Saturated two-photon absorption of single-frequency radiation in gaseous media

A saturated nonresonant two-photon absorption (TPA) theory of quasi-monochromatic radiation by an atom is developed in a model of a three-level cascade quantum system. It is shown that doubled-frequency radiation, arising from a multipole interaction of radiation with the dipole-forbidden transition, experiences spatial oscillations at arbitrary intensities of the pump. The influence of the total phase of the waves with the initial and doubled frequencies on TPA is considered under conditions of ring frequency mixing in a medium.