Numerical bifurcation analysis for multi-section semiconductor lasers

We investigate the dynamics of a multi-section laser resembling a delayed feedback experiment where the length of the cavity is comparable to the length of the laser. Firstly, we reduce the traveling-wave model with gain dispersion (a hyperbolic system of partial differential equations) to a system of ordinary differential equations (ODEs) describing the semiflow on a local center manifold. Then, we analyse the dynamics of the system of ODEs using numerical continuation methods (AUTO). We explore the plane of the two parameters feedback phase and feedback strength to obtain a complete bifurcation diagram for small and moderate feedback strength. This diagram allows to understand the roots of a variety of nonlinear phenomena like, e. g., self-pulsations, excitability, hysteresis or chaos, and to locate them in the parameter plane