  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.
