X-ray third-order nonlinear diffraction in the asymmetric reflection geometry

X-ray third-order nonlinear asymmetrical diffraction has three independent parameters: the asymmetry angle, the incident wave intensity and the deviation from the exact Bragg orientation. In contrast to the linear case, in the nonlinear case the total reflection region does not exist for all intensity values and asymmetry angles. Theoretical consideration leads to analytical conditions of the total reflection region, and the analysis can be carried out by a graphical method. An exact solution in the total reflection region is found. The numerical solutions of the third-order nonlinear diffraction allow one to find the reflection curves for a fixed asymmetry angle or for a fixed intensity. For very large or very small asymmetry factors the third-order nonlinear effects can be observed for beams with very low intensities.