  We investigate the dynamics of a two-photon laser under conditions where the
spatial variation of the cavity field along the cavity axis is important. Main
attention is paid to linear stability analysis and numerical investigation of a
two-photon laser for the Maxwell-Bloch equations. 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 eigenvalue and analytic information are
obtained in some realistic limits, such as very large reflectivity, very small
cavity losses, or very small population relaxation rate. The results are
illustrated with an application to a specific atomic system (Potassium) as an
amplifying medium.
