This paper presents a study of planar silicon lens antennas with up to three steppedimpedance matching regions. The eective permittivity of the matching regions is tailor-made by etching periodic holes in the silicon substrate. The optimal thickness and permittivity of the matching regions were determined by numerical optimization to obtain the maximum wide-band aperture eciency and smallest side-lobes. We introduce a new geometry for the matching regions, referred to as shifted matching regions. The simulation results indicate that using three shifted matching regions results in twice as large aperture eciency as compared to using three conventional concentric matching regions. By increasing the number of matching regions from one to three, the band-averaged gain is increased by 0.3 dB when using concentric matching regions, and by 3.7 dB when using shifted matching regions, which illustrates the advantage of the proposed shifted matching region design.
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