Electromagnetic waves scattering by dielectric ellipsoids applying integral equation approach

Summary form only given: 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. Preliminary results indicate similar agreement is observed with what was previously achieved by implementing Mie theory and other established numerical algorithms for homogeneous spherical or ellipsoidal dielectric scatterers. The strength of our model is that the main integration and equations solved are in the spatial frequency domain. As a result, the angular scattering pattern is strongly connected to the Spatial Fourier Transform of the scatterer; hence, for electrically small particles the angular spectrum is relatively smooth, the number of pivots required (in k-space) and complexity of the linear equations solved are relatively low as evident.