Research Article: Spatial displacement of forward-diffracted X-ray beams by perfect crystals

Date Published: March 01, 2018

Publisher: International Union of Crystallography

Author(s): A. Rodriguez-Fernandez, V. Esposito, D. F. Sanchez, K. D. Finkelstein, P. Juranic, U. Staub, D. Grolimund, S. Reiche, B. Pedrini.


The first experimental observation of transverse spatial echoes generated by forward Bragg diffraction of an X-ray beam propagating through a perfect thin crystal is reported.

Partial Text

Hard X-ray free-electron lasers (XFELs) are novel photon sources, which rely on the self-amplified spontaneous emission (SASE) process to obtain peak brightnesses in the soft and hard X-ray regime that are orders of magnitude larger than those achieved with insertion devices at third-generation synchrotron light sources (Margaritondo & Rebernik Ribic, 2011 ▸). The ultrashort pulse length opens new avenues for investigations of phenomena at the femtosecond timescale. The SASE radiation arises from amplification of stochastic noise in the electron bunch. Therefore, it consists of many longitudinal modes (Wark & Lee, 1999 ▸), and exhibits strong shot-to-shot fluctuations of both the mean pulse energy and the pulse spectrum. Furthermore, the relative bandwidth at an XFEL operating in SASE mode is typically of the order of 10−3. Many XFEL experiments require a much narrower bandwidth and excellent spectral stability (Alonso-Mori et al., 2015 ▸). These beam properties can be enforced by inserting a monochromator in the X-ray beam path, at the expense of losing a large fraction of the beam intensity.

Fig. 7 ▸ shows results obtained from an energy scan at 12 keV with the C400µm (110) crystal; the reflection presented is the (220) reflection in symmetric Bragg geometry, which corresponds to the first simulation described in §2.2. Panel (a) shows the measured reflectivity curve , which allows discrimination between the off- and on-diffraction conditions. Panels (b) and (c) display the image of the transmitted beam for the off- and on-diffraction conditions, respectively. The intensity humps in the vertical direction appear only in the latter case, in agreement with the simulation results shown in Figs. 3 ▸(d) and (e).

Experiments on FBD by a thin crystal were performed decades ago to study the Pendellösung effect [in Bragg gemetry by Kato & Lang (1959 ▸) and in Laue geometry by Batterman & Hildebrandt (1968 ▸)], which consists of oscillations of the transmitted-beam intensity upon small variations of the incidence angle or wavelength of the incoming plane wave. These are far-field experiments, for which the X-ray intensity is detected as a function of the propagation angle, i.e. as . Analogous studies were also done on the diffracted beam (Mocella et al., 2000 ▸). In contrast, the generation by FBD of echoes is a near-field phenomenon, and involves interference of plane waves of different photon energies and/or different incidence angles. As mentioned in §1, this phenomenon has been investigated deeply from the theoretical point of view in recent years, in relation to the X-ray self-seeding possibilities at XFEL facilities. Indirect experimental evidence for the retardation of temporal echoes is given by the fact that self-seeding at an XFEL has been implemented, while for the transverse spatial displacement the hints come from the fact that the trajectory of the electron beam in the downstream undulator section has to be adjusted correspondingly.

We have reported the first experimental observation of transversely displaced echoes generated via forward Bragg diffraction of an X-ray beam propagating through a perfect thin crystal. The agreement of the experimental echo signal with that obtained from simulations relying on the dynamical diffraction theory is very good. This paves the way for the imaging of the echoes as a tool to diagnose forward-diffracted beams as applied in self-seeding modules or to study temporal strain effects in thin perfect crystals.




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