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We discuss the issue of identifying the forward/backward nature of modes in bounded one-dimensional periodic structures. This identification is based on the possibility of adequately and uniquely defining the phase velocity in these types of structure. We propose a general definition of phase velocity for one-dimensional scalar waves and show that, according to that general definition, the voltage and current waves in nonhomogeneous lossless transmission lines with positive per-unit-length capacitance and inductance are necessarily forward waves. We analyze in detail the particular case of periodic transmission lines and question the conclusions about the forward/backward nature of their modal solutions that are traditionally drawn from the inspection of the Brillouin diagrams. Numerical results for the case of corrugated parallel-plate waveguides support the idea that all modes can be considered forward-like as long as a periodic transmission line model remains a sensible and reliable description of the problem. In more general scenarios, we show that an appropriate definition of the phase velocity can still be found for electromagnetic waves with at least one linearly polarized field and that they are also necessarily forward waves if they propagate through media with positive $\varepsilon$ and $\mu$ parameters. Finally, we relate our discussion to the effective refractive index of periodic structures, highlighting that although its definition is not valid for a general periodic structure, it can be useful in many practical cases.

The Physical Optics (PO) method is used to derive simplified expressions to compute the radiation electric fields of planar graded-index and geodesic lenses based on a parallel-plate waveguide (PPW) implementation. If the PO method is combined with ray-tracing (RT) techniques, the resulting RT-PO procedure is capable of computing radiation patterns and gain of the PPW-based lens antennas when their apertures have a general shape and the electric field is vertically polarized. The RT-PO method is validated by comparing it with the full-wave simulation results of the commercial software ANSYS HFSS for three application cases. The results show that the RT-PO approach is not only very efficient from a computational point of view but also accurate, thus being a very convenient analysis/design tool for this kind of antenna.

The application of lenses combined with array antennas (also known as dome arrays or dome antennas) to the next generation of terrestrial and satellite communication systems brings a wide range of advantages in terms of improved radiation performance, reconfigurability in the use case, and reduction in power consumption. To facilitate the industrial implementation of dome antennas, highly efficient simulation tools are required. In this paper, we present a streamlined implementation of ray tracing for fast and efficient numerical analysis of the far-field radiation performance of 2D multilayer dielectric lenses combined with phased arrays. Unlike commercial physical-optical methods, our proposed ray-tracing method is capable of computing the effects of internal reflections in the dome in a multilayer configuration. In addition, the method estimates the absorption losses as a result of the Joule effect. To demonstrate the effectiveness of the proposed approach, we provide comparisons of the simulated radiation patterns using our proposed ray tracing with the results obtained from commercial full-wave simulation tools.

In this work, we examine the methodology for numerically computing the dispersion diagram of three-dimensional periodic structures using commercial electromagnetic simulators. Examples of periodic structures based on body-centered cubic, face-centered cubic, and monoclinic lattices are used to illustrate this methodology. We first outline the characteristics of these structures in both physical and reciprocal spaces from a theoretical point of view. On this basis, we provide a comprehensive explanation of how to adjust the setting in simulation software commonly used in microwave engineering to generate the dispersion diagrams of these structures. The appropriate simulation conditions are tabulated to serve as a further guide for other researchers. This study also explores the influence of the elements of the unit cell on the dispersion characteristics. Additionally, we evaluate and contrast the dispersion properties of identical periodic elements when having simple cubic, body-centered cubic, and face-centered cubic arrangements. We found that symmetries, such as those seen in body-centered cubic and face-centered cubic arrangements, can improve the isotropy and maintain low-dispersion characteristics over a wider frequency range. The monoclinic structure is also taken as an example to demonstrate that the reported analysis method can be applied to the dispersion analysis of other more complex noncubic lattices. Our findings offer useful information for the examination and engineering of three-dimensional periodic structures, which can be used to design microwave and antenna devices.

In this paper, a novel dual-slant polarized three-dimensional (3D) periodic Luneburg lens with a diameter of 390 mm ( $4.6\lambda _{0}$ at 3.55 GHz) is presented. Copper-plated cubes with truncated corners are placed in a body-centered cubic (BCC) lattice and held together with layers of Rohacell foam. The sizes of the cubes are varied to realize the gradient refractive index (GRIN) profile of a generalized Luneburg lens at a low cost, with a low weight and loss. The designed Luneburg lens operates from 3.3 to 3.8 GHz with a total weight of 1 kg. The quasi-isotropic response of the proposed periodic structure allows a wide angle coverage. Measured results show that the lens antenna can achieve a peak gain of 22 dBi with a scanning loss of less than 0.4 dB in a wide angular range in both the azimuth and the elevation plane. Importantly, the proposed lens antenna design achieves a cross-polarization level below peak gain of less than −19 dB at all angles for the two slant polarizations of the feed, while comparable designs report up to −11 dB at given angular directions. This high-gain multi-beam antenna with a commercially viable design is suitable for wireless communications at low microwave frequencies.

