LASER WITH INJECTED SIGNAL - PERTURBATION OF AN INVARIANT CIRCLE

We study the locked-unlocked transition for a class of lasers with inj ected signal. The transition is produced by a parametric breaking of t he invariant circle that represents the free running laser. A Hopf-sad dle-node codimension two bifurcation coupled with a phase-drift re-inj ection mechanism organizes the flow. Fixed points (locked states), per iodic orbits and tori, T-2, of two inequivalent types as well as heter o-homoclinic loops are found by using methods of bifurcation theory an d are illustrated with computer simulations. We discuss the dependence of the flow patterns with respect to the laser parameters and, in par ticular, we show that the detuning between atomic and cavity frequenci es plays a fundamental role for the dynamics.