Modified spherical wave functions with anisotropy ratio: Application of the analysis of scattering by multilayered anisotropic shells

Abstract—We describe a novel and rigorous vector eigenfunc-tion expansion of electric-type Green’s dyadics for radially multi-layered uniaxial anisotropic media in terms of the modified spher-ical vector wave functions, which can take into account the effects of anisotropy ratio systematically. In each layer, the material con-stitutions and are tensors and distribution of sources is arbi-trary. Both the unbounded and scattering dyadic Green’s func-tions (DGFs) for rotationally uniaxial anisotropic media are de-rived in spherical coordinates (). The coefficients of scat-tering 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 spe-cific model is proposed for the scattering and absorption character-istics of multilayered uniaxial anisotropic spheres, and some novel performance regarding anisotropy effects is revealed. Index Terms—Anisotropic ratio, dyadic Green’s functions (DGFs), modified spherical wave functions, radially multilayered structures, recurrence matrix, scattering and absorption, vector eigenfunction expansion. I