Modified Spherical Wave Functions With Anisotropy Ratio: Application to the Analysis of Scattering by Multilayered Anisotropic Shells

We describe a novel and rigorous vector eigenfunction expansion of electric-type Green's dyadics for radially multi- layered uniaxial anisotropic media in terms of the modified spherical vector wave functions, which can take into account the effects of anisotropy ratio systematically. In each layer, the material constitutions e and epsiv macrmu macr are tensors and distribution of sources is arbitrary. Both the unbounded and scattering dyadic Green's functions (DGFs) for rotationally uniaxial anisotropic media are derived in spherical coordinates (r, thetas, phi). The coefficients of scattering DGFs, based on the coupling recursive algorithm satisfied by the coefficient matrix, are derived and expressed in a compact form. With these DGFs obtained, the electromagnetic fields in each layer are straightforward once the current source is known. A specific model is proposed for the scattering and absorption characteristics of multilayered uniaxial anisotropic spheres, and some novel performance regarding anisotropy effects is revealed.

I. Introduction

The dyadic Green's functions (DGFs) technique [1]–[3] has been widely used to characterize electromagnetic wave propagation and to solve electromagnetic boundary value problems for the last decades. The dyadic Green's function serves as a kernel of the integral and has to be defined or formulated beforehand. However, with the complexity of media growing, the dyadic Green's function representations for media also become more complicated. In recent years, due to the advances in material science and technology which have manifested fabrication of various kinds of complex materials, considerable attention has been paid to the interaction of electromagnetic waves with anisotropic materials [4]–[6], bianisotropic media [7] and chirowaveguides [8].