Application of the boundary integral equation method to very small wavelength-to-period diffraction problems

Abstract

Diffraction from 1D multilayer gratings having arbitrary border profiles including edges is considered for small wavelength-to-period (λ/d) ratios, the most difficult case for any rigorous numerical method. The boundary integral equation theory is so flexible that we can indicate a few areas where it can be modified. In this work, special attention is paid to the main aspects of the Modified Boundary Integral Equation Method for λ/d ≪ 1 as well as to a more general treatment of the energy conservation law applicable to multilayer absorption gratings. Three types of small λ/d problems are known from optical applications: (a) shallow gratings working in the X-ray and extreme ultraviolet ranges, both at near-normal and grazing angles, (b) deep echelle gratings with a steep working facet illuminated along its normal by light of any wavelength, and (c) rough mirrors and gratings in which rough boundaries can be represented by a large-d grating, and which contain a number of random asperities illuminated at any angle and wavelength. Numerical examples of diverse in-plane diffraction problems are presented.