Quasi-Static Homogenization of Glide-Symmetric Holey Parallel-Plate Waveguides With Ultra-Wideband Validity

Glide-symmetric (G-S) waveguides made of metallic metasurfaces are a wideband, low-loss, low-cost, and conformable alternative to dielectric materials for the design of antenna lenses at millimeter waves. However, computing the effective refractive index of glide-symmetric waveguides with existing full-wave analysis techniques results in cumbersome parametric studies for each new design. This article presents a new analytic homogenization technique for glide-symmetric holey parallel-plate waveguides (PPWs). The dispersion equation of these structures, found by way of mode-matching, is simplified at low frequency using the properties of the modes resonating within the holes, independently of the hole shape. This simplified equation yields a closed-form expression of the effective refractive index, relying on the eigenmodes of the hole cross section. This formula avoids solving a 3-D full-wave problem and is fully analytic in the case of canonical hole shapes. Although derived in the quasi-static regime, it characterizes propagation over an ultrawide band, due to the low dispersive properties of glide symmetric structures. It is a function of the angle of propagation within the waveguide and can thus be used to study anisotropic properties. Its efficiency is demonstrated with the example of glide-symmetric PPWs with rectangular and circular holes.