Semiclassical theory of two-photon induced Raman scattering

Stimulated two-photon induced Raman scattering (hyper-Raman scattering) in an amplifier consisting of four-level atoms is analyzed semiclassically, via the coupled density matrix and Maxwell equations. We consider conditions typically encountered in the optical regime and in vapors. We show that even in the linear regime, it is characterized by a significant depletion of the atomic ground-state population, thus invalidating perturbative analyses based, for instance, on the nonlinear susceptibility tensor. Two major regimes of operation are found, one in which the population is completely consumed by the interaction ("linear regime"), and one in which the pump laser is depleted ("nonlinear regime"). Both regimes are, however, characterized by small photon conversion efficiencies. The tuning range is also briefly discussed.