Dyadic Green's Function Expansions in Spherical Coordinates

The complete eigenfunction expansion of the electric field dyadic Green's function in spherical coordinates is presented with particular attention given to the significance of the longitudinal eigenfunctions in this expansion. It is shown that the spectrum of the transverse eigenfunctions contribute zero frequency static like modes that cancel the longitudinal modes outside the source region. Inside the source region the cancellation is not complete but the non-cancelling part can be expressed as a delta function contribution in full agreement with the results obtained by Tai by a different method. Various representations for the dyadic Green's function in free space and in a spherical cavity are presented. The paper includes a brief historical survey of the development of the eigenfunction expansion method for the dyadic Green's function in order to highlight some of the early difficulties that were encountered.