We propose a systematic and efficient extension of the multimodal transfer-matrix method to obtain the dispersion diagram of structures with 2-D periodicity specifically targeted to primitive unit cells that possess internal symmetries. When symmetry planes can be applied, the study of the unit cell can be simplified to a number of 1D-periodic scenarios that depend on the boundary conditions imposed by the symmetry planes. The study of these 1D-periodic scenarios is simpler, more accurate, and requires less computational cost. The proposed methodology has been validated with different examples of periodic structures with different lattices (squared, rectangular, and hexagonal), symmetries, and motifs. Furthermore, this approach brings about a deeper understanding of the study of the Brillouin zone (BZ) and the relationship between phase shift and paths on its irreducible Brillouin zone (IBZ).

This communication presents a Luneburg-like geodesic lens antenna with a defined footprint operating from 60 to 70 GHz. Traditionally, geodesic lens antennas are rotationally symmetric and consequently possess a large footprint. By defining the outline of the lens footprint, the overall size of the lens can be reduced while introducing new degrees of freedom to optimize its performance. An in-house ray-tracing algorithm was used to aid the design process of the lens. In the case presented, the geometric parameters were selected for the overall port performance. A final prototype was manufactured using laser powder-bed fusion (LPBF), with measurements agreeing closely with the simulated results. The proposed antenna finds applications in future wireless communication networks.

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.

This paper investigates the dispersion properties exhibited by three different three-dimensional (3D) periodic arrangements of metallic spheres with the following underlying lattices: simple cubic (sc), body-centered cubic (bcc) and face-centered cubic (fcc) lattice. Their Brillouin zone (BZ) and the corresponding irreducible BZ are introduced. We then examine the dispersion properties along the edges of their respective irreducible BZs. The findings demonstrate that structures with a non-sc arrangement and higher symmetry can improve design versatility while simultaneously reducing the anisotropy of the structure and broadening the operating frequency range. These advantages are beneficial for the development of 3D graded-index (GRIN) lenses.

The Luneburg lens is of significant interest for microwave and optical devices due to its wide-angle focusing properties. However, the inhomogeneous refractive index of the lens is restrictive and can be difficult to realize, especially at high frequency (typically millimeter-waves and above). Here, we present an inhomogeneous lens referred to as the collimating truncated virtual image lens, which is derived as a combination of the recently proposed virtual image lens and a conventional extended hemispherical lens. We investigate the operation of the proposed lens and we demonstrate that it provides similar focusing properties as the Luneburg lens, but with a flexible refractive index profile. This flexibility can be used to alleviate the strict manufacturing constraints typically associated with the Luneburg lens. We validate the properties of the proposed lens with a demonstrator at millimeter-wave frequencies showing that an antenna based on the proposed lens can obtain similar directivity and sidelobe levels to those obtained in an ideal Luneburg lens antenna, while the proposed lens is easier to realize. The collimating truncated virtual image lens is attractive for instruments and antennas at high frequency.

This paper proposes a combined ray-tracing and physical-optics model to analyze parallel-plate-waveguide lens antennas with a flat aperture. A family of rays is traced from the source to a set of target points on the lens radiating aperture, giving a description of the aperture electric field. On the basis of the physical-optics approximation, an equivalent magnetic current is then assumed and used to evaluate the far-field radiation characteristics in every direction. This numerical approach is validated by applying it to a particular planar Mikaelian lens antenna and comparing the results with those obtained using a commercial full-wave simulator.

In millimeter-wave applications, it is essential to use highly directional and steerable antennas. Phased array antennas are the most common choice, but they have restricted scanning coverage because of their effective aperture. To enhance the scanning coverage, a dielectric lens can be placed on top of the array. However, full-wave simulations require a lot of computing time to simulate this type of structure. In this work, a two-dimensional ray-tracing model has been adapted and improved to efficiently compute the radiation pattern of arrays combined with multilayered dielectric radomes for satellite communications applications. Moreover, this model can also calculate the absorption and reflection losses and the transmitted power required to comply with the regulatory mask. This model has been used to design a lens that increases the scanning range of an array while maintaining a maximum height and ensuring that it complies with the regulatory masks for satellite communications.

We explore the dispersion properties of quasi-twist-symmetric structures using the multimode transfer-matrix method.Unlike periodic structures, these aperiodic structures do not have a translation periodicity because they are formed by translation and rotation by an angle s2π of a given subunit cell, being s an irrational number.In this work, this structure is exemplified by a pin-loaded coaxial transmission line, and it cannot be directly analyzed using commercial software due to the lack of periodicity.The results indicate that the dispersion diagrams of this kind twist-symmetric structures lie between the dispersion diagrams of periodic structures with similar rotation angles.

In this work, we present a modeling methodology to solve the eigenvalue problem for periodic structures with a hexagonal lattice. The method is based on the previously proposed multi-modal transfer matrix method, which is a hybrid method that takes into account the coupling between the multiple modes of the ports surrounding the single unit cell. Commercial software can be used to obtain the generalized scattering parameters which are subsequently applied to set up and solve the eigenvalue problem of the periodic structure. This approach has the ability to obtain complex solutions and thus makes it possible to analyze the attenuation in the stopbands. Here, we extend the multimodal transfer matrix method to the efficient solution of the resulting eigenvalue problem for the case of a hexagonal lattice, detailing the selection of the appropriate supercells and the appropriate irreducible Brillouin zones. Two types of structures are analyzed: a mirror-symmetric structure and a glide-symmetric structure. Very good agreement is obtained with commercial software, limited to the real part of the dispersion diagrams.

This paper introduces a computationally efficient ray-tracing approach to study the radiation pattern of a leaky-wave antenna embedded in a lens with an arbitrary shape. The ray-tracing technique, based on geometrical optics, is used to calculate the phase and amplitude of the fields at the lens aperture, taking into account reflections due to the transition from the lens to the free space. To validate the results, the radiation patterns obtained in some examples are compared with full-wave simulations, demonstrating a considerable time reduction in the analysis of up to 99.6% in some cases.