The Forward-Scattering Theorem Applied to the Scattering Dyadic

From the forward-scattering theorem we have relations between the absorption and scattering cross sections, and the forward scattering. The scattered fields are represented by a scattering dyadic times the incident plane wave. This allows one to reformulate the results in terms of the scattering dyadic, exhibiting some general characteristics of this dyadic. This is extended (for lossless scatterers) by analytic continuation away from the $j \omega$ axis out into the complex $s$ plane and applied to poles in the singularity expansion method.