Design and characterisation of half-Maxwell fish-eye lens antenna in 76–81 GHz band B. Fuchs, O. Lafond, S. Rondineau, M. Himdi and L. Le Coq A new inhomogeneous lens, made up of three hemispherical shells, is proposed. By approximating the Maxwell fish-eye law, this gradient index lens exhibits interesting focusing properties. A prototype of this lens fed by a waveguide has been measured in the 76–81 GHz band, showing an average gain of 21.7 dBi. Introduction: The electromagnetic behaviour of inhomogeneous lenses has been well known for a few decades. Because their designs are based on geometrical optics [1], they can operate over a broad band of frequencies. Since the development in millimetre-wave frequency applications, dielectric lenses are now again of interest because they exhibit attractive characteristics and performance in this frequency range. Indeed, their directivity and surface efficiency for a given volume and weight make them especially suitable for embedded communication systems [2]. In this Letter, a new kind of inhomogeneous lens is presented, namely the three-shell half-Maxwell fish-eye (HMFE) lens [3]. Appli- cation is aimed at automotive radar, hence the operating frequency band of 76–81 GHz, which covers long and short range systems. Antenna design: The HMFE lens is a hemispherical dielectric gradi- ent index lens. Its theoretical relative permittivity, e r th , varies radially from 4 at the centre to 1 at the surface according to the law [1]: e th r ðrÞ¼ 4=½1 þðr=aÞ 2  2 where r denotes the distance from the centre of the lens and a is the radius of the lens. However, having a smooth varying dielectric constant along a given direction is not easy to manufacture. Therefore we propose use of the shell technique. It consists in assembling three concentric homogeneous dielectric hemispherical shells. We deviate thereby from the ideal continuous law by doing a stepwise approximation, as shown in Fig. 1. Fig. 1 Theoretical and approximated relative permittivity law of lens a b h Fig. 2 Lens image and lens antenna schematic a Top view of lens with its support b 3D view of simulated lens antenna The shells have the same thickness, i.e. 4 mm, and their permittivity equals 4.0, 2.5 and 1.5. They are made by Emerson & Cuming (Eccostock 1 HiK500F K ¼ 4 and K ¼ 2.5, Eccostock LoK K ¼ 1.5). At 77 GHz the free-space wavelength l 0 is approximately equal to 3.9 mm and thus the lens diameter is nearly 6.15l 0 . A foam support (Eccostock SH-2), the relative permittivity of which reaches 1.04, is used to support the lens. Fig. 2a shows a top view of the lens with its support. 23.0 22.5 22.0 21.5 21.0 20.5 20.0 b roa d s id e di rect i v i ty , dB D 0 distance between source and lens , h l 0 2/10 4/10 6/10 8/10 1 Fig. 3 Variation of computed broadside directivity D 0 of lens antenna against distance h 0 -5 -10 -15 -20 -25 -30 -35 -40 normalised amplitude, dB angle, deg –80 –60 –40 –20 0 20 40 60 80 b 0 -5 -10 -15 -20 -25 -30 -35 -40 normalised amplitude, dB a H plane E plane Fig. 4 Measured and simulated far-field radiation pattern of lens antenna in E- and H-planes at 77 GHz a E-plane b H-plane —— Measured co-polarisation  Measured cross-polarisation ------ Simulated Simulations (not reported here for brevity) show that increasing beyond three the number of shells does not result in a significant increase in directivity. For precision, commercial software based on ELECTRONICS LETTERS 2nd March 2006 Vol. 42 No. 5