Design and characterization of half Maxwell fish-eye lens antennas in millimeter waves

This paper presents the performance of multilayered half Maxwell fish-eye (HMFE) lenses fed by aperture-coupled microstrip patch antennas. Manufacturing techniques are reviewed and the shell technique is retained. Many lens configurations are investigated and compared using a full-wave electromagnetic software at 50 GHz. We report the effects of the number of shells, diameter of the lens, and distance between the primary source and the lens on the input impedance, broadside directivity, and aperture efficiency. Thus, we show that aperture efficiencies up to 95% can be obtained for a one-wavelength-diameter lens with only three shells, justifying the interest in such lenses. An analytical optimization method is also proposed and detailed to choose the thickness and permittivity of a three-shell HMFE lens to approach the radial permittivity law as well as possible. Simulations of lens antennas whose shell characteristics are determined by various ways show that the optimized lens is the one that provides the highest broadside directivities. Finally, measurements done with a three-shell four-wavelength diameter lens fed by a 2 times 2 patch antenna array show the validity of these simulations. To our knowledge, this represents the first layered HMFE lens carried out in the millimeter-wave frequency range