Dynamics and linear stability analysis in semiconductor lasers with phase-conjugate feedback

Dynamics of semiconductor lasers with phase-conjugate feedback are studied. At a certain feedback level, the laser output evolves into periodic oscillations due to the undamped relaxation oscillation which corresponds to the highest mode of the linear stability analysis. With increasing feedback level, the second mode is excited in quasi-periodic oscillations. Though the second mode frequency in the conventional feedback is almost the same as the external cavity mode frequency, the frequency in the phase-conjugate feedback is completely different from that. We study the dynamics of the phase-conjugate feedback, showing the time series, power spectrum, and attractors, and compare the results with those in the conventional feedback. The transition of the linear modes is also studied from the linear stability analysis. The results derived from the linear stability analysis and the mode transition are compatible with those of the simulations based on the rate equations.