Analytical theory of external cavity modes of a semiconductor laser with phase conjugate feedback

The rate equations describing a laser with phase conjugate feedback are analyzed in the case of non-zero detuning. For low feedback rates and detuning, the stability diagram of the steady state is similar to the laser subject to injection. A stable steady state may loose its stability through a Hopf bifurcation exhibiting a frequency close to the relaxation oscillation frequency of the solitary laser. We also construct time-periodic pulsating intensity solutions exhibiting frequencies close to an integer multiple of the external cavity frequency. These solutions have been found numerically for the zero detuning case and play an important role in the bifurcation diagram.