Transformation Optics Research Articles

Quasi-Optical Multi-Beam Antenna Technologies for B5G and 6G mmWave and THz Networks: A Review

Multi-beam antennas are critical components in future terrestrial and non-terrestrial wireless communications networks. The multiple beams produced by these antennas will enable dynamic interconnection of various terrestrial, airborne and space-borne network nodes. As the operating frequency increases to the high millimeter wave (mmWave) and terahertz (THz) bands for beyond 5G (B5G) and sixth-generation (6G) systems, quasi-optical techniques are expected to become dominant in the design of high gain multi-beam antennas. This paper presents a timely overview of the mainstream quasi-optical techniques employed in current and future multi-beam antennas. Their operating principles and design techniques along with those of various quasi-optical beamformers are presented. These include both conventional and advanced lens and reflector based configurations to realize high gain multiple beams at low cost and in small form factors. New research challenges and industry trends in the field, such as planar lenses based on transformation optics and metasurface-based transmitarrays, are discussed to foster further innovations in the microwave and antenna research community.

Calculating Millimeter-Wave Modes of Copper Twisted-Pair Cables Using Transformation Optics

Recent research has indicated considerable potential for millimeter-waves in copper access, with data-rate estimations up to 1 Terabit per second for a reach of 100 m. This line of research exploits millimeter-waves and their corresponding higher-order propagation modes inside the twisted pair cable binder. Unlike the conventionally used transmission-line mode (currents through copper wires), the approach relies on the copper and plastics present in these cables to form a low-loss waveguide. Here, we take a closer look at the potential of millimeter-wave propagation in twisted pair cables by refining the idealized assumptions, used by Cioffi et al. , and identifying the limiting factors. To this end, we introduce the concept of transformation optics as an efficient method of calculating the propagating modes on a twisted pair. Leveraging this technique allows us to calculate modal propagation using realistic material parameters, exposing an important trade-off between loss and confinement. Our modeling results yield achievable data rates that are orders of magnitude lower than those achieved under idealized assumptions. According to our results, 1 Terabit per second can be achieved up to a distance of about 10 m over a twisted-pair with a plastic sheath.

Pseudo‐Hermitian Systems Constructed by Transformation Optics with Robustly Balanced Loss and Gain

Non‐Hermitian systems with parity‐time symmetry are found to exhibit real spectra of eigenvalues, indicating a balance between the loss and gain. However, such a balance is not only dependent on the magnitude of loss and gain but also easily broken due to external disturbance. Herein, a transformation‐optics approach is proposed to construct a unique class of non‐Hermitian systems with robustly balanced loss and gain, irrespective of the magnitude of loss/gain and the environmental disturbance. Through transformation‐optics operators such as space folding and stretching, loss and gain can be generated and separated in the real space. However, in the virtual space, the loss and gain are still combined to each other, rendering a balance of energy that is far more robust than other non‐Hermitian systems. This amazing feature is verified by finite‐element simulations. This work reveals a class of non‐Hermitian systems in which loss and gain are balanced robustly, thereby denoted as pseudo‐Hermitian systems.

Transformation optics for plasmonics: from metasurfaces to excitonic strong coupling

Nous passons en revue les dernières avancées dans l’application du cadre de l’optique transformationnelle pour la description analytique des phénomènes électromagnétiques en régime fortement sub-longueur d’onde. En premier lieu, nous présentons une description générale de la technique, ainsi que son exploitation usuelle dans la conception et l’optimisation des métamatériaux dans différentes disciplines de la physique des ondes. En second lieu, nous discutons en détail de la conception de métasurfaces plasmoniques, y compris la description de géométries singulières qui permettent une absorption sur une large plage de fréquences dans les plates-formes ultra-minces. Enfin, nous discutons du traitement quasi-analytique du couplage fort plasmon–exciton dans les nanocavités au niveau d’un seul émetteur.

