Two modes of wave propagation manifested in vertical electric dipole radiation over a sphere

The radiation of a vertical electric dipole over an electrically homogeneous sphere is considered anew, starting with a novel mathematical formulation. Both the dipole and the point of observation are assumed to lie on the spherical interface. The analysis is valid for a sphere whose radius is much larger than the wavelength in the outside region. Contributions to the value of the fields come, on the one hand, from the waves that propagate along the interface and, on the other hand, from the waves that propagate through the sphere by successive reflections.