Self-pulsations and excitability in lasers with saturable absorber

Bernd Krauskopf, Department of Engineering Mathematics, University of Bristol

We consider the Yamada model, a set of three differential equations constituting a simple model for self-pulsations in (semiconductor) lasers with saturable absorber. A complete picture of all possible dynamics is presented in terms of two-dimensional bifurcation diagrams, in which we find a Bogdanov-Takens bifurcation as an organizing center. This shows that pulses are created in a homoclinic bifurcation (or saddle connection). The laser is also found to be excitable before threshold. We discuss the possibility of using this fact for the generation of pulse trains with minimal jitter.