Transient Lenses for Transmission Systems and Antennas

Abstract

In the design of waveguide transitions we desire to transmit a TEM wave, ideally with no reflection or distortion, from one transmission line to another. Such waveguide transition regions are usually referred to as EM lenses or more specifically, transient lenses. This goal is accomplished by specifying the lens geometry and constitutive parameters (i.e., the shape and medium of the EM lens). The physical properties of these lenses, given by the permeability μ and the permittivity ∈, may be a function of position, but we assume that these properties are frequency independent. The conductivity of the medium is taken to be zero, and cross sectional dimensions are large compared to the wavelengths at the high frequencies of interest. This is in contrast to a lens such as the Luneburg lens or Maxwell fish eye lens, both of which are based on a geometric optics approximation. The need for a low dispersion system also argues for TEM guiding structures. Since we may also wish to change the direction of propagation of a wave being transmitted from one region to another, we must also allow for distortion introduced at bends. While in many cases we can obtain exact solutions to the lens design problem, approximations are generally involved in the practical realizations of most EM lenses. For example, one may have to cut off lenses that are theoretically infinite in extent. Moreover, frequency independence may not be realized exactly. The exact solutions to design problems are usually obtained by one of two basic approaches [1], The first method is a differential-geometric approach, while the second method is a differential-impedance-matching and transit-time-conservation approach.