On singularities of dyadic green functions and long-wavelength scattering

An expression for the singularity (or near-field) structure of the dyadic Green function (of the electric type) of an anisotropic dielectric medium is presented by using an operational procedure. The permittivity dyadic of the dielectric medium is assumed to be real symmetric biaxial that makes the result applicable to a wide variety of substances and materials which are, in one form or another, of interest in electromagnetic field problems. Subsequently we use the obtained delta-function singularity of the dyadic Green function as a key ingredient to obtain the effective properties of a discrete random composite made of spherical inclusions dispersed in an anisotropic host medium. By employing the long-wavelength scattering approximation we are able to establish Maxwell Garnett estimates of the effective constitutive dyadics of such a composite, which in our case is an essemble of small bianisotropic spheres embedded in a general dielectric host medium.