A broadband gradient index (GRIN) metamaterial lens for gain enhancement of circularly polarized antennas has been automatically designed, fabricated and investigated. The GRIN metamaterial lens consists of an isotropic dielectric plate with a corresponding distribution of deep-subwavelength drill holes each with the same diameter. Such drill holes have a negligible influence on both the polarization state and the spectral response of the electromagnetic wave transmitting through the resulting GRIN metamaterial lens. Therefore, the GRIN metamaterial lens is polarization-insensitive and can efficiently transform spherical waves into planar waves over a very broad frequency range keeping the initial polarization states (e.g. linear or circular) scarcely changed. In the following we have derived analytical formulas that enable the setup of distribution rules for the drill holes on the plate. Based on these formulas, the GRIN metamaterial lens can be automatically designed and easily fabricated using circuit board engraving machines. The proposed GRIN metamaterial lens has been tested by placing it on the aperture of a circularly polarized conical horn antenna. The agreement between simulation and measurement results shows that the gain of the horn antenna has been significantly increased within the whole X-band (i.e. from 8 GHz to 12 GHz) and the largest gain enhancement reaches up to 5.7 dB. In particular, the axial ratio of the horn antenna with the GRIN metamaterial lens is less than 1.6 dB.
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