Absorption and scattering by structured interfaces in X-rays

Promising achievements of resonance inelastic X-ray scattering and other spectroscopy studies in the range from hard X-ray to extreme ultraviolet require the development of exact tools for modeling energy characteristics of state-of-the-art optical instruments for bright coherent X-ray sources, space science, and plasma and superconductor physics. Accurate computations of the absorption and scattering intensity by structured interfaces in short wavelength ranges, i.e. realistic gratings, zone plates and mirrors, including multilayer-coated, are not widely explored by the existing methods and codes, due to some limitations connected, primarily, with solving difficult problems at very small wavelength-to-period (or to correlation length) ratios and accounting for random roughness statistics. In this work, absorption integrals and scattering factors are derived from a rigorous solution of the vector Helmholtz equations based on the boundary integral equations and the Monte Carlo method. Then, using explicit formulae (in quadratures), the author finds the absorption and scattering intensity of one- and bi-periodic gratings and mirrors, which may have random roughnesses. Examples of space and spectral power distributions for gratings and mirrors working in X-rays are compared with those derived using the usual indirect approach and well known approximations.