Time Compression of X-ray Free-electron Laser Pulses under Conditions of Bragg Diffraction

In the last years several laboratories actively work on construction of X-ray free electron lasers (XFEL) with wavelength of radiation of the order λ ~ 0.1 nm. Theoretical calculations show, that self-induced amplification of spontaneous radiation on the exit of an XFEL undulator forms a pulse composed of many ultra-short peaks with duration from a fraction up to tens femtosecond. A further tailoring of the X-ray radiation parameters is necessary for most experimental application. A quite natural solution for this task is diffraction on ideal single crystals. A dynamical theory of diffraction of X-ray pulses with arbitrary form in the Bragg and the Laue cases was developed, which allows to consider special and temporal distribution of reflected and transmitted pulses at any given distance from a crystal with account of diffuse spreading of these pulses in the process of their propagation in space. It is shown, that super-short pulses with the duration about 0.1-1 fs are strongly widened in time and are deformed in form by the diffraction process. In the present paper I investigate the possibility of time compression of pulses, i.e. the reduction of their duration by means of the Bragg reflection. It is shown, that in the case of incident chirp pulses, for which the instantaneous frequency of radiation has a linear time dependence, and the phase – a quadratic one, it is possible to achieve for 1-10 fs incident pulse a reduction of duration by a factor of 10. The effect is based on a large spectral width of the chirp pulses, comparable or even exceeding the typical width of a Bragg reflection for the plane wave case.