidemodes in the intensity correlation spectrum occur. For larger negative detuning the delayed feedback gives rise to a frequency locking between the light pulse frequency and the modulation frequency