What is it about?
Linear and third order nonlinear time dependent dynamical diffraction of X-ray pulses in crystals theoretically is considered. Numerical simulations have been performed. The analytical solutions have been found. The pulse is assumed to have restricted size in the diffraction plane.
Why is it important?
Usually the diffraction of an X-ray pulse inside a crystal is considered as linear. and the front of the pulse is suggested to by infinite. In this work the pulse front is considered to be finite ant the nonlinear case of diffraction is investigated. Passing to the frame connected with the pulse the dynamical diffraction equations are written in the stationary frame, which allows directly to write the solution in linear case and easily integrate the dynamical diffraction equations numerically in nonlinear case. This method allows to find the solutions as numerically as well as analytically also for deformed crystals