EM Field Induced in Inhomogeneous Dielectric Spheres by External Sources

Scalar Equations for Scattering by Rotationally Symmetric Radially Inhomogeneous Anisotropic Sphere

“…Using the scalar integral equation formulation [26], and expanding the unknown function in Dini or Neumann series the problem can be transformed to an algebraic one. Alternatively the vector Dini series method [21,22] can, also, be applied.…”

“…An EM field of arbitrary direction is imposed. The method that has been developed for inhomogeneous dielectric spheres [21], can be easily extended to the present case. Using the expansions for the field inside the sphere (r ≤ α)…”

“…where the various symbols have been defined in [21], we derive again the following equations, as in [21], which are repeated here for convenience…”

“…When the medium is isotropic but inhomogeneous a handy method based on a volume integral equation has been developed [21,22]. In this method the unknown function is expanded in a vector Dini series, which allows direct calculation of the resulting integrals containing the Green function.…”

Unified Derivation of the Translational Addition Theorems for the Spherical Scalar and Vector Wave Functions

“…Addition theorems are needed when it is necessary to expand fields in more than one system of co-ordinates. This happens, for example, in the case of multiple scattering from a collection of spheres [1], in evaluation of a field in spheres due to external sources [2] and in antenna measurements [3]. More recently, there has been a renewed interest in the addition theorems because of their important role in fast multipole methods [4][5][6][7].…”