Integral Equations for 3-D Scattering: Finite Strip on a Substrate

Abstract

Abstract-Singular integral equations that determine the exact fields scattered by a dielectric or conducting finite strip on a substrate are presented. The computation of the image of such a scatterer from these fields by Fourier optics methods is also shown.

Electromagnetic scattering by a finite strip on a substrate

“…A microscope image is then constructed from the fields in V 1 at a plane above the scatterer using equations from Fourier optics [6]. Far fields that are restricted to a given collection numerical aperture focused at a plane near the substrate determine the image.…”

“…If this simpler approach no longer gives accurate results, we have to consider scattering of monochromatic plane waves of circular frequency ω by finite strips, which requires the solution of the three-dimensional Maxwell equations [2]. We use a generalization of the single-integral-equation formulation [3] that reduces the number of unknowns on the interfaces in three-dimensional problems such as a particle in a layer [4], a doublet of spheres [5], and a finite strip on a substrate [6], where we show the integral equations for the unknown tangential vector fields on the boundaries and the simulation of image formation. Here we show details of the scattering by a finite strip, such as the parameters defining the configuration of an oblique strip, the handling of the surface divergence term, and the reduction to algebraic equations, including self-patch contributions [7].…”