IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 10, 2011 37 Axisymmetric Resonant Lens Antenna With Improved Directivity in Ka-Band Anthony Rolland, Mauro Ettorre, Artem V. Boriskin, Member, IEEE, Laurent Le Coq, Member, IEEE, and Ronan Sauleau, Senior Member, IEEE Abstract—A compact-size shaped dielectric lens antenna (DLA) is designed and optimized in Ka-band (29.5 GHz) using a new syn- thesis tool based on the combination of a genetic algorithm and BoR-FDTD solver. The antenna is fabricated in Rexolite and fed by a circular waveguide with a flange and an optimized integrated dielectric taper. As demonstrated, the proposed antenna combines features intrinsic to lens, resonant, and reflector antennas. The at- tractive performance of the antenna (in terms of directivity and sidelobe level) is demonstrated numerically and experimentally by comparison to a conventional extended hemispherical DLA. Index Terms—Dielectric lens antenna (DLA), electromagnetic optimization, finite-difference time-domain technique for bodies of revolution (BoR-FDTD), shaped lens. I. INTRODUCTION D IELECTRIC lens antennas (DLAs) are very attractive at millimeter waves and have already been studied for a number of applications, e.g., [1]–[5]. In most cases, the lens shapes are either defined analytically (e.g., [3]) or synthesized numerically using advanced surface optimization algorithms [2], [6], [7]. To reach the desired specifications in radiation, reliable and robust analysis tools must be implemented since the use of the most popular lens design method—the so-called geometrical optics/physical optics technique (e.g., [2] and [6])—may lead to nonaccurate and noncontrollable results, especially when dealing with small-size lenses [8]. To overcome these limitations, full-wave formulations have been recently developed to analyze and op- timize (using genetic algorithms) the performance of dielectric lens antennas. They are mainly based on the Muller boundary integral equations [9] and the finite-difference time-domain technique for bodies of revolution (BoR-FDTD) [10]–[12]. The former has been applied only for 2-D problems, whereas the latter perfectly suits optimization of axisymmetric 3-D devices. Manuscript received December 06, 2010; accepted January 15, 2011. Date of publication January 31, 2011; date of current version March 14, 2011. This work was supported in part by HPC resources from GENCI-IDRIS under Grant 2010-050779, the Université Européenne de Bretagne, Rennes, France, under the “International Chair” Program and the OPTIMISE Project, and the Conseil Régional de Bretagne under the CREATE/CONFOCAL Project. A. Rolland, M. Ettorre, L. Le Coq, and R. Sauleau are with the Institute of Electronics and Telecommunications of Rennes (IETR), UMR CNRS 6164, University of Rennes 1, Rennes 35042, France (e-mail: anthony.rolland@univ- rennes1.fr). A. V. Boriskin is with Institute of Radiophysics and Electronics, National Academy of Sciences of Ukraine (IRE NASU), Kharkov 61085, Ukraine, and also with the Institute of Electronics and Telecommunications of Rennes (IETR), UMR CNRS 6164, University of Rennes 1, Rennes, France (e-mail: artem.boriskin@ieee.org). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LAWP.2011.2109931 Fig. 1. Antenna configuration. (a) Overall view. (b) Dielectric and metallic ta- pers. The shaped lens with a dielectric taper is shown in gray. The profile of the extended hemispherical lens of same height and diameter is depicted by the dashed line in (a). Here , we apply the BoR-FDTD technique to synthesize a reduced-size integrated DLA with improved directivity com- pared to a conventional extended hemispherical DLA of the same dimensions. II. ANTENNA CONFIGURATION AND DESIGN PROCEDURE The generic antenna configuration studied here is axis-sym- metric (Fig. 1) and consists of a shaped homogeneous dielectric lens placed above a finite-size ground plane of circular shape (diameter ). The maximum diameter and central height of the lens are labelled and , respectively. The lens is made in a low-permittivity and low-density material (Rexolite, , at 60 GHz) so as to reduce the losses and weight of the antenna. The lens is fed by a standard air-filled circular waveguide (di- ameter ) operating in its fundamental mode . Such a feed ideally fits the selected design methodology thanks to its axisymmetric geometry and azimuthal-mode decomposition re- quired by the BoR-FDTD formulation. Moreover, it enables an easy antenna assembling. To improve the impedance matching between the feed and the lens, a dielectric taper in Rexolite is integrated inside the waveguide. The taper diameter is shrunk to guarantee single-mode propagation ( ). All geometrical parameters characterizing the shapes of the metallic and dielectric tapers are defined in Fig. 1(b). In simulation, the optimization goal is defined as follows: to find the antenna configuration that belongs to the antenna family defined in Fig. 1 and provides the best directivity at broadside. In 1536-1225/$26.00 © 2011 IEEE