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-principles dynamical model based on delay algebraic equations. We show that the third-order dispersion stemming from the lasing microcavity 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 forms of behavior 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 diagrams of the two models and assess their good agreement.