Abstract
The design of spatially varying lens antennas based on artificial materials is of high interest for their wide range of applicability. In this paper, we propose a novel design procedure relying on an inverse formulation of the scattering matrix method (SMM). Differently from many adopted approaches, which resort to global optimizations or homogenization procedures, the inverse SMM (I-SMM) allows the synthesis of optimal parameters (geometrical and/or electromagnetic) for the inclusions realizing the overall device in a very effective manner. With reference to the 2D TM case, the proposed tool has been successfully assessed through the synthesis of different kinds of lenses radiating a pencil beam.
Highlights
Lens antennas whose electromagnetic characteristics vary in space deserve a high interest in the literature because of their potential application to different purposes, starting from the enhancement of antenna performance, to imaging or automotive radar applications [1]
The radially varying dielectric permittivity allows the conversion of a plane wave into a spherical wave (Luneburg and Half Maxwell Fish Eye), and vice-versa, while in the case of the Luneburg lens, their circular symmetry allows the radiation properties to obey a rigid steering of the field in the case of an angular variation of the primary source
But not least, it has been shown that the adoption of a proper representation basis for the unknown, allowing for the direct synthesis of an artificial-materials-based lens, is able to overcome results based on the search of a smoothly varying profile followed by homogenization procedures. We propose in this contribution a design strategy based on a different tool; that is, the scattering matrix method (SMM) [28]
Summary
Lens antennas whose electromagnetic characteristics vary in space deserve a high interest in the literature because of their potential application to different purposes, starting from the enhancement of antenna performance, to imaging or automotive radar applications [1]. Since the permittivity function is represented by an analytical expression arising from the solution of the Maxwell’s equations, both the Luneburg lens and the Maxwell Fish Eye lens can be considered canonical lenses operating in a strictly given fashion, i.e., with assigned and well-defined properties on the radiated patterns. A possibility to manage the lens permittivity distribution to achieve desired radiation characteristics has been offered by the inverse scattering problem (ISP) framework [20,21,22,23]. We turn the SMM into a design tool for artificial-materials-based lenses, i.e., we adopt the SMM formulation to retrieve the electromagnetic properties of the constituent small inclusions allowing for the best fitting of the assigned (total) field (or power pattern) specifications.
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