Beltrami fields within continuous source regions, volume integral equations, scattering algorithms and the extended Maxwell-Garnett model

Singularities of three- and quasi-two-dimensional frequency-domain Green's dyadics are used to derive expressions for a Beltrami field in its source region. The mathematical developments are utilized to set up three-dimensional volume integral equations and scattering algorithms for scattering by inhomogeneous bianisotropic scatterers embedded in a homogeneous biisotropic ambient medium. Application is also made towards the effective medium properties of a particulate composite formed by randomly dispersing bianisotropic particles in a biisotropic host medium.