Modelling of a geodesic lens antennas using a raytracing model

In order to meet the demands of low latency and high data rates, mobile networks are migrating to higher frequency bands. With increased frequency, both path and material losses increase as well creating a need for low loss and highly directive antennas. Fully metallic lens antennas offer an interesting solution to this problem. Lens antennas can provide a highly directive beam that can be steered using electronic switching, avoiding complex beam steering methods such as mechanical steering or phased arrays. Additionally, the fully metallic implementation of lenses mitigates material losses since no dielectric materials are needed. One possible way of realizing fully metallic lenses is by taking advantage of geodesic surfaces. These surfaces can mimic the refractive index of gradient-index dielectric lenses such as the Luneburg lens or the Maxwell-Fish Eye lens [M. Šabort & T. Tyc, “Spherical media and geodesic lenses in geometrical optics,” J. Opt., 2013]. Modeling these lenses in commercial full-wave simulation software is however time-consuming since lenses are typically large in terms of wavelength. It is, therefore, impractical to design such a lens using these simulation tools, especially if the lens is to be optimized for a certain performance, e.g. side-lobe levels or a desired beamwidth. A procedure that is efficient in terms of computational time while being sufficiently accurate is provided by the ray tracing technique. This technique has been widely used to study gradient-index dielectric lenses and is here applied to also deal with geodesic metallic lenses [R. F. Rinehart, “A family of designs for rapid scanning radar antennas,” Proc. IRE, vol. 40, no. 6, pp. 686–688, 1952]. A possible disadvantage of the design of lens antennas using geodesic surfaces, compared to e.g. metasurfaces, is the increased profile of the lens since the direction orthogonal to the beamforming plane is employed to generate the geodesic surface. A solution to this problem was long ago addressed in [K. S. Kunz, “Propagation of microwaves between a parallel pair of doubly curved conducting surfaces,” J. Appl. Phys., vol. 25, no. 5, pp. 642–653, 1954]. This author proposed to fold the geodesic surface so that the height profile was reduced without affecting the performance of the lens. Moreover, this folding can be applied any number of times to achieve the required compression. An important practical drawback caused by these foldings is the appearance of slope discontinuities at the folding locations. The profile in these regions should then be “smoothed” and, in doing so, the geodesic surface is being changed with the undesired risk of a degraded performance of the lens. To maintain the required performance of the lens, the profile used at the folding locations has to be optimized, but this task is rather impractical if carried out by means of full-wave commercial simulators. The raytracing technique is here a perfect candidate for a more efficient modeling. In summary, in this presentation a raytracing code will be presented capable of an efficient modeling a folded geodesic lens antennas. The results obtained by the code are then compared to results achieved by full-wave simulation software

Application of the multimodal transfer matrix method in dielectric periodic structures with higher symmetries

The Multimodal Transfer Matrix Method (MMTMM) is a hybrid method to compute the propagation constants of periodic structures that combines in-house/commercial software and later post-processing [1], [2]. Its main advantage over commercial eigensolvers is the possibility to find the attenuation constant not only due to material losses but also to electromagnetic bandgaps and/or radiation. However, thanks to the use of commercial software, any complex structure with different materials and/or arbitrary geometry can be analyzed, as opposed to other quasi-analytical and numerical approaches found in the literature such as circuit models [3] or mode matching [4]. The MMTMM models the unit cell of a periodic structure as a multiport network where each pair of ports accounts for a propagative/evanescent/leaky mode in the structure. This means that the coupling between higher order modes is considered in the simulation, which is more accurate in general, and essential in other cases, such as in the study of higher-symmetric periodic structures. In this work, we propose the use of the MMTMM to obtain the attenuation constant, as well as having a fundamental understanding of two periodic dielectric structures with higher symmetries. A periodic structure possesses a higher symmetry if it is invariant after more than one geometrical operator [5]. Two main spatial higher symmetries can be found in the literature: glide and twist. A glide-symmetric structure is invariant after a mirroring and a translation of half of the period. Differently, a periodic structure possesses twist symmetry after a number N of rotations and translations. The first structure under study is a glide-symmetric dielectric-filled corrugated waveguide. As previously reported in [6], this structure allows for the propagation of backward modes below the hollow waveguide cut-off frequency. This backward mode was analyzed with a convergence study of the MMTMM to investigate the waveguide modes that contribute to its propagation. The second structure under study is a twist-symmetric dielectric waveguide. In [7], it was reported that the employed three-fold configuration of this structure allows for the propagation of circularly-polarized modes that makes it polarization selective in a specific frequency band. This polarization selection band is characterized with the MMTMM to estimate the losses of both left and right-handed modes

Removing singular refractive indices with sculpted surfaces

Open Access JournalThe advent of Transformation Optics established the link between geometry and material properties, and has resulted in a degree of control over electromagnetic fields that was previously impossible. For waves confined to a surface it is known that there is a simpler, but related, geometrical equivalence between the surface shape and the refractive index, and here we demonstrate that conventional devices possessing a singularity - that is, the requirement of an infinite refractive index - can be realised for waves confined to an appropriately sculpted surface. In particular, we redesign three singular omnidirectional devices: the Eaton lens, the generalized Maxwell Fish-Eye, and the invisible sphere. Our designs perfectly reproduce the behaviour of these singular devices, and can be achieved with simple isotropic media of low refractive index contrast.Engineering and Physical Sciences Research Council (EPSRC

Efficient Integral Equation Approach for the Modelling of Glide-Symmetric Structures

For the design of advanced microwave and antenna components, efficient and accurate electromagnetic methods are required. In this work, we present a technique to fast simulate mirror- and glide-symmetric periodic structures. More concretely, a novel Green’s function is proposed which allows to reduce the computational domain to one half of the unit cell. Full dispersion diagrams are computed for metallic glide- and mirror-symmetric structures with three stages of mesh refinement. The results converge with the meshing and agree well with conventional eigenmode analyses

Transformation optics for antennas: why limit the bandwidth with metamaterials?

