Semiclassical stability analysis of a two-photon laser

We explain in this paper in simple terms the behavior of two-photon lasers and describe recent results that have led to the realization of the first c ontinuous-wave two-photon optical laser. We stress the differences between one- and two-photon lasers to develop an appreciation of their dynamics and the difficulties associated with achieving two-photon lasing. We find simi larities and significant differences between the one- and two-photon polari zations of the medium, population inversion and mode-pulling formula. The t heory is treated semiclassically by using Maxwell-Bloch equations. We study the linear stability analysis of the steady state of the system which is t aken to be contained in a ring cavity. The results are illustrated with an application to a specific atomic system in a long sample of sodium vapor as an amplifying medium, in which the possibility of short pulse train genera tion is exhibited.