The presence of glide symmetries in periodic structures can introduce beneficial modifications in their electromagnetic properties. The difference between glide and non-glide periodic structures is due to the distinctive coupling between their constituent sub-unit cells. In this paper, we describe the recent discoveries on the remarkable properties of glide-symmetric periodic structures, which include widened stopbands, reduced dispersion, as well as enhanced anisotropy and magnetic response. These properties are explained through canonical structures simulated with two methods: mode matching and multimode transfer-matrix analysis. We also review the recent use of these distinctive properties for solving technological problems in practical devices such as filters, gap waveguide components, low-leakage flanges, compressed lenses, low-reflected material transitions and leaky-wave antennas with applications in 5G terrestrial communication systems, millimetre-wave satellite systems and automated contactless measurement techniques.

In this work, two novel efficient leaky-wave antennas (LWAs) with stable radiation patterns operating in the 60-GHz band are proposed. The LWAs are implemented in groove-gap waveguide (GGW) technology. To mitigate the beam squint due to the dispersive nature of LWAs, complementary-dispersive prisms are coupled to the LWA radiation aperture. The antennas are implemented in fully-metallic purely holey periodic structures, resulting in a more cost-effective and robust manufacturing process compared to previously reported pin-based structures. Two prisms are proposed, one with mirror symmetry and one with glide symmetry. When the prism possesses a glide symmetry, much fewer holes are required while maintaining a similar performance, which even further decreases the fabrication costs. The complex propagation constant is optimized for low side lobe levels (SLLs) with tailored hole diameters and waveguide dimensions, thus for the first time demonstrating the capability of using glide-symmetric holes to control the leakage rate. Two prototypes with mirror-and glide-symmetric prisms are theoretically synthesized and validated by simulated and experimental results. A frequency bandwidth of 11% is achieved for both prototypes with the beam squint within ±0.9° (mirror) and ±1.7° (glide), SLLs below -15 dB (mirror) and -13 dB (glide), total efficiency almost 90%, and realized gain of 17 ± 0.5 dB at a fixed observing angle. The developed antennas are intended for mm-wave point-to-point communications.

The dispersion characteristics of a glide-symmetric holey periodic surface are investigated, with special emphasis on a detailed study of its stopbands. The unit cell is modeled as a multiport network associated with multiple modes at each of the lattice boundaries. Enforcing the periodic conditions, the real and imaginary parts of the wavenumbers of the Floquet modes are calculated through an eigenproblem posed in terms of the generalized multimodal transfer matrix, which is computed from the scattering parameters obtained with a full-wave simulator. This procedure allows us to take into account the higher order modal couplings between adjacent unit cells that are crucial for accurate dispersion analysis. The resulting simulation-assisted approach provides both a convenient computational tool and a very fruitful physical insight that reveals the existence of complex modes, the convergence of opposite-parity modes, and the anisotropy in both passband and stopband. This approach enables a precise calculation of the attenuation constant, which is not possible with conventional techniques as the eigenmode solvers of commercial software. Based on this approach, an extensive parametric study is carried out, rigorously establishing a set of critical criteria for the use of such a periodic surface as an electromagnetic bandgap structure in gap waveguide technology. Moreover, the analysis of the directional properties of the structure is applied to further suppress the leakage.

A systematic and efficient multimodal transfer-matrix approach is proposed for the comprehensive Bloch analysis of general 1-D/2-D/3-D periodic structures. We provide a linearization procedure for transforming the original nonlinear eigenvalue problem associated with 2-D/3-D structures to a standard one that can easily be solved without the need of a zero-searching algorithm in the complex plane. The proposed approach has been validated with bounded/open structures with complex geometries and/or inhomogeneous lossless/lossy materials. It demonstrates a significantly reduced computational time and leverages the strengths of full-wave simulators to deal with general problems and ad hoc quasi-analytical methods to give a fundamental understanding of the behavior of the structure. Also, it allows for an accurate evaluation of the imaginary part of the wavenumber, which offers information of material dissipation, stopband rejection, leakage, and complex modes.

A double-layer lens consists of a first gradient-index/geodesic profile in an upper waveguide, partially surrounded by a mirror that reflects the wave into a lower guide where there is a second profile. Here, we derive a new family of rotational-symmetric inhomogeneous index profiles and equivalent geodesic lens shapes by solving an inverse problem of pre-specified focal points. We find an equivalence where single-layer lenses have a different functionality as double-layer lenses with the same profiles. As an example, we propose, manufacture, and experimentally validate a practical implementation of a geodesic double-layer lens that is engineered for a low-profile antenna with a compact footprint in the millimeter wave band. Its unique double-layer configuration allows for two-dimensional beam scanning using the same footprint as an extension of the presented design. These lenses may find applications in future wireless communication systems and sensing instruments in microwave, sub-terahertz, and optical domains.

In this paper, 1-D periodic structures possessing higher symmetries are proposed and investigated in terms of their dispersion properties. The proposed structures are coaxial lines with coaxial rings periodically loaded on their inner or outer conductors. The higher symmetries, namely, glide and twist symmetries, are obtained by performing an additional geometrical operation within the unit cell of the periodic structure. We demonstrate that the propagating modes exhibit a lower frequency dispersion in higher symmetric coaxial lines. Moreover, the conventional stopbands of periodic structures at their Brillouin zone boundaries can be controlled by breaking the higher symmetry or changing the order of the twist symmetry. A circuit-based analytical method is proposed to calculate the dispersion diagram of the glide-symmetric coaxial lines. The results are validated with a full-wave simulation. Moreover, several prototypes of the twist-symmetric coaxial lines are manufactured and measured. A remarkable agreement is achieved between the measurements and simulations, validating the theoretical results. The proposed structures find potential applications in leaky-wave antennas and fully metallic reconfigurable filters and phase shifters.