Experimental verification of dynamical diffraction focusing by a bent crystal wedge in Laue geometry

X-ray focusing by bent crystals: focal positions as predicted by the crystal lens equation and the dynamical diffraction theory

The location of the beam focus when monochromatic X-ray radiation is diffracted by a thin bent crystal is predicted by the `crystal lens equation'. This equation is derived in a general form valid for Bragg and Laue geometries. It has little utility for diffraction in Laue geometry. The focusing effect in the Laue symmetrical case is discussed using concepts of dynamical theory and an extension of the lens equation is proposed. The existence of polychromatic focusing is considered and the feasibility of matching the polychromatic and monochromatic focal positions is discussed.

A finite-element approach to dynamical diffraction problems in reflection geometry

A finite-element approach to the numerical solution of the Takagi–Taupin equations expressed in a weak form is presented and applied to simulate the X-ray reflectivity curves, spatial intensity distributions and focusing properties of bent perfect crystals in symmetric reflection geometry. The proposed framework encompasses a new formulation of the Takagi–Taupin equations, which appears to be promising in terms of robustness and stability and supports the Fresnel propagation of the diffracted waves. The presented method is very flexible and has the potential of dealing with dynamical X-ray or neutron diffraction problems related to crystals of arbitrary shape and deformation. The reference implementation based on the commercial COMSOLMultiphysicssoftware package is available to the relevant user community.

Dynamical focusing by bent, asymmetrically cut perfect crystals in Laue geometry

A semi-analytical approach based on the influence functions of a point source located on the crystal surface has been adopted to show that the focusing ability of cylindrically bent Laue crystals may be strongly enhanced by replacing symmetrically cut crystals with asymmetrically cut crystals. This approach is generally applicable to any distance between the X-ray source and the focusing bent crystal. A mathematically straightforward method to simplify the derivation of the already known expression of the influence functions in the case of deformed crystals with a constant strain gradient (e.g.cylindrically bent crystals) is also presented.

Spectrometer for hard X-ray free-electron laser based on diffraction focusing

X-ray free-electron lasers (XFELs) generate sequences of ultra-short spatially coherent pulses of X-ray radiation. A diffraction focusing spectrometer (DFS), which is able to measure the whole energy spectrum of the radiation of a single XFEL pulse with an energy resolution of ΔE/E 2 × 10(-6), is proposed. This is much better than for most modern X-ray spectrometers. Such resolution allows one to resolve the fine spectral structure of the XFEL pulse. The effect of diffraction focusing occurs in a single-crystal plate due to dynamical scattering, and is similar to focusing in a Pendry lens made from a metamaterial with a negative refraction index. Such a spectrometer is easier to operate than those based on bent crystals. It is shown that the DFS can be used in a wide energy range from 5 keV to 20 keV.

Bent perfect crystals as X-ray focusing polychromators in symmetric Laue geometry

The focusing properties of cylindrically bent crystals in symmetric Laue geometry are discussed using the formalism of Fresnel diffraction and the analytical solution of the Takagi-Taupin equations for a point source on the entrance surface. The existence of a focal shift in the dynamical focusing effect is pointed out and discussed. The present theoretical framework is applied to experiments performed at the energy-dispersive X-ray absorption spectroscopy beamline of the European Synchrotron Radiation Facility concerning the position and the size of the focal spot obtained from a polychromatic source at a large distance from the bent crystal.