Spectrally-Accurate Analysis of EM Scattering by Material and Metamaterial, Isotropic or Anisotropic, Radially Inhomogeneous Spherical Objects

Abstract

We study electromagnetic (EM) plane wave scattering by material and metamaterial radially inhomogeneous spherical objects that are either isotropic or uniaxially anisotropic with radial anisotropy. Using field representations in terms of scalar Hertz potentials, we reformulate Maxwell’s equations into two systems of first-order ordinary differential equations, which we then convert into equivalent second-kind linear Volterra matrix integral equations. The discretization scheme uses a high-order, entire domain, Nystrom method that employs the Gauss–Legendre–Radau quadrature rule. The proposed algorithms have spectral convergence and apply to either single-layer or multilayer structures with continuous or sectionally continuous profiles.