Goray Leonid
Alferov University, 8/3 Let. A Khlopin St., St Petersburg 194021, Russia.
J Synchrotron Radiat. 2021 Jan 1;28(Pt 1):196-206. doi: 10.1107/S160057752001440X.
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.
共振非弹性X射线散射以及从硬X射线到极紫外波段的其他光谱学研究取得了令人瞩目的成果，这就需要开发精确的工具，用以模拟适用于明亮相干X射线源、空间科学以及等离子体和超导物理学的先进光学仪器的能量特性。对于短波长范围（即实际的光栅、波带片和镜子，包括多层镀膜的）内结构化界面的吸收和散射强度进行精确计算，现有方法和代码尚未广泛涉及，这是由于一些限制因素，主要是在处理非常小的波长与周期（或相关长度）比时存在难题，以及难以考虑随机粗糙度统计。在这项工作中，吸收积分和散射因子是基于边界积分方程和蒙特卡罗方法，从矢量亥姆霍兹方程的严格解中推导出来的。然后，作者利用显式公式（以积分形式）求出了可能具有随机粗糙度的单周期和双周期光栅及镜子的吸收和散射强度。将X射线波段工作的光栅和镜子的空间和光谱功率分布示例，与采用常规间接方法和熟知近似方法得出的结果进行了比较。