This work is part funded by the Ministry of Defence and is published with the permission of the Defence Science and Technology Laboratory on behalf of the Controller of HMSO

Realising superoscillations: A review of mathematical tools and their application

Superoscillations are making a growing impact on an ever-increasing number of real-world applications, as early theoretical analysis has evolved into wide experimental realisation. This is particularly true in optics: the first application area to have extensively embraced superoscillations, with much recent growth. This review provides a tool for anyone planning to expand the boundaries in an application where superoscillations have already been used, or to apply superoscillations to a new application. By reviewing the mathematical methods for constructing superoscillations, including their considerations and capabilities, we lay out the options for anyone wanting to construct a device that uses superoscillations. Superoscillations have inherent trade-offs: as the size of spot reduces, its relative intensity decreases as high-energy sidebands appear. Different methods provide solutions for optimising different aspects of these trade-offs, to suit different purposes. Despite numerous technological ways of realising superoscillations, the mathematical methods can be categorised into three approaches: direct design of superoscillatory functions, design of pupil filters and design of superoscillatory lenses. This categorisation, based on mathematical methods, is used to highlight the transferability of methods between applications. It also highlights areas for future theoretical development to enable the scientific and technological boundaries to be pushed even further in real-world applications

Roadmap on Transformation Optics

Transformation Optics asks Maxwell's equations what kind of electromagnetic medium recreate some smooth deformation of space. The guiding principle is Einstein's principle of covariance: that any physical theory must take the same form in any coordinate system. This requirement fixes very precisely the required electromagnetic medium. The impact of this insight cannot be overestimated. Many practitioners were used to thinking that only a few analytic solutions to Maxwell's equations existed, such as the monochromatic plane wave in a homogeneous, isotropic medium. At a stroke, Transformation Optics increases that landscape from `few' to `infinity', and to each of the infinitude of analytic solutions dreamt up by the researcher, corresponds an electromagnetic medium capable of reproducing that solution precisely. The most striking example is the electromagnetic cloak, thought to be an unreachable dream of science fiction writers, but realised in the laboratory a few months after the papers proposing the possibility were published. But the practical challenges are considerable, requiring meta-media that are at once electrically and magnetically inhomogeneous and anisotropic. How far have we come since the first demonstrations over a decade ago? And what does the future hold? If the wizardry of perfect macroscopic optical invisibility still eludes us in practice, then what compromises still enable us to create interesting, useful, devices? While 3D cloaking remains a significant technical challenge, much progress has been made in 2- dimensions. Carpet cloaking, wherein an object is hidden under a surface that appears optically flat, relaxes the constraints of extreme electromagnetic parameters. Surface wave cloaking guides sub-wavelength surface waves, making uneven surfaces appear flat. Two dimensions is also the setting in which conformal and complex coordinate transformations are realisable, and the possibilities in this restricted domain do not appear to have been exhausted yet. Beyond cloaking, the enhanced electromagnetic landscape provided by Transformation Optics has shown how fully analytic solutions can be found to a number of physical scenarios such as plasmonic systems used in electron energy loss spectroscopy (EELS) and cathodoluminescence (CL). Are there further fields to be enriched? A new twist to Transformation Optics was the extension to the space-time domain. By applying transformations to space-time, rather than just space, it was shown that events rather than objects could be hidden from view; Transformation Optics had provided a means of effectively redacting events from history. The hype quickly settled into serious nonlinear optical experiments that demonstrated the soundness of the idea, and it is now possible to consider the practical implications, particularly in optical signal processing, of having an `interrupt-without-interrupt' facility that the so-called temporal cloak provides. Inevitable issues of dispersion in actual systems have only begun to be addressed. Now that time is included in the programme of Transformation Optics, it is natural to ask what role ideas from General Relativity can play in shaping the future of Transformation Optics. Indeed, one of the earliest papers on Transformation Optics was provocatively titled `General Relativity in Electrical Engineering'. The answer that curvature does not enter directly into transformation optics merely encourages us to speculate on the role of Transformation Optics in defining laboratory analogues. Quite why Maxwell's theory defines a `perfect' transformation theory, while other areas of physics such as acoustics are not apparently quite so amenable, is a deep question whose precise, mathematical answer will help inform us of the extent to which similar ideas can be extended to other fields. The contributors to this roadmap review, who are all renowned practitioners or inventors of Transformation Optics, will give their perspectives into the field's status and future development

Printable all-dielectric water-based absorber

Abstract The phase interplay between overlapping electric and magnetic dipoles of equal amplitude generated by exclusively alldielectric structures presents an intriguing paradigm in the manipulation of electromagnetic energy. Here, we offer a holistic implementation by proposing an additive manufacturing route and associated design principles that enable the programming and fabrication of synthetic multi-material microstructures. In turn, we compose, manufacture and experimentally validate the first demonstrable 3d printed all-dielectric electromagnetic broadband absorbers that point the way to circumventing the technical limitations of conventional metal-dielectric absorber configurations. One of the key innovations is to judicially distribute a dispersive soft matter with a high-dielectric constant, such as water, in a low-dielectric matrix to enhance wave absorption at a reduced length scale. In part, these results extend the promise of additive manufacturing and illustrate the power of topology optimisation to create carefully crafted magnetic and electric responses that are sure to find new applications across the electromagnetic spectrum