  In this paper, we study the wave propagation in a metallic parallel-plate
structure with glide-symmetric elliptical holes. To perform this study, we
derived a mode-matching technique based on the generalized Floquet theorem for
glide-symmetric structures. This mode-matching technique benefits from a lower
computational cost since it takes advantage of the glide symmetry in the
structure. It also provides physical insight on the specific properties of
Floquet modes propagating in these specific structures. With our analysis, we
demonstrate that glide-symmetric structures with periodic elliptical holes
exhibit an anisotropic refractive index over a wide range of frequencies. The
equivalent refractive index can be controlled by tuning the dimensions of the
holes. Finally, by combining the anisotropy related to the elliptical holes and
transformation optics, a Maxwell fish-eye lens with a 33.33% size compression
is designed. This lens operates in a wideband frequency range from 2.5 GHz to
10 GHz.
