Theoretical study of a laser with injected signal. I. Analytical results on the dynamics

We have analyzed a model which describes a laser with an injected signal (LIS). We have used a simplified model, keeping only the complex-field equation. By means of standard mathematical methods, we have investigated the vicinity of a Hopf bifurcation point that it presents, and derived the normal form of the laser response. The parameter plane is fully analyzed in terms of the periodic-solution stability. A second branch of periodic solutions is also shown to be present in the system. Numerical simulations are carried out following the parameter-plane analysis and lead to the full set of bifurcation diagrams that this model can present. Finally, a global and complete view of the LIS dynamics is deduced.