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

I.V Kozhevnikov,R Van Der Meer,K.-J Boller,H.M.J Bastiaens,F Bijkerk

doi:10.1364/oe.18.016234

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.

Highlights

Multilayer mirrors (MM) are widely used as dispersive elements in the soft-x-ray (SXR) region
Using the coupled waves approach (CWA) presented in this paper, we derive that for small lamellar widths, Lamellar Multilayer Amplitude Gratings (LMAG) operates in a single-order regime in which there is no significant overlap of the zeroth order diffraction efficiency with higher orders
Using our coupled waves approach (CWA), we have identified a high-resolution, highreflectivity single-order operating regime for Lamellar Multilayer Amplitude Gratings (LMAG) for the soft-x-ray (SXR) region

Summary

Introduction

Multilayer mirrors (MM) are widely used as dispersive elements in the soft-x-ray (SXR) region. For the design of LMAGs with enhanced performance, in terms of resolution and reflectivity, adequate theory for the modeling of the diffraction of the incident SXR beam is required. Its mathematical formulation is based on a general expansion of the field reflected from the LMAG, in terms of the waves diffracted into different orders, and is very understandable from the physical point of view This CWA allows the implementation of arbitrary lamellar shapes, arbitrary depth distributions of the dielectric permittivity in the multilayer structure. Using the CWA presented in this paper, we derive that for small lamellar widths, LMAGs operates in a single-order regime in which there is no significant overlap of the zeroth order diffraction efficiency with higher orders.

Basic equations of the coupled waves approach

Calculation of LMAG diffraction efficiency

LMAG single-order operating regime

Findings

Conclusions