On the eigenfunction expansion of electromagnetic dyadic Green's functions

A relatively simple approach is described for developing the complete eigenfunction expansion of time-harmonic electric (Ē) and magnetic (H̄) fields within exterior or interior regions containing an arbitrarily oriented electric current point source. In particular, these results yield directly the complete eigenfunction expansion of the electric and magnetic dyadic Green's functions̄ₑand̄ₘthat are associated withĒandH̄, respectively. This expansion of̄ₑand̄ₘcontains only the solenoidal type eigenfunctions. In addition, the expansion of̄ₑalso contains an explicit dyadic delta function term which is required for making that expansion complete at the source point. The explicit dyadic delta function term in̄ₑis found readily from a simple condition governing the behavior of the eigenfunction expansion at the source point, provided one views that condition in the light of distribution theory. These general expressions for the eigenfunction expansion of̄ₑand̄ₘreduce properly to those obtained previously for special geometries by Tai.