Asymmetrically cut crystals for synchrotron radiation monochromators

Abstract

Asymmetrically cut crystals are interesting for use in synchrotron radiation monochromators because of their good energy resolution characteristics and their focusing properties. Ray tracing codes, such as SHADOW, are very efficient in the design and development of new optical devices. In order to determine the convenience of using asymmetrically cut crystals for x-ray monochromators, SHADOW has been extended to include these kinds of crystals. The physical approach to ray tracing asymmetrically cut crystals is based on the coexistence of two periodic structures. One of these is the bulk periodic structure of the Bragg planes. Such a structure determines the existence of a rocking curve near the Bragg condition, and is implemented in SHADOW following the Darwin–Prins formalism of the dynamical theory of diffraction. The second periodic structure is a one-dimensional grating on the crystal surface, formed by the truncation of the lattice planes with the surface. This grating is responsible for the focusing properties of these crystals and plays an essential role in determining the trajectory of the rays. The combination of an asymmetric crystal and a nonplanar surface can be easily achieved by bending (Johann case) to provide improved properties. More complex cases such as the ground-bent crystals (i.e., Johansson geometry) can be considered as a particular case of asymmetrical crystals in which the angle between the Bragg planes and the surface change along the crystal surface. All these cases have been implemented in SHADOW.