Multimode laser with an injected signal: Steady-state and linear stability analysis

We discuss the steady-state and the linearized response of a multimode laser with an injected signal. The steady-state analysis is carried out for arbitrary values of the laser gain and resonator parameters, while the linearized stability calculation is limited to parameter ranges where the mean-field assumption is a reasonable approximation. For suitably large values of the polarization and population decay rates, we review the problem of the adiabatic elimination of the atomic variables and demonstrate explicitly the existence of possible pitfalls and how to avoid them.