Diffraction of X-ray Pulse in Crystals

Recently the investigation of the extremely short (subpicosecond) X-ray pulses interaction with crystals takes interest because of the development of linac-driven X-ray Free Electron Laser, operating in the SASE mode and X-ray Volume Free Electron Laser [1, 2]. According to the analysis [3] short X-ray pulse passing through a crystal is accompanied by the significant time delay of radiation. The δ−pulse delay law for the Bragg diffraction is proportional to ∼ J 1 (at) t 2 , where J 1-is the Bessel function, a-a coefficient will be defined below, t-time. In the present paper the delay law dependence on the diffraction asymmetry parameters is analyzed. It is shown that the use of subpicosecond pulses allows to observe the phenomenon of the time delay of pulse in crystal and to investigate the delay law experimentally. It is also shown that the pulse delay law depends on the quanta polarization. Let us consider the pulse of electromagnetic radiation passing through the medium with the refraction index n(ω). The wave packet group velocity is as follows: v gr = ∂ωn(ω) c∂ω −1 = c n(ω) + ω ∂n(ω) ∂ω , (1) where c-is the speed of light, ω-is the quantum frequency. In the X-ray range (∼tens of keV) the index of refraction has the universal form n(ω) = 1 − ω 2 L 2ω 2 , ω L is the Langmour frequency. Additionally, n − 1 ≃ 10 −6 ≪ 1. Substituting n(ω) to (1) one can obtain that v gr ≃ c 1 − ω 2 L ω 2. It is clear that the group velocity is close to the speed of light. Therefore the time of wave packet delay in a medium is much shorter than the that needed for passing the length equal to the target width in a vacuum.