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

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