Efficient Calculation of the Electromagnetic Scattering by Lossless or Lossy, Prolate or Oblate Dielectric Spheroids

Abstract

In this paper, we study the electromagnetic scattering of a plane wave by a prolate or oblate dielectric spheroid, which can be lossless or lossy. The presented efficient solution is obtained by applying a perturbation technique to the problem of the sphere using the spherical eigenvectors. This method allows a closed-form solution for the fields and the scattering cross sections, which is valid for small eccentricities of the spheroid. Alternatively, we construct the exact solution of the problem using the separation of variables in terms of the spheroidal eigenvectors and updated spheroidal algorithms that allow complex arguments. We compare the closed-form solution versus the exact solution and we conclude about its accuracy. Both polarizations are studied and numerical results are given for various values of the parameters.

Fast Solution of the Electromagnetic Scattering by Composite Spheroidal–Spherical and Spherical–Spheroidal Configurations

“…T HE electromagnetic scattering by composite objects is useful in many applications, like radar engineering for the calculation of the scattering patterns due to dielectric coated metallic objects [1], [2], for the design of microwave dielectric resonators, used as microwave filters or for permittivity measurements [3], in spherical/spheroidal microstrip structures where a spherical or spheroidal dielectric substrate covers a metallic spherical or spheroidal core [4], for improving electromagnetic scattering techniques used to explain the operation of high-frequency components [5]- [8], or in the future validation of other numerical methods. Moreover, spheroidal-spherical configurations can be also used for approximating other less tractable 3-D particles.…”

“…The concept of the equiphase sphere was used by Chen et al in [24] to study dielectric spheroidal particles. Finally, Zouros et al in [8] applied a shape perturbation method on spherical eigenvectors to study prolate or oblate dielectric spheroids. Apart from the simple metallic or homogeneous dielectric structures, composite configurations were also studied.…”

Διάδοση Και Σκέδαση ΗΜ Κυμάτων Σε Ελλειπτικές Κυλινδρικές Και Σφαιροειδείς Διατάξεις

“…Many works examine the EM scattering from conducting or isotropic spheroids, employing a variety of approaches. In particular, methods based on the separation of variables in spheroidal coordinates have been extensively used [40,42,43,45,47]. These methods employ the spheroidal wave functions for the expansion of the fields and proceed to satisfy appropriate boundary conditions at the scatterer's surface, thus leading to an infinite system of linear non homogeneous equations for the unknown field expansion coefficients, that is solved by truncation.…”

“…These methods employ the spheroidal wave functions for the expansion of the fields and proceed to satisfy appropriate boundary conditions at the scatterer's surface, thus leading to an infinite system of linear non homogeneous equations for the unknown field expansion coefficients, that is solved by truncation. Another approach is the asymptotic technique employed in [42,68,69], where, for small values of its eccentricity, the spheroid is considered as a perturbation of the respective sphere and closed-form expressions can be extracted for the scattering cross sections. Also, general methods for the calculation of EM scattering from three-dimensional non spherical bodies may be used to simulate spheroidal shapes, including the integral equation method [54], the extended boundary condition method (EBCM) that leads to the computation of the so-called T-matrix [56], and the discrete-dipole approximation (DDA) [63].…”

“…All previous works employing spheroidal functions are limited to isotropic permittivities. Furthermore, we use a different expansion for the transmitted field-as compared to the one in [42] for isotropic spheroids-by introducing the irrotational spheroidal eigenvector into the formulation, and finally arrive at a new system of equations. To the writer's knowledge, the irrotational spheroidal eigenvector has not been used before in published works on the scattering from spheroids.…”