Transition from the lowest linewidth mode operation to coherence collapse in a semiconductor laser with feedback from a distant reflector

The influences of optical feedback from a distant reflector on single-mode semiconductor laser operation are analyzed theoretically. The stable operation in the lowest linewidth mode and the feedback parameter for the onset of coherence collapse are systematically derived. In the feedback regime for the lowest linewidth mode operation, the laser principally operates at the emission frequency of the solitary laser at the beginning of the operation with the feedback. It is shown exactly by asymptotic analysis of the equation for the field phase in the semiconductor cavity considering the time-lag of the feedback that the laser comes to operate in the lowest linewidth mode. In the lowest linewidth mode operation, the laser is stably phase-locked to the feedback. In the semiconductor cavity, the field amplitude and the field phase oscillate in almost the same phase in the fluctuation modes related to the relaxation oscillations, In the lowest linewidth mode operation, the phase oscillations enhance the amplitude oscillations through the feedback-action's dependence upon the phase difference between the field in the semiconductor cavity and the feedback. Thus, the damping of the relaxation oscillations decreases with further increased feedback and the transition to the coherence collapse occurs.