An efficient method of moments for analysis of electromagnetic scattering from a multilayered arbitrary-shape anisotropic dielectric object

Abstract

This paper introduces an efficient method of moments (MoM) designed to explore electromagnetic scattering in multilayered anisotropic structures. Each layer is made up of a dielectric anisotropic material characterised by a generalised tensor for permittivity, which is unrestricted in its geometrical configuration. The authors’ approach analyses each layer independently, employing the surface equivalence theorem to substitute the interfaces between layers with suitable equivalent electric and magnetic surface current densities. The authors derive the necessary surface integral equations (SIEs) for each interface by implementing the proper boundary conditions. The analysis utilises rotated dyadic Green's functions that populate the infinite space with the material properties specific to each anisotropic layer. The rotation angle corresponds to the deviation between the local principal coordinate system of the material and the global coordinate system, which is determined by diagonalising the full dielectric tensor of the respective anisotropic material given in the global coordinate system. To address the SIEs for determining the unknown equivalent electric and magnetic surface current densities, Galerkin's MoM is applied. This involves expanding the unknown surface currents using suitable basis functions, simplifying the issue to a matrix equation solved through the inversion of a block-tridiagonal impedance matrix. The diagonal nature and sparse structure of the impedance matrix, along with an effective block-inversion method, significantly boost computational efficiency and reduce memory demands. To demonstrate the feasibility of the proposed method, the authors present a detailed derivation of the impedance matrix for the case of non-magnetic uniaxial anisotropic media for which the Green's functions are available in closed form. The validity and efficiency of the proposed SIE-MoM scheme are demonstrated by comparing the results of several case studies against those found in literature and results obtained via commercial numerical codes.