Abstract It is demonstrated that combining phased array antennas with dielectric lenses constitutes a suitable solution to increase the energy efficiency in next‐generation communication systems. A dielectric lens is designed to increase the gain of an array antenna working in the 3GPP n257 band (26.5–29.5 GHz). The simulated results demonstrate that the dielectric lens increases the gain between 0.4 and 1.3 dB in a large scanning range from 0° to 60° at 28 GHz; meaning that the output RF power can be decreased by up to 26% for a same equivalent isotropic radiated power required from the base station.

This article investigates the dispersion properties of metasurfaces with hexagonal lattices, including potential higher symmetric configurations. We explore the relationships between the periodicity of hexagonal lattices and their dispersion properties, paying special attention to how hexagonal periodic structures can be analyzed with either a hexagonal primitive unit cell or a rectangular supercell. We also study the possibility of introducing higher symmetries into hexagonal periodic structures, including glide symmetry and mirrored half-turn symmetry. To complement and validate the analysis, we designed a graded-index Luneburg lens antenna with a dielectric-filled hexagonal holey structure working in the K$_{\mathrm{a}}$-band. The antenna generates steerable highly directive beams from 26 GHz to 30 GHz, which corroborates our analysis. Our findings provide valuable insight into the dispersion properties of hexagonal-lattice metasurfaces and demonstrate the feasibility of using such structures in practical applications.

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. A family of such lens profiles are derived.

Spherically-symmetric lenses can create sharp virtual images, but a general expression for their refractive index profiles had not yet been developed. Here, this expression is provided via analogy between classical mechanics and geometrical optics, yielding solutions complementary to existing lenses obtained from the generalized Luneburg lens problem.

This paper reports on the design and experimental validation of a fully-metallic double-ridged waveguide 10 × 10 Rotman lens additively manufactured as a single part. The wide band operation of this quasi-optical beamformer enables us to cover the uplink and downlink frequencies allocated to satellite communications in the K/Ka-band, from 17.3 GHz to 30 GHz. The feeding port design was adjusted to enable vertical printing, thus minimizing the use of supporting structures. A prototype was manufactured and tested. The reported results indicate losses in the range of 0.5 dB in the lower-frequency band and 0.8 dB in the upper-frequency band, including the waveguide transitions added for test purposes. The measured reflection and coupling coefficients remain below −11.5 dB over the operating band. The standard deviation of the residual phase error across the array ports is below 5° in simulation and below 10° in measurements. Array factors synthesized using the scattering parameters confirm the good stability of the beamforming functionality over the wide frequency band analyzed. This monolithic design is a promising step toward more integrated antenna systems, such as a compact dual-stack configuration for planar array design.

Abstract Conformal transformation optics is employed to enhance an H-plane horn’s directivity by designing a graded-index all-dielectric lens. The transformation is applied so that the phase error at the aperture is gradually eliminated inside the lens, leading to a low-profile high-gain lens antenna. The physical space shape is modified such that singular index values are avoided, and the optical path inside the lens is rescaled to eliminate superluminal regions. A prototype of the lens is fabricated using three-dimensional printing. The measurement results show that the realized gain of an H-plane horn antenna can be improved by 1.5–2.4 dB compared to a reference H-plane horn.

Abstract A parallel‐plate waveguide half‐Luneburg geodesic lens is designed and experimentally validated in the Ka‐band. The geodesic lens profile is modulated using spline functions to reduce its height, while the symmetry halving the lens enables reduction of its in‐plane dimensions. This design provides high gain, equivalent to that of a full‐Luneburg lens, over a reduced angular range of ±20° to ±30° in azimuth. The specific design reported here has a maximum realized gain of 23.3 dBi in measurement, compared with 23.8 dBi for a full‐Luneburg lens twice the size of this design. Very wideband operation is demonstrated both in simulations and measurements. This design is of interest for applications having limited space like millimetre‐wave systems on board cubesats and small satellites.

