Nonlinear theory of a free-electron laser exploiting media with a periodically modulated refractive index

The nonlinear theory of a free-electron laser (FEL) exploiting media with a periodically modulated refractive index is presented. The gain and the saturation parameters are found for different operating regimes of such a FEL. The system discussed could be used for the amplification of light in the optical and ultraviolet regions of the spectrum.