X-ray quasi-lamellar etched multilayers: analysis by coupled-mode theory

Abstract

An etched multilayer (EM) is a two-dimensional structure obtained by etching a periodic multilayer following the profile of a grating. Generally a laminar grating shape, i.e. with a rectangular shape, is desired. However, we observe that different EM give different diffraction efficiency curves. We implement the coupled-mode theory to calculate the diffraction pattern of the EM as a function of the shape of the etching profile. Thus, we try to correlate the variability of the experimental reflectivity curves to various shapes of the profiles, rectangular and trapezoidal, and the corresponding simulated reflectivity curves.Keywords: X-ray mirrors, Multilayers, Gratings, Reflectivity, Coupled-mode theory Highlights: Coupled-mode theory is used to calculate the diffraction pattern of the etched multilayers and then compared to experiments. Reflectivity measurements show different curve shapes depending on the sample preparation. This is explained by the various shapes of the etching profile and partially confirmed by the calculations.2

Design, development and applications of etched multilayers for soft X-ray spectroscopy

“…Recently, the coupled-mode theory was implemented to calculate the diffraction pattern of the EM as a function of the shape (rectangular or trapezoidal) of the etching profile for different values of Γ [20]: these calculations show that (i) the secondary peaks observed in Figure 4 originate from the coupling of the 1st order of diffraction by the multilayer with the orders of diffraction by the grating (ii) the relative intensity of the secondary peaks depends on the shape of the lines of the grating. The limited gain in bandwidth (∼1.5) in the B K region can be improved by diminishing the period D of the grating (the grating diffraction orders would then be better separated from the 1st multilayer diffraction order [21]) and by a better control of the rectangular patterning of the grating lines.…”

“…3.2) has shown that unfortunately, although optimized for the B K domain, the structure does not allow a significant reduction of the width of the Bragg peak in that region due to the coupling of the 1st order of diffraction by the multilayer with the orders of diffraction by the grating [20]. On the other hand, in the C K range, despite a low reflectance (0.65 %), the gain in spectral resolution is valuable.…”