Elementary Radial Electric Dipole Excitation of Graphene Spherical Disk on Dielectric Sphere

We consider the antenna shaped as a spherical dielectric lens with a conformal graphene disk on its surface, fed with elementary source. The latter is a radial electric dipole placed on the lens rotation axis. The electrical properties of graphene are characterized with the aid of the Kubo formulas, which are based on the quantum-theory description. First, we cast the wave-scattering problem to the dual series equations for the field expansion in terms of the spherical harmonics. Then, using the static part analytical inversion with the aid of the Abel integral transform, we reduce the dual series equations to an infinite matrix equation of the Fredholm type with elements depending on the elementary functions. This procedure guarantees the convergence and enables us to accurately characterize the considered lens antenna performance, in particular, its radiation resistance and directivity, in the THz frequency range.