Semiclassical stability analysis of a two-photon laser including spatial variation of the cavity field

We investigate the dynamics of a two-photon laser under conditions where th e spatial variation of the cavity field along the cavity axis is important. The model assumes pumping to the upper state of the two-photon transition. We consider the Maxwell-Bloch equations on the basis of which we study the stability analysis of the steady state of the system. The system is taken to be contained in a ring-laser cavity. Asymptotic expansion of the eigenva lue and analytic information are obtained in some realistic limits, such as very large reflectivity, very small cavity losses, or very small populatio n relaxation rate. The results are illustrated with an application to a spe cific atomic system (potassium) as an amplifying medium.