Radiation patterns of interfacial dipole antennas

The radiation pattern of an infinitesimal electric dipole is calculated for the case where the dipole is vertically located on the plane interface of two dielectric half spaces and for the case where the dipole is lying horizontally along the interface. For the vertical case, it is found that the radiation pattern has nulls at the interface and along the dipole axis. For the horizontal case, it is found that the pattern has a null at the interface; that the pattern in the upper half space, whose index of refraction is taken to be less than that of the lower half space, has a single lobe whose maximum is normal to the interface; and that in the lower half space, in the plane normal to the interface and containing the dipole, the pattern has three lobes, whereas in the plane normal to the interface and normally bisecting the dipole, the pattern has two maxima located symmetrically about a minimum. Interpretation of these results in terms of the Cerenkov effect is given.