The performance impact of material loss, unit cell anisotropy, and macro scale permittivity quantization in additively manufactured Luneburg lens antennas
Date
2022
Authors
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Publisher
University of Delaware
Abstract
Used as a focusing objective, the Luneburg lens in combination with a suitable array of antenna feeds, produces a steerable and highly directional radiation pattern. Other factors being equal, a square phased array with its sides equal in length to the diameter of a spherical Luneburg lens, will have the same radiation pattern as the lens-based system. Whereas the lens boresight is adjustable in discrete angular steps, the adjustment for the phased array is nearly continuous. In circumstances where the beam overlap of the lens antenna is sufficient to avoid appreciable dropout, the system design is greatly simplified by opting for the lens-based approach. Because of this, there is a surge of interest by researchers in applying the Luneburg lens for mobile communications, satellite communications, and onboard automotive radar. Furthermore, since the invention of additive manufacturing, the spatially varying permittivity distribution of the Luneburg lens can be fabricated with single piece construction and with high precision. The research proposed herein, addresses fundamental material and design decisions that impact performance of an additively manufactured Luneburg lens, and which have not been reported on previously. Moreover, it uses effective media theory and finite element analysis to study these effects. ☐ Firstly, although previous studies have certainly demonstrated the ability to additively manufacture graded index lenses of a variety of sorts, this research is the first to systematically demonstrate how the choice of material and unit cell architecture influences the overall loss within the Luneburg lens, and thus the overall gain. Secondly, additively manufactured graded index lenses, such as the Luneburg lens, often result in some degree of uniaxial anisotropy in the effective permittivity distribution. Although, this anisotropy has been recognized previously, this research is the first to demonstrate the impact. Finally, the research examines the effect of quantizing the lens permittivity distribution into electrically large and otherwise square blocks except at the lens surface, such that each block is comprised of many identical unit cells. The resulting rectilinear grouping of unit cells is advantageous in the sense it can reduce overall print time. Thus, establishing the tradeoff in performance between a lens with this type of spatial quantization and that of an ideal Luneburg lens, is of practical importance. The research concludes by comparing the block quantized lens with concentric stepped designs that divide the lens into a series of discrete concentric shells.
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Keywords
Additive manufacturing, Anisotropic lens, Dielectric loss, Effective medium theory, Lens antenna, Luneburg lens