Instabilities in a Simple Model of a Laser with a Fast Saturable Absorber

Abstract
We study the effect of adding a fast saturable absorber to the single-mode Maxwell-Bloch equations which are otherwise isomorphic to the Lorenz equations. The modified system, which includes a nonlinear loss term in the field equation, exhibits both the Lorenz instability and the Q-switching instability within a single framework. We show that adding the saturable absorber lowers the threshold for the Lorenz instability, making it more accessible to experimental observation.