Self consistent Green's function formalism for acoustic and light scattering, Part 2: Dyadic notation

A self consistent dyadic Green's function formalism in spherical coordinates, related to the vector wave equation, is presented. As already discussed in a previous paper (Part 1, this issue page 254-269) dealing with the scalar Helmholtz equation there are four essential quantities. These are the dyadic volume Green's function, the dyadic surface Green's function, the dyadic free-space Green's function and the dyadic interaction operator. Huygens' principle expressed in terms of these quantities serves as a starting point. From this, we obtain Lippmann-Schwinger equations for the dyadic volume Green's function and the interaction operator as well as appropriate series expansions for both the dyadic volume and surface Green's functions. These quantities can then be used to solve electromagnetic scattering and radiation problems in the presence of nonspherical obstacles, such as light scattering. The developed formalism provides a common mathematical basis for a variety of different numerical approaches developed so far.