High-frequency analysis of the surface induced currents on elliptical dielectric lens antennas

Dielectric elliptical lens antennas are often used in millimeter and sub-millimeter wave applications as a valid alternative to parabolic reflectors, in order to obtain high directivity with integrated technology. A method which consists of integrating the physical optics (PO) equivalent currents on the lens surface, although accurate enough for the prediction of the input impedance perturbation, does not provide a good estimation of the far field pattern far from the boresight. This may attributed to the additional radiation mechanism produced by the lateral wave excited at the dielectric-air interface, in the vicinity of the critical angle of incidence. This critical angle occurs for those rays that impinge on the lens surface at the perimeter of the maximum section. In the vicinity of this region, the geometrical optics (GO) approximation for the determination of the equivalent currents, (i.e., the PO approximation) fails due to proximity of the excitation condition of the lateral wave, that produces a transition field. In this paper, this transition field is considered by a proper uniform asymptotic evaluation of the field pertaining to the infinite dielectric half-space which locally matches the lens considering surface.