Instabilities in lasers with an injected signal

A laser with an injected signal, in which the polarization can be adiabatically eliminated is considered, the stability of the steady-state solutions is studied, and the time-dependent solutions are discussed. For the laser alone, the only possible solution is consistent intensity. However, the introduction of an external field, with an amplitude that does not satisfy the injection-locking condition, destabilizes the system. In such a case, numerical results show the existence of a self-Q-switching process, which induces relaxation oscillations. The frequency of the giant pulses is directly related to the amplitude of the external field, whereas the frequency of the relaxation oscillations depends on the damping rates. It is shown also that, depending on the value assigned to control parameters, the interaction between these frequencies leads to a chaotic behavior through intermittency or period-doubling bifurcations. Finally, topological equivalence between the laser system and a unidimensional circle map is shown for some values of control parameters.