Abstract

Diffracting and focusing elements become more and more popular in soft and hard X-ray spectral domain in view of achieving studies of spectroscopy, luminescence, photoemission, microscopy, etc … Concerning diffraction elements, i.e. gratings, two main types have to be distinguished. The first type consists of bare metallic gratings, usually gold or platinum coated, which cover a wide range of wavelength, from 6 A° to 1000 A°, and are classical gratings used under grazing incidence. As "classical gratings" with finite conductivity, their theory was already published [1, 2] at the beginning of the 1970's. However, due to the high number of propagating orders resulting from wavelength-to-groove-spacing ratio (λ/d) less than 1/100 or even 1/1000, the use of the Integral Theory was precluded in this spectral domain, at least with the computers available at that time. It is only in 1979 that we recognized [3] that due to the specificities of X-ray gratings, namely low groove-depth-to-groove spacing ratios (h/d) plus refractive indices close to unity, the coupling between the eigenmodes or diffracted orders was weak enough so that it was possible to get accurate results with the Differential Theory by truncating the Fourier series of the field to an order much less than the number of propagating orders. This discovery opened the X-ray domain to the use of electromagnetic theory of gratings, and since that time, the Differential Theory was used to study and optimize many X-ray gratings for Synchrotron Radiation Instrumentation and important space missions [4-5]. A computer software was recently developed in order to determine a given number of grating parameters (e.g. groove depth, incidence, groove spacing …) in order to optimize a desired efficiency in TE, TM polarization or natural light for a specified used. Spectacular agreement was found between theoretical predictions and measurements so that the diffraction of X-rays by a metallic grating can be considered as a well resolved problem. The modal method [6] developed in the mean time and used by several authors led to identical results with comparable computation time.

© 1996 Optical Society of America