A semiclassical theory of hyper-Raman scattering and three-photon resonant ionization via the coupled density-matrix and Maxwell equations is presented. A simplified three-level atom model is obtained, which includes two-photon resonant pumping and time-dependent photoionization rates. We consider conditions typically encountered in atomic vapors to simulate numerically the pulse propagation. A strong depletion of the photoionization probability in the hyper-Raman field-saturation regime is predicted.
