Coherently controlling Raman-induced grating in atomic media

We consider dynamically controllable periodic structures, called Raman induced gratings, in three- and four-level atomic media, resulting from Raman interaction in a standing-wave pump. These gratings are due to periodic spatial modulation of the Raman nonlinearity and fundamentally differ from the ones based on electromagnetically induced transparency. The transmission and reflection spectra of such gratings can be simultaneously amplified and controlled by varying the pump field intensity. It is shown that a transparent medium with periodic spatial modulation of the Raman gain can be opaque near the Raman resonance and yet at the same time it can be a non-linear amplifying mirror. We also show that spectral properties of the Raman induced grating can be controlled with the help of an additional weak control field.