Dispersive instabilities in Passively Mode-Locked Integrated External-Cavity Surface-Emitting Lasers

We analyze the dynamics of passively mode-locked integrated external-cavity surface-emitting Lasers (MIXSELs) using a first-principle dynamical model based upon delay algebraic equations. We show that the third order dispersion stemming from the lasing micro-cavity induces a train of decaying satellites on the leading edge of the pulse. Due to the nonlinear interaction with carriers, these satellites may get amplified thereby destabilizing the mode-locked states. In the long cavity regime, the localized structures that exist below the lasing threshold are found to be deeply affected by this instability. As it originates from a global bifurcation of the saddle-node infinite period type, we explain why the pulses exhibit behaviors characteristic of excitable systems. Using the multiple time-scale and the functional mapping methods, we derive rigorously a master equation for MIXSELs in which third order dispersion is an essential ingredient. We compare the bifurcation diagram of both models and assess their good agreement.