Radiation characteristics of a finite-length electric dipole in hyperbolic materials

The hyperbolic materials exist naturally and can also be fabricated artificially as an assembly of electrically thin parallel sheets or wires. These materials have an axis of symmetry and two permittitivity scalars to characterize the response of electric field in the directions along the symmetry axis and perpendicular to the symmetry axis. However, one of the permittivity scalar has a negative real part while the other a positive real part giving rise to hyperbolic dispersion curve. To understand the radiation characteristics of finite-sized elementary sources, we have derived the expressions of radiation by finite-length electric dipole in hyperbolic materials. The analytical results and radiation patterns are presented.