Wave Propagation in Periodic Metallic Structures with Equilateral Triangular Holes

Abstract

This paper studies wave propagation in a periodic parallel-plate waveguide with equilateral triangular holes. A mode-matching method is implemented to analyze the dispersion diagram of the structure possessing glide and mirror symmetries. Both structures present an unexpected high degree of isotropy, despite the triangle not being symmetric with respect to rotations of 90°. We give some physical insight on the matter by carrying out a modal decomposition of the total field on the hole and identifying the most significant modes. Additionally, we demonstrate that the electrical size of the triangular hole plays a fundamental role in the physical mechanism that causes that isotropic behavior. Finally, we characterize the influence of the different geometrical parameters that conform the unit cell (period, triangle size, hole depth, separation between metallic plates). The glide-symmetric configuration offers higher equivalent refractive indexes and widens the stopband compared to the mirror-symmetric configuration. We show that the stopband is wider as the triangle size is bigger, unlike holey structures composed of circular and elliptical holes where an optimal hole size exists.

Dispersion and Filtering Properties of Rectangular Waveguides Loaded With Holey Structures

“…Nevertheless, from certain hole depth, the dispersion diagram remains unchanged since the modes are evanescent inside the holes. This effect also occurs in holey metasurfaces [32], [35], [37], [40]. This enables an interesting cost-effective manufacturing of waveguide structures with holey unit cells by through holes if the selected hole depth is large enough.…”

On the Benefits of Glide Symmetries for Microwave Devices

“…The solution of this problem gives not only the required dispersion diagram, but also useful physical insight into the structure. First of all, a decomposition of the field on the hole surface in terms of hole modes is obtained, which can explain the propagation properties (anisotropy, frequency dispersion) when the shape of the hole is modified [51] or the effect of tightly spaced metasurfaces [43]. Furthermore, symmetry properties of the Floquet harmonics propagating between the metasurfaces are also naturally obtained.…”

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

“…This stop-band has been used to design low-cost gap waveguides [26] and filters [27] and to reduce the leakage between waveguide flanges [28,29]. These attractive properties have inspired the development of several semi-analytical methods for the analysis of glide-symmetric structures using circuit models [25,30,31], mode-matching [32][33][34][35], or the multimode transfer-matrix approach [36][37][38]. These methods provide a fast means of studying glide-symmetric structures and give insight into the physics of glide symmetry.…”