Zhuang, Y.; Huang, Q.; Kozhevnikov, I.V.; Feng, J.; Qi, R.; Sokolov, A.; Senf, F.; Zhang, Z.; Wang, Z.: Theoretical analysis and development of high efficiency tender x-ray multilayer coated gratings. In: Oleg Chubar, Kawal Sawhney [Ed.] : Advances in Computational Methods for X-Ray Optics V. Bellingham, WA: SPIE, 2020 (Proceedings of SPIE ; 11493). - ISBN 978-1-5106-3793-1, p. 114930R/1-10
10.1117/12.2567578

Abstract:
The low efficiency of conventional single layer gratings at the tender X-ray region (E=1~5 keV) significantly limits the photon flux of the beamline and the development of related imaging and spectroscopy experiments in this region. To overcome this issue, multilayer coated gratings have been proposed and developed. The diffraction behavior of a multilayer grating is more complex than a single layer grating. To understand the diffraction behavior and exert the maximum potential of this new optics, we have built an analytical theory based on coupled wave theory. A high efficiency single order diffraction regime was first identified which means only one diffraction order will be excited with a certain incidence angle and structure parameters. This is applicable to blazed multilayer gratings (BMGs). To achieve maximum efficiency, the optimum grating and multilayer structures were analyzed. The highest theoretical efficiency of a BMG can reach the same value of the coated multilayer reflectance. Moreover, blazed multilayer gratings exhibit the advantage of high harmonics suppression. For the BMG, the conventional condition of maximal diffraction efficiency, Dsinα = nd, where D and d is the grating period and multilayer period, respectively, α is blaze angle, n is diffraction order, has been proved invalid. This is due to the contribution of anti-blaze facets to diffraction and effect of strongly asymmetric diffraction. Based on these, a Cr/C BMG was fabricated in collaboration with the Department for Nanometer Optics and Technology in BESSY-II. Maximum efficiency of up to 60% was demonstrated at 3 keV which is close to the theoretical prediction.