Analysis of the radiation efficiency of a horizontal electric dipole on a grounded dielectric slab

The radiation efficiency of a horizontal infinitesimal electric dipole on a grounded dielectric slab as a function of its electrical thickness is investigated thoroughly. It is shown that, in contrast to a common belief, the efficiency does not decay monotonically with increasing electrical thickness (or, equivalently, with increasing frequency for a given slab), but oscillates in correlation with the onset of surface waves. Specifically, the efficiency maxima and minima are shown to occur at the cutoff frequencies of the TE and TM surface-wave modes, respectively (excluding the cutoff-less TM0 mode), using a spectral transmission line analysis in conjunction with a simple auxiliary dipole collocated with the source. From this auxiliary dipole, the efficiency maxima and minima are essentially explained in terms of equivalent PMC and PEC walls at the position of the source. To the best of our knowledge, this is the first complete explanation of the oscillatory behavior of the efficiency of a dipole on a grounded substrate. The finding has a fundamental implication for electrically thick planar antennas, which include most millimeter-wave antennas: such antennas may be specifically designed to exhibit their operation frequency at a local maximum of the efficiency even if the substrate is electrically very thick.