Understanding ultrafast x-ray 'echoes' diffracted from single crystals

Abstract

Multiple x-ray beams generated by interference processes in perfect crystals were imaged with a resolution of about 100nm using tele-ptychography in the diffraction direction. These multiple wave-fields, also known as x-ray diffraction echoes, are related to the process known as the Pendelloesung effect and are described by dynamical diffraction theory. The echoes are produced by the constructive interference of diffracted x-rays at the exit surface of the crystal sample. In the imaged diffraction peak, we observed 10 echoes maxima with a total signal length of 78 um. Which translates into a total temporal delay in the signal of less than 108 fs.This makes the echoes of high importance for x-ray optics at x-ray Free Electron Laser sources, as the effect could be used for future ultrafast x-ray beam splitters. In addition to this application, echoes can be exploited to follow ultrafast processes in single crystal micro-structures such as melting or strain propagation.

Figures (4)

• Figure 1: Sketch of the experimental geometry. The incoming x-ray beam was focused with a Fresnel zone plate (FZP) to 73nm onto the center of rotation of the goniometer. The Si wafer was positioned at the focus and set to the (220) Laue diffraction condition in the horizontal plane. A pinhole with diameter 3µm was located at 5mm from the rear surface of the crystal. The distance between sample and detector was of 5.285m.
• Figure 2: (a) Intensity of the reconstructed wavefronts at the pinhole plane for the (220) reflection of a 100µm Si thick crystal at 8.346keV. (b) propagation of the reconstructed wavefront back to the rear surface of the crystal. (c) Simulated dynamical diffraction wavefront of the Laue symmetric $(220)$ reflection for a 100µm thick crystal at 8.346keV (d) projection along the y direction of the measured diffraction intensity in (b) (black stars) and simulated dynamical diffraction signal (dash line).
• Figure 3: (a) Spatio-temporal simulation of the diffracted signal for a Si crystal of 100µm set for the (220) Laue geometry reflection at 8.346keV with a beam size of 100nm, using a monochromatic beam with a pulse length of 10fs. (b) Projection of the intensity of the simulated signal along the time direction.
• Figure 4: Propagation of the reconstructed x-ray diffracted beam along the $z$ direction (a) for the vertical plane and (b) the horizontal plane where diffraction takes place.