Nonlinear optics at maximum coherence

We describe nonlinear optical processes in a medium with maximal coherence on a Raman transition. The nonlinear polarization of such a medium is of the same order of magnitude as the linear polarization. This allows efficient frequency conversion and generation of a wide spectrum of Raman sidebands. The phase of the coherence can be controlled through a small two-photon detuning from the Raman resonance. An appropriate choice of the phase improves nonlinear generation and propagation of sidebands through an inhomogeneous gaseous medium.