Self-starting of passively mode-locked lasers with fast saturable absorbers

Self-starting of passively mode-locked lasers with fast saturable absorption is studied. Our basic assumption is that the lasers will self-start when cw operation is unstable and mode-locked operation is stable. We start with a standard model, closely related to the Ginzburg-Landau equation, that is valid when the change in the time variation of the laser light during one round trip through the laser is small, and we determine the parameter regime in which cw mode operation becomes unstable. Coupled with previous results on the stability of mode-locked operation, these results allow us to determine when a laser will self-start. We apply our theory to figure-eight lasers with external gain.