Fast and numerically stable Mie solution of EM near field and absorption for stratified spheres

• Published in: Compel 2022-05, Vol.41 (3), p.1011-1023
• Main Authors: Csernyava, Olivér, Horváth, Bálint Péter, Badics, Zsolt, Bilicz, Sándor
• Format: Article
• Language: English
• Subjects: Algorithms; Approximation; Bones; Finite element method; Head; Iterative methods; Linear polarization; Mathematical models; Millimeter waves; Plane waves; Spheres; Spherical waves; Wave scattering
• ISSN: 0332-1649; 2054-5606
• DOI: 10.1108/COMPEL-03-2021-0081

Purpose The purpose of this paper is the development of an analytic computational model for electromagnetic (EM) wave scattering from spherical objects. The main application field is the modeling of electrically large objects, where the standard numerical techniques require huge computational resources. An example is full-wave modeling of the human head in the millimeter-wave regime. Hence, an approximate model or analytical approach is used. Design/methodology/approach The Mie–Debye theorem is used for calculating the EM scattering from a layered dielectric sphere. The evaluation of the analytical expressions involved in the infinite sum has several numerical instabilities, which makes the precise calculation a challenge. The model is validated through an application example with comparing results to numerical calculations (finite element method). The human head model is used with the approximation of a two-layer sphere, where the brain tissues and the cranial bones are represented by homogeneous materials. Findings A significant improvement is introduced for the stable calculation of the Mie coefficients of a core–shell stratified sphere illuminated by a linearly polarized EM plane wave. Using this technique, a semi-analytical expression is derived for the power loss in the sphere resulting in quick and accurate calculations. Originality/value Two methods are introduced in this work with the main objective of estimating the final precision of the results. This is an important aspect for potentially unstable calculations, and the existing implementations have not included this feature so far.