Global view of complicated dynamics in optically injected semiconductor lasers

We use advanced techniques from bifurcation theory to examine the dynamics of single-mode semiconductor lasers with optical injection, modeled by three-dimensional rate equations. Key bifurcations, namely saddle-node, Hopf, period-doubling, saddle-node of limit cycle and torus bifurcations, are followed over a wide range of injection strengths and detunings for different fixed values of the linewidth enhancement factor α. Combining the stability diagram in parameter space with phase portraits provides a global and detailed view of complex dynamics of injected semiconductor lasers. In particular, we concentrate here on different routes to phase locking, which can be surprisingly complicated. Our analysis reveals many regions of chaotic behaviour and multistability in good agreement with experimental studies.