Analysis and Applications of Glide-Symmetric Holey Metasurfaces

Abstract

Glide symmetry is a particular case of higher symmetries defined with a translation for half a period followed by a reflection with respect to a glide plane. It has been demonstrated that by applying glide symmetry to periodic structures, a higher value of equivalent refractive index is achieved [1], and the first stop-band in the dispersion diagram is eliminated [2]. The later property causes a dramatic reduction in the frequency dispersion of periodic structures which makes glide-symmetric structures an excellent candidate for designing wideband graded-index flat lens antennas [3]–[4]. In addition, glide-symmetric all-metal holey metasurfaces find applications in designing efficient Luneburg lens antennas for 5G communications systems [4]–[5]. Furthermore, compared to the conventional pin-type structures, glide-symmetric holey structures provide a wide and cost-effective electromagnetic band gap (EBG) at the millimeter band [6]. For all of these applications, designing a unit cell that produces a desirable dispersion diagram is the first step. For this purpose and in order to obtain a physical view to the fields propagating in glide-symmetric structures, a mode-matching technique can be used for dispersion analysis of glide-symmetric holey metasurfaces [7]–[9]. In [7], a mode matching formulation was derived and applied to the glide-symmetric corrugations. Applying a generalized Floquet theorem, which takes into account the higher symmetry in the structure, reduces the computational domain and consequently the computational time. In [8], the generalized Floquet theorem proposed by Oliner [10] was applied to holey structures with square and rectangular holes. Later, this formulation was extended to glide-symmetric holey metasurfaces with an arbitrary shape of the hole and applied to the case with circular holes in [9]. We demonstrated in [7]–[9] that this is an accurate method for computing the dispersion properties of glide-symmetric holey metasurfaces. In addition, it is much faster than the eigenmode solver in commercial software based on the finite-method algorithms such as CST Microwave Studio. Here, we apply the formulation presented in [9] to glide-symmetric holey metasurfaces with elliptical holes to investigate their anisotropic behavior. These anisotropic unit cells can be used for designing graded-index lens antennas which require anisotropic materials, for instance optically transformed lenses with compressed size. Using our proposed formulation, we demonstrate in a fast and efficient way that a metasurface with glide-symmetric elliptical holes provides an anisotropic behavior stable over a much wider range of frequency if compared to its non-glide counterpart. In addition, the tuning of their anisotropy by adjusting suitable geometrical dimensions of the unit cell is investigated.