X-Ray Bragg Diffraction in Asymmetric Backscattering Geometry

Abstract

We observe three effects in the Bragg diffraction of x rays in backscattering geometry from asymmetrically cut crystals. First, exact Bragg backscattering takes place not at normal incidence to the reflecting atomic planes. Second, a well-collimated (approximately 1 microrad) beam is transformed after the Bragg reflection into a strongly divergent beam (230 microrad) with reflection angle dependent on x-ray wavelength--an effect of angular dispersion. The asymmetrically cut crystal thus behaves like an optical prism, dispersing an incident collimated polychromatic beam. The dispersion rate is approximately 8.5 mrad/eV. Third, parasitic Bragg reflections accompanying Bragg backreflection are suppressed. These effects offer a radically new means for monochromatization of x rays not limited by the intrinsic width of the Bragg reflection.

X-ray Echo Spectroscopy

“…Extension into the hard x-ray regime is therefore nontrivial. In this regard, as was demonstrated in [6,7], the angular dispersion in the hard x-ray regime can be achieved by Bragg diffraction from asymmetrically cut crystals, i.e., from crystals with the reflecting atomic planes not parallel to the entrance surface. This is a hard x-ray analog of the optical diffraction gratings or optical prisms.…”

“…These are relatively large values. Typically, in a single Bragg reflection, a maximum dispersion rate is D 6−8 µrad/meV for photons with energy E 10 keV [7,15]. As mentioned before, multi-crystal arrangements can be used to enhance the dispersion rate [8].…”

“…This is achieved, first, by using strongly asymmetric Bragg reflections close to backscattering [6,7], and, second, by enhancing the single-reflection dispersion rate considerably by subsequent asymmetric Bragg reflections from crystals in special arrangements [8] exemplified below. In the following two steps, we will show how the principle scheme of a generic echo spectrometer presented above, can be realized in the hard x-ray regime by using multi-crystal arrangements as dispersing elements.…”

“…Diffraction gratings are not practical in the hard x-ray regime. However, as was demonstrated in [6,7], the angular dispersion in the hard x-ray regime can be achieved by Bragg diffraction from asymmetrically cut crystals or from special arrangements of asymmetrically cut crystals [8,9], which are a hard x-ray analog of the * Electronic address: shvydko@aps.anl.gov optical diffraction gratings and optical prisms. In the space-domain echo-spectrometer proposed here, an image of a point-like x-ray source is defocused by a dispersing system comprised of asymmetrically cut Bragg diffracting crystals.…”

Ultra-high Resolution Optics for EUV and Soft X-ray Inelastic Scattering

“…For high energy xray applications, there is a unique opportunity to use an asymmetrically cut crystal as an ultra-high density grating [15][16][17]. Unfortunately, it is difficult, if not impossible, to find a crystal with a lattice constant, large enough for soft x-ray applications [18].…”