Abstract
A volume integral equation known as Fredholm Integral Equation (FIE) approach for solving plane electromagnetic (EM) waves scattering by small dielectric particles is presented. In this paper we adapted FIE method published in previous work by (A.R. Holt, N.K. Uzunoglu and B.G. Evans, IEEE Trans., 26, 706–712, 1978) to solve scattering of plane EM waves by homogeneous dielectric ellipsoidal scatterers. In contrast to previous work, the basis of numerical integration are not represented as an expansion in a set of polynomials (Gegenbauer polynomial) but as a direct spatial integration. We assume discretization of the scattering particle into grid or cell points of unit cube in a regular lattice field. The homogeneous dielectric scatterer is modelled by assuming general ellipsoid equation centred at the origin of the regular lattice field which aligns with the Cartesian coordinate system axes. The first and second Born approximation terms are evaluated for a cell in the regular lattice field, while the contributions for all other cells weighted according to content are evaluated efficiently applying Fourier Shift Theorem.
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