Stability of locking in mutually delay-coupled semiconductor lasers

We investigate the continuous wave solutions of a system of two mutually delay coupled semiconductor lasers. These continuous wave solutions, which we refer to as compound laser modes (CLMs), are locked solutions of the coupled laser system where both lasers lase at a common frequency. We model the system by a set of delay differential rate equations, where we assume that, apart from possible detuning in their free running optical frequencies, the lasers are identical. We show how the structure and the stability of the CLMs depend on the main parameters, namely, the feedback phase, the feedback rate, the pump parameter, and the detuning. We identify two mechanisms for creating CLMs. First, CLMs emerge from the off-state of the coupled laser system in Hopf bifurcations. Second, CLMs are created in pairs in saddle-node bifurcations. For the special case of zero detuning we also find pitchfork bifurcations that organize the CLM structure. We show in which parameter regions CLMs exist, where they are stable, and which bifurcation curves form the boundary of the stable locking region.