Amplified short-wavelength light scattered by relativistic electrons in   the laser-induced optical lattice
  The scheme of the XUV/X-ray free electron laser based on the optical undulator created by two overlapped transverse laser beams is analyzed. A kinetic theoretical description and an ad hoc numerical model are developed to account for the finite energy spread, angular divergence and the spectral properties of the electron beam in the optical lattice. The theoretical findings are compared to the results of the one- and three-dimensional numerical modeling with the spectral free electron laser code PLARES. 
I.A. Andriyash, V.T. Tikhonchuk, V. Malka, E. d'Humi\`eres, Ph. Balcou
physics.optics physics.plasm-ph