Connecting networks for two-dimensional beamforming matrices are discussed. They provide a suitable interconnection between the output ports of a Butler matrix and antenna array ports, transforming a square (and more generally, rectangular) lattice of beams into a triangular lattice of beams. This change in lattice improves the crossover between beams, reducing gain roll-off over the field of view for a given multiple fixed beam coverage. A general description of the concept is provided and numerical results are reported, which confirm a reduction in crossover level between 1 and 1.5 dB. The proposed solution is further validated through the design and test of a 4 × 4 open-ended waveguide array in K-band. The connecting network has a length of 70 mm, compared to 226 mm for the 2D Butler matrix, with a design frequency of 19.55 GHz. Good agreement is found between simulated and measured data. The desired triangular lattice of beams is confirmed with the measured multiple beams. This solution is of interest for multiple-beam millimeter-wave communication systems, considered for next generation of terrestrial and non-terrestrial networks.

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.

This paper presents the design and fabrication of a mechanically reconfigurable filter at W band based on the concept of glide symmetry. The tunability is achieved by breaking and regenerating the glide symmetry. The filters are made of two glide-symmetric pieces that can be displaced in a certain direction, and therefore, break the symmetry. The high filtering capacity of these designs is demonstrated by simulation and measurement and can also be adjusted mechanically. The transmission level in the manufactured filter varies from a value between −1 and −2 dB when the filter is in the glide symmetry position to values close to −40 dB in the stop-band when it is in the broken symmetry position. The transmission band obtained in the symmetrical mode is around 20%, but, after breaking the symmetry, it is split into two passbands of 6.5% and 11% separated by a stop-band of 6%. The position, bandwidth, filtering level and filter roll-off can be adjusted for both modes of operation by appropriately selecting the unit cell design parameters and the number of unit cells.

In this paper, we present a general mode matching formulation to analyze the wave propagation in glide-symmetric metallic surfaces drilled with periodic holes with an arbitrary cross section. A generalized Floquet theorem is applied to reduce the computational cost by imposing boundary conditions only on one of the two surfaces. With a small modification, the formulation can be used also for dispersion analysis of a holey metallic surface with or without a metal plane above it. The method is fast and efficient, and it provides physical insight on the specific symmetry properties of Floquet harmonics in glide-symmetric structures. The formulation is applied to obtain dispersion diagrams of glide-symmetric structures with circular holes as this kind of hole is usually used in practical applications to realize gap waveguides or wideband planar lenses. The results agree well with the reference results from commercial software CST Microwave Studio.

This work studies the propagation characteristics of a rectangular waveguide with aligned/misaligned double-sided dielectric-filled metallic corrugations. Two modes are found to propagate in the proposed double-sided configuration below the hollow-waveguide cutoff frequency: a quasi-resonant mode and a backward mode. This is in contrast to the single-sided configuration, which only allows for backward propagation. Moreover, the double-sided configuration can be of interest for waveguide miniaturization on account of the broader band of its backward mode. The width of the stopband between the quasi-resonant and backward modes can be controlled by the misalignment of the top and bottom corrugations, being null for the glide-symmetric case. The previous study is complemented with numerical results showing the impact of the height of the corrugations, as well as the filling dielectric permittivity, on the bandwidth and location of the appearing negative-effective-permeability band. The multi-modal transmission-matrix method has also been employed to estimate the rejection level and material losses in the structure and to determine which port modes are associated with the quasi-resonant and backward modes. Finally, it is shown that glide symmetry can advantageously be used to reduce the dispersion and broadens the operating band of the modes.

Lenses are used for multiple applications, including communications, surveillance and security, and medical instruments. In homogeneous lenses, the contour is used to control the electromagnetic propagation. Differently, graded-index lenses make use of inhomogeneous materials, which is an extra degree of freedom. This extra degree of freedom enables the design of devices with a high performance. For instance, rotationally symmetric lenses without spherical aberrations, e.g., the Luneburg lens, can be designed. However, the manufacturing of such lenses is more complex. One possible approach to implement these lenses is using metamaterials, which are able to produce equivalent refractive indices. Here, we propose a new type of three-dimensional metamaterial formed with two independent sets of wires. The double-mesh twin-wire structure permits the propagation of a first mode without cut-off frequency and with low dispersion and high isotropy. These properties are similar to periodic structures with higher symmetries, such as glide symmetry. The variations of the equivalent refractive index are achieved with the dimension of the meandered wires. The potential of this new metamaterial is demonstrated with simulated results of a Luneburg meta-lens.

