Impact of spontaneously emitted photon on the dynamic behaviors of injection-locked semiconductor lasers

Starting from the mean-field rate equations describing the dynamic behaviors of the slave laser (SL) in the injection-locked master-slave semiconductor laser system (MSL), applying the perturbation method and the Cardan formula, analytical solutions to the evolutions of perturbations from the fixed point have been derived. The dynamic behaviors of the SL perturbed by a spontaneously emitted photon have been analyzed by using the above solutions. Finally, the phase space portraits with different phase between the spontaneously emitted photon and the injection field have also been investigated.