The Q-switching instability in passively mode-locked lasers

A new asymptotic analysis of the equations for a mode-locked laser exhibiting a Q-switching instability is proposed. We determine the Hopf bifurcation point responsible for this instability and discuss its behavior in terms of the laser parameters. Our analysis is valid for all class B lasers exhibiting slowly damped relaxation oscillations which include solid state and semiconductor lasers. In the limit of weak nonlinearities, we recover Haus stability conditions. In the case of strongly nonlinear losses, as for the usual picosecond and femtosecond laser devices, we determine the stability conditions.