Nonlinear dynamics of additive-pulse mode-locked lasers in four cavity topologies

Coupled-cavity mode-locked lasers, useful as they may be, can have a tendency to display dynamic instabilities; the mechanisms for this phenomenon are poorly understood. We show here by analytic means, supplemented with numerics, how these instabilities arise from the coupling of nonlinear resonators and how the thresholds for instability depend strongly on the topology of the laser. Four different topologies are considered, the Michelson, the Fabry-P\'erot, and two further configurations. The results of this comprehensive theory identify the most stable and the most unstable configuration and explain empirical findings of several authors.