Exact linear stability analysis of the plane-wave Maxwell-Bloch equations for a ring laser

Abstract

We perform an exact linear stability analysis of the Maxwell-Bloch equations for a unidirectional ring laser. The model analyzed in this paper is based on the plane-wave assumption for the cavity field, but it allows arbitrary values of all the other parameters for the cavity and for the active medium. This problem had been solved previously only under exact resonance conditions, or in the uniform-field (mean-field) limit, or after adiabatic elimination of the atomic polarization.