Strong nonlinear regime of resonant four-wave mixing in a gas

The explicit solution is obtained for Raman four-wave mixing $\omega_4=\omega_1-\omega_2+\omega_3$ of two strong fields $E_1, E_3$ and two weak fields $E_2, E_4$ in a four-level system with the large Doppler broadening. The resonance of the mixing coefficient vs intensity is found near equal Rabi frequencies of strong fields and interpreted as an intersection of quasi-energy levels. Up to 6 peaks appear in the dependence of conversion coefficient on the detuning of the probe field. An unexpected additional pair of peaks is a result of averaging over velocities and disappears at low temperature. The effects allow explaining saturation behavior in recent experiments on the mixing in sodium molecular vapor.