Electromagnetic field representations and computations in complex structures II: Alternative Green's functions

In this second paper of the three-part sequence, we deal with alternative Green's function (GF) representations for the subdomain (SD) problem in the complexity architecture of Part I. The relevant GFs for systematic analytic modelling are those associated with at least partially vector and co-ordinate separable boundary conditions. Such 'canonical' GFs, when 'matched' to a real problem, can form background kernels which simplify the numerical complexity of real-problem exact integral equations. The analytic machinery involves Sturm-Liouville (SL) theory for the reduced one-dimensional (1D) spectral GF problems resulting from separation of variables in various co-ordinates, set in its most general form in the complex spectral wavenumber domain. Spectral synthesis in the complex spectral wavenumber planes for 2D and 3D co-ordinate-separable full GFs lays the foundation for direct construction (via contour deformations, branch point, and pole residue evaluations) of alternative field representations, and their correspondingly different wave-physical phenomenologies. Illustrative examples show the connection between the canonical GFs and their network representations.