Bifurcation analysis of frequency locking in a semiconductor laser with phase-conjugate feedback

We present a detailed study of the external-cavity modes (ECMs) of a semiconductor laser with phase-conjugate feedback. Mathematically, lasers with feedback are modelled by delay differential equations (DDEs) with an infinite dimensional phase space. We employ new numerical bifurcation tools for DDEs to continue steady states and periodic orbits, irrespective of their stability. In this way, we show that the periodic orbits corresponding to the ECMs are connected to the steady state solution associated with the locking range of the laser. We also identify symmetric and non-symmetric homoclinic orbits and hysteresis in the system.