We propose a circular twist-symmetric dielectric waveguide that is polarization-selective. In the practical implementation of optical fibers, a selective circular polarization is more convenient than its linearly polarized counterpart where previous knowledge of the emitted polarization from the transmitter is unknown. The analysis of the waveguide was conducted with three methods: an eigenmode approach, simulation of a truncated structure, and the so-called multimodal transfer-matrix method (MMTMM). The presented simulations demonstrate that the operational band can be manipulated by tuning the parameters of the structure. Furthermore, the MMTMM allows for a direct and accurate calculation of the attenuation constant of the rejected circular polarization.

A mode-matching formulation is presented and used to analyze the dispersion properties of twist-symmetric transmission lines. The structures are coaxial lines periodically loaded with infinitely thin screens, which are rotated with respect to each other to possess twist symmetry. The results obtained using the proposed formulation are in good agreement with those of commercial simulators. Furthermore, using the presented mode-matching formulation, it is demonstrated that the propagation characteristics in the twist-symmetric structures are linked to the scattering and coupling of the higher order modes. The physical insight offered by this analysis is valuable for the design of various electromagnetic devices, such as filters, antennas, and phase-shifters.

We demonstrate the beneficial effects of introducing glide symmetry in a two-dimensional periodic structure. Specifically, we investigate dielectric parallel plate waveguides periodically loaded with Jerusalem cross slots in three configurations: conventional, mirror- and glide-symmetric. Out of these three configurations, it is demonstrated that the glide-symmetric structure is the least dispersive and has the most isotropic response. Furthermore, the glide-symmetric structure provides the highest effective refractive index, which enables the realization of a broader range of electromagnetic devices. To illustrate the potential of this glide-symmetric unit cell, a Maxwell fish-eye lens is designed to operate at 5 GHz. The lens is manufactured in printed circuit board technology. Simulations and measurements are in good agreement and a measured peak transmission coefficient of −0.5 dB is achieved.

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.

This work presents a new configuration to create glide-symmetric structures in a single plane, which facilitates fabrication and avoids alignment problems in the assembly process compared to traditional glide-symmetric structures based on several planes. The proposed structures can be printed on the metal face of a dielectric substrate, which acts as a support. The article includes a parametric study based on dispersion diagrams on the appearance of stop-bands and phase-shifting by breaking the symmetry. In addition, a procedure to regenerate symmetry is proposed that may be useful for reconfigurable devices. Finally, the measured and simulated S parameters of 10 × 10 unit-cell structures are presented to illustrate the attenuation in these stop-bands and the refractive index of the propagation modes. The attenuation obtained is greater than 30 dB in the stop-band for the symmetry-broken prototype.

In this article, we demonstrate how twist symmetries can be employed in the design of flat lenses. A lens design is proposed, consisting of 13 perforated metallic sheets separated by an air gap. The perforation in the metal is a two-dimensional array of complementary split-ring resonators. In this specific design, the twist symmetry is local, as it is only applied to the unit cell of the array. Moreover, the twist symmetry is an approximation, as it is only applied to part of the unit cell. First, we demonstrate that, by varying the order of twist symmetry, the phase delay experienced by a wave propagating through the array can be accurately controlled. Secondly, a lens is designed by tailoring the unit cells throughout the aperture of the lens in order to obtain the desired phase delay. Simulation and measurement results demonstrate that the lens successfully transforms a spherical wave emanating from the focal point into a plane wave at the opposite side of the lens. The demonstrated concepts find application in future wireless communication networks where fully-metallic directive antennas are desired.

Here we propose the use of twist and glide symmetries to increase the equivalent refractive index in a helical guiding structure. Twist- and glide-symmetrical distributions are created with corrugations placed at both sides of a helical strip. Combined twist-and glide-symmetrical helical unit cells are studied in terms of their constituent parameters. The increase of the propagation constant is mainly controlled by the length of the corrugations. In our proposed helix antenna, twist and glide symmetry cells are used to reduce significantly the operational frequency compared with conventional helix antenna. Equivalently, for a given frequency of operation, the dimensions of helix are reduced with the use of higher symmetries. The theoretical results obtained for our proposed helical structure based on higher symmetries show a reduction of 42.2% in the antenna size maintaining a similar antenna performance when compared to conventional helix antennas.

A circular graded index lens is conformally transformed to an elliptical shape using a closed-form transformation. The proposed transformation is then employed to compress a Maxwell fish-eye and its generalized version. Since the transformation is conformal, the electromagnetic properties of the device are perfectly preserved after the transformation with fully isotropic and dielectric-only materials. Ray-tracing and full-wave simulations are carried out for several cases to verify the functionality of the optically transformed lenses in geometrical optics and wave optics regimes.