Two-shell Circularly-layered Dielectric Lens Antennas: Design and Characterization A.V. Boriskin 1,2 , A. Vorobyov 3 , and R. Sauleau 3 1 Institute of Radiophysics and Electronics NASU, Kharkov, Ukraine 2 Université Européenne de Bretagne, Rennes, France a_boriskin@yahoo.com 3 Institut d’Electronique et de Télécommunications de Rennes, Université de Rennes 1, 35042 Rennes, France Abstract— The paper describes a procedure for designing two- shell circularly-layered dielectric lens antennas (DLA) with radiation characteristics compatible with conventional multi- layer uniformly-layered Luneburg lens (LL) antennas. It is demonstrated that a two-shell lens with the favorable collimating capabilities can be designed using standard low-permittivity materials provided the proper selection of shells thickness. Analysis is performed in the 2-D formulation using the exact Mie-type series approach. The outlined recommendations are then validated on the example of two-shell spherical DLAs excited by a horn antenna modelled using commercial software. I. INTRODUCTION Circularly-layered dielectric lenses remain in the focus of engineers attention for many years thanks to their good focusing/collimating properties and capability to share the aperture with multiple feeds. These features make them an attractive solution for various wireless applications, including communication systems [1, 2], radars [3-5], and even more exotic application such as invisible coatings [6]. Although classical design of a Luneburg lens (LL) assumes radial inhomogeneity [7], in most practical applications such lenses are fabricated as multi-shell structures, e.g. [8]. A critical aspect in the design of multi-shell LLs is a limited number of available low-loss dielectric materials whose permittivity belongs the range of 1 ~ 2 suggested by the ray- optics focusing rule [7]: ε(r) = 2 – (r/R) 2 or its discrete analogue for the uniformly-layered lens (t s = R M /M): ε s = 2 – ((s – 0.5) / M ) 2 , where indices s and M correspond to the s-th and M-th (outer) layers, respectively. There are well known ways to fabricate artificial materials with desired properties via milling holes or adding compounding materials. Nevertheless each of them increases complexity and cost of the technology especially for multi- shell designs. Therefore a favorable solution of low-cost spherical lenses is a double-shell design with layers made of the available low-loss dielectric materials, e.g. [2]. As demonstrated in [9], it is possible to design a non- uniform double-shell lens with characteristics compatible with a classical uniform multi-shell LL. Nevertheless the suggested design (a dense quartz-like inner core covered with a quarter- wavelength matching layer) has drawbacks critical for practical applications, namely: increased overall weight, difficulties with fabrication and further exploitation of a fragile matching layer, and finally involvement of the Whispering Gallery (WG) modes whose Q-factors (and thus impact on the antenna characteristics) grow exponentially with increase of the dielectric contrast between the layers [10]. R 1 E z t 2 R 2 x y ε 1 ε 2 δ CSP 0 Fig. 1. Geometry and notations of the problem. The lens is symmetric with respect to the x-axis. The inset illustrates the encoding scheme used for representation of the lens profile. Dielectric materials Permittivity (ε) Loss factor (tan δ) PUF (Polyurethane foam) 1.2 20 x 10 -4 PTFE (Teflon) 1.96 6 x 10 -4 PP (Polypropylene) 2.25 8 x 10 -4 Rexolite 2.53 5 x 10 -4 The paper describes a simple procedure for designing two- shell non-uniform dielectric lenses with good collimation properties. Special attention is dedicated to possibilities of designing such lenses made of standard low-loss dielectric materials (Table I). The analysis is carried out in the two- dimensional (2-D) formulation using in-house software based on the exact Mie-type series (MS) solution [10]. The software is capable of ultimately fast and accurate characterization of multi-shell lenses focusing and collimating capabilities with full account of resonant features and effects related to the directive nature of the primary feed. Here, the feed is simulated by a complex-source point (CSP) beam [12, 13]. In particular, MS-based software enabled us to accurately describe the impact of WG modes that is a bottle-neck for TABLE I DIELECTRIC MATERIAL CONSIDERED AS SUITABLE CANDIDATES FOR DESIGN OF A DOUBLE-SHELL SPHERICAL LENS [11] 28 -30 September 2010, Paris, France Proceedings of the 40th European Microwave Conference 978-2-87487-016-3  2010 EuMA 743