Theoretical investigation of cylindrical dielectric-rod antennas

Present-day theory of uniform cylindrical dielectric-rod antennas rests on the three theoretical treatments of Horton, Bouix and Fradin (leaky-guide theory), and on Brown´s end-fire theory. A digression on the general relationship between Schelkunoff´s equivalence principle and the vector Kirchhoff formula reveals that these radiation formulas may only be applied to regions in which the vector potentials are known to satisfy the inhomogeneous wave equation. On applying this axiom to the theories, all but Brown´s are shown to be fallacious. A detailed application of the vector Kirchhoff formula to uniform cylindrical dielectric rods supporting the HE11 mode produces an expression for the far-field radiation pattern, which, when computed, gives good agreement with existing experimental data. The analysis allows for dielectric losses and can also be extended to nonuniform dielectric antennas with gradual tapers. Fresnel interaction of the apertures and lens effects are considered. Finally, some design recommendations for dielectric rod antennas are made.