X-ray focusing within a single-crystal waveguide under grazing-incidence diffraction conditions

X-ray-beam propagation through a parallel-plate waveguide is investigated with allowance for grazing-incidence Bragg diffraction at the crystalline structure of the plates. Expressions for the waveguide modes are derived. It is demonstrated that undamped waveguide modes exist at angles exceeding the critical value (total external-reflection angle), thereby making it possible to increase the angle of capture of radiation incident on the waveguide. The calculated output intensities of the waveguide are compared with the waveguide-mode intensities in absence of grazing-incidence diffraction in the waveguide material.