Dispersion Analysis of Metasurfaces With Hexagonal Lattices With Higher Symmetries

This article investigates the dispersion properties of metasurfaces with hexagonal lattices, including potential higher symmetric configurations. We explore the relationships between the periodicity of hexagonal lattices and their dispersion properties, paying special attention to how hexagonal periodic structures can be analyzed with either a hexagonal primitive unit cell or a rectangular supercell. We also study the possibility of introducing higher symmetries into hexagonal periodic structures, including glide symmetry and mirrored half-turn symmetry. To complement and validate the analysis, we designed a graded-index Luneburg lens antenna with a dielectric-filled hexagonal holey structure working in the K$_{\mathrm{a}}$-band. The antenna generates steerable highly directive beams from 26 GHz to 30 GHz, which corroborates our analysis. Our findings provide valuable insight into the dispersion properties of hexagonal-lattice metasurfaces and demonstrate the feasibility of using such structures in practical applications.