High-resolution, high-reflectivity operation of lamellar multilayer amplitude gratings: identification of the single-order regime

Abstract

High resolution while maintaining high peak reflectivities can be achieved for Lamellar Multilayer Amplitude Gratings (LMAG) in the soft-x-ray (SXR) region. Using the coupled waves approach (CWA), it is derived that for small lamellar widths only the zeroth diffraction order needs to be considered for LMAG performance calculations, referred to as the single-order regime. In this regime, LMAG performance can be calculated by assuming a conventional multilayer mirror with decreased density, which significantly simplifies the calculations. Novel analytic criteria for the design of LMAGs are derived from the CWA and it is shown, for the first time, that the resolution of an LMAG operating in the single-order regime is not limited by absorption as in conventional multilayer mirrors. It is also shown that the peak reflectivity of an LMAG can then still be as high as that of a conventional multilayer mirror (MM). The performance of LMAGs operating in the single-order regime are thus only limited by technological factors.

Spectral tailoring of nanoscale EUV and soft x-ray multilayer optics

“…143,144 Kozhevnikov et al then identified the single-order operating regime for the multilayer grating. 146,147 In this scheme, only one diffraction order will be excited and the reflected power is concentrated in this single order, if the angular width of the zeroth or higher order peak is much smaller than the angular distance between the adjacent orders. Thus, an SLMG can achieve the same maximum reflectance as a standard multilayer mirror, while the bandwidth is reduced by a factor of C, with C being the lamella-to-period ratio of the grating, assuming that the number of bilayers is increased by a factor 1/C.…”

Design of a multilayer-based collimated plane-grating monochromator for tender X-ray range

“…The simulations of the single-layer blazed gratings and plane mirrors are carried out with REFLEC software (Schafers & Krumrey, 1996), and the reflectivities of the multilayers are calculated using the IMD program (Windt, 1998). The calculations for BMGs are based on a rigorous coupled wave approach well suited for analysis of SXR multilayer gratings of various types with different shape of grating grooves (Kozhevnikov et al, 2010;Yang et al, 2015;van der Meer et al, 2013). The simplest model of the BMG is considered in the present paper, assuming 90 anti-blaze angle and neglecting the effects of both interfacial roughness and corrugations of interfaces above the anti-blazed facets.…”

Analysis by Coupled-Mode Theory of X-ray Multilayer Gratings

“…In this operating regime, the incident plane wave only excites one single grating order [7]. Let us assume this order to be the zero th one; this case corresponds to the specular reflection of interest in the application of the narrow bandwidth monochromator.…”

“…The multilayer gratings (MGs), consisting of a periodic stack of bilayers with nanometric thickness laterally etched according to a periodic pattern, belong to this class of 2D photonic crystals that has opened up new ways for x-ray optics. Thus lamellar multilayer gratings (LMGs) can be used as efficient polychromators [1] and can also be implemented as improved monochromators with respect to mere multilayer Bragg mirrors for the soft-x-ray domain [2][3][4][5][6][7][8].…”