The sagittal focusing of x-ray beam diffracted on symmetrically cut crystals with a longitudinal parabolic groove on their diffraction surfaces has been proved experimentally and the results have been already published. This kind of focusing is based on the refraction phenomena occurring during Bragg x-ray diffraction. In this paper our new developments in this field are reported. First, it was shown experimentally that in some cases a channel-cut crystal monochromator with longitudinal parabolic grooves can be replaced by a single crystal with a round hole drilled parallel to diffracting planes. This substantially simplifies the manufacturing of such a focusing monochromator. Second, it has been experimentally proved that the refraction effect, on which the focusing is based, may be substantially enhanced by cutting the longitudinal parabolic groove into the surface of an asymmetrically cut crystal (or drilling a hole whose axis is tilted with respect to the diffracting planes). A very simple formula describing the focusing properties for this case is derived. Finally, the results of the first experiment on the meridional focusing of x-ray beam diffracted on a crystal with a transversal groove on its surface are reported. Some experimental results are compared with the results of ray-tracing simulations, which were developed for this purpose.
