An analytical study of a periodically driven laser with a saturable absorber

We consider the rate equations for a laser with ail intracavity saturable absorber and subject to a periodically modulated pump. By deriving simplified equations for a map valid for strongly pulsating regimes, analytical conditions are determined that specify the properties of both frequency-locked and unlocked behaviors. As the strength of the modulation is increased, quasiperiodic and period-doubling bifurcations are predicted. However. only the transition from locking to non-locking through a quasiperiodic bifurcation is possible for realistic values of the parameters. Our results are consistent with previous numerical and experimental studies of modulated lasers with a saturable absorber.