Glide-Symmetric Metallic Structures With Elliptical Holes for Lens Compression

Abstract

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 glidesymmetric 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.

On the Benefits of Glide Symmetries for Microwave Devices

“…With these graphs, it is demonstrated that glide symmetry produces more stable elliptical contour lines for a larger range of frequencies. Additionally, as demonstrated in [17], [52], glide symmetry is able to produce higher refractive indices than conventional unit cells. This is beneficial, for example, for compressing the size of lenses with transformation optics, or for creating optical illusions.…”

“…More recently, it has been demonstrated that glide symmetry can also be employed to increase the level of anisotropy (on-axis) of periodic structures. In particular, this concept was demonstrated for rectangular [19] and elliptical holes [52] in a parallel plate, and in dielectric slabs with holey cladding on top and bottom [17].…”

“…In [17], elliptical glide-symmetric holes were proposed to produce an enhanced anisotropic response in the design of a planar compressed Luneburg lens. Similarly, in [52], elliptical holes in parallel plate configuration were proposed to produce a compressed Maxwell fish-eye lens. The electric field for the compressed lens proposed in [52] is represented in Fig.…”

“…Similarly, in [52], elliptical holes in parallel plate configuration were proposed to produce a compressed Maxwell fish-eye lens. The electric field for the compressed lens proposed in [52] is represented in Fig. 11.…”

Dispersion Analysis of Periodically Loaded Transmission Lines with Twist Symmetry Using the Mode-Matching Technique

“…Additionally, it has been demonstrated that glide-symmetric structures are less dispersive [12,13] and can provide a higher effective refractive index [13][14][15][16], effective permeability [17], and level of anisotropy [18], compared to their non-glide counterparts. These properties have been used to design planar lenses in [13,[19][20][21][22]. Furthermore, while the stop-band between the first two modes is suppressed in glide-symmetric structures, a large stop-band exists at higher frequency [23][24][25].…”