Pulsing behavior of a three-level laser with saturable absorber

A numerical study of a three-level laser model that includes a saturable absorber is presented. The theory models the laser as a lumped element. This assumption is valid as long as the laser pulses are much longer than the cavity. The model is intended to be somewhat representative of an erbium-doped fiber laser without trying to mimic the operating parameters of such a laser too closely. As expected, the presence of the saturable absorber causes the laser to be unstable under certain operating conditions. The question of stability is explored by examining small perturbations of the steady-state solutions of the rate equations. It is found that the predictions of this stability analysis are in excellent agreement with the behavior of the solutions of the full time-dependent rate equations. It is also found that under certain conditions the laser may pass from pulsed to stable operation simply by raising the pump power