Theory and simulation of the dynamics and stability of actively modelocked lasers

A new model is proposed for the active modulation component of a mode-locked laser cavity. By using Jacobi elliptic functions to capture the periodic forcing to the cavity, we are able to construct exact solutions representing a mode-locked pulse train. Two families of pulse-train solutions are generated: one in which neighboring pulses are in-phase and a second in which neighboring pulses are out-of-phase. We show that only out-of-phase solutions allow for stable mode-locked pulse trains. Further, pulse-to-pulse interactions can generate instabilities that destroy the pulse train altogether or lead to Q-switching.