We investigate dispersion properties of a hexagonal dielectric periodic structure that can be used to engineer dielectric graded-index lenses. The connection between the geometry of the hexagonal periodic structure and its symmetries is explained. Furthermore, we demonstrate that a hexagonal structure with increased symmetry is more isotropic than its conventional counterpart. To validate our analysis, we designed, manufactured, and measured a planar Luneburg lens antenna. The antenna has a neat fan-shaped beam from 23 to 31 GHz. The results validate the broadband operation of the periodic structure and could be of interest for the design of cost-effective antennas.
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2023
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