Radiation of hertzian dipoles embedded in planarly layered biaxial media

Twork presented in this paper concerns the determination of far field radiation patterns of arbitrarily oriented Hertzian dipoles. The sources exist within an arbitrarily oriented biaxial layer of a multi-layer planar structure whose layer boundaries are aligned with Cartesian coordinates. In order to evaluate the electric field, dyadic Green's functions for the geometries under consideration are derived in the spectral domain. The dyads constituting the Green's function are based on the natural eigenvector solutions of the medium. These eigenvectors can be developed both mathematically and via geometric considerations. Using the dyadic Green's functions and linear operator theory, integral equations for the electric field in the isotropic region are derived. Finally, asymptotic methods are applied in order to develop closed form solutions for the radiation fields.