Numerical simulations of dynamically diffracted ultrashort x-ray free-electron laser pulses

The diffraction of femtosecond x-ray pulses by crystals will play a central role in the development of the optics of x-ray free-electron lasers (XFELs). Making use of Fourier analysis, we calculate the temporal dynamical diffraction of an incident delta function by single- and double- symmetric Bragg crystal monochromators. The time-dependent intensity of ultrashort XFEL pulses diffracted by perfect crystals is discussed. Our simulations show modifications in the time structure of incident 8 keV, 280-fs-duration, microbunched XFEL pulses after diffraction by the crystal optics. Finally, we investigate the statistical fluctuations of the time-integrated intensity from shot to shot.