Coupling with field focusing between two dielectric resonator antennas

A dielectric antenna is a solid dielectric, of say pillbox shape, excited by an interior antenna, say, monopole. Coupling between two monopole antennas, in free space, is well known, with the amplitude of the mutual impedance decreasing monotonically with increasing monopole separations. Coupling between two dielectric resonator antennas, i.e. between two monopoles that are encased in dielectric pillboxes, still has basically decreasing mutual impedance amplitude but with significant ripples especially at small separations of the resonators. Such ripples are due to the focusing effects of the dielectric bodies. The ripples are significant in the design of antenna arrays with closely spaced dielectric resonators.