Diffraction of X-ray free-electron laser femtosecond pulses on single crystals in the Bragg and Laue geometry

A solution of the problem of dynamical diffraction for X-ray pulses with arbitrary dimensions in the Bragg and Laue cases in a crystal of any thickness and asymmetry coefficient of reflection is presented. Analysis of pulse form and duration transformation in the process of diffraction and propagation in a vacuum is conducted. It is shown that only the symmetrical Bragg case can be used to avoid smearing of reflected pulses.