Reflectionless spatial beam benders with arbitrary bending angle by introducing optic-null medium into transformation optics* *Project supported by the National Natural Science Foundation of China (Grant Nos. 61971300, 11604292, 61905208, 11674239, and 11621101), the Scientific and Technological Innovation Programs (STIP) of Higher Education Institutions in Shanxi Province, China (Grant Nos. 2019L0159 and 2019L0146), and the Postdoctoral Science Foundation of China

By introducing an optic-null medium into the finite embedded transformation, a reflectionless spatial beam bender is designed, which can steer the output beam by a fixed pre-designed angle β for an arbitrary incident angle. The bending angle β of the beam bender is determined by the geometrical angle of the device, which can be changed by simply choosing different geometrical angles. For various bending angles, the designed spatial beam bender can be realized by the same materials (i.e., an optic-null medium), which is a homogenous anisotropic material. Numerical simulations verify the reflectionless bending effect and rotated imaging ability of the proposed beam bender. A reduction model of the optic-null medium is studied, which can also be used for a reflectionless spatial beam bender with a pre-designed bending angle.

WITHDRAWN: Transformation electromagnetics: Mathematical viewpoint

Abstract Coordinate transformation of electromagnetic field relations by specific mathematical model or technique acquired great attention in twenty-first century electromagnetic devices modelling. The Transformation Electromagnetics [TFEM] has another familiar name transformation optics [TFO]. The building block concept of TFEM is that Maxwell equations do not change their form when the coordinates are transformed. TFEM based device design mainly uses artificial materials such as DNG (Double Negative), EBG (Electromagnetic Bandgap) materials. The material properties may change with coordinate transformation; still Maxwell equations do not change their form. The steps involved in their mathematical modelling are discussed in this paper.

Surface wave direction control on curved surfaces

Transformation optics (TO) has been recognized as an established scheme that can precisely manipulate electromagnetic surface wave propagations. Utilising the advantages of the TO technique, we proposed a TO device which can control the propagation direction of surface waves. The device is based on a generalized Eaton lens and can be realized on curved surfaces. Such a device can be composed of stacked ring layers, where the refractive index of each ring segment can be individually engineered. By engineering the refractive index, the stacked ring structure can guide the propagation direction of the surface wave. It may open a new door to manipulate surface wave propagation on demand.

Compact and broadband multimode waveguide bend by shape-optimizing with transformation optics

Multimode waveguide bend is one of the key components for realizing high-density mode-division multiplexing systems on chip. However, the reported multimode waveguide bends are either large, bandwidth-limited or fabrication-complicated, which hinders their applications in future high-density multimode photonic circuits. Here we propose a compact multimode waveguide bend supporting four TE modes simply by shape-optimizing with transformation optics. The shape of the waveguide is optimized in the virtual space with gradient distribution of the refractive index, so that the scattering loss and intermode cross talk are well suppressed. After conformal mapping back into the physical space, a compact (effective radius of 17 μm) multimode bending waveguide is obtained. Simulations show that the proposed multimode waveguide bend has little loss ( < 0.1 dB ) and low cross talk ( < − 20 dB ) throughout an ultrabroad wavelength range of 1.16–1.66 μm. We also fabricated the shape-optimized multimode bending waveguide on a silicon-on-insulator wafer. At 1550 nm wavelength, the measured excess losses for the four lowest-order TE modes are less than 0.6 dB, and the intermode cross talks are all below − 17 dB . Our study paves the way for realizing high-density and large-scale multimode integrated optical circuits for optical interconnect.

Deterministic design of focusing apodized subwavelength grating coupler based on weak form and transformation optics.

The focusing apodized subwavelength grating coupler (F-ASGC) has advantages of high coupling efficiency, small footprint and simple fabrication process, which make it a popular component for chip-scale coupling and testing of integrated optical circuit. However, the design of F-ASGC based on effective medium theory lacks accuracy, causing the drawbacks of peak wavelength deviation and performance degradation. In this work, we propose a deterministic design method of F-ASGC. Our grating coupler is formed by assembling various subwavelength grating units according to their complex effective indexes. The complex effective indexes of these grating units are accurately obtained by the weak form calculation. Then combining with transformation optics, we strictly analyze the F-ASGC for the first time. The simulation results show that the deterministically designed F-ASGC has high coupling efficiency of -2.51 dB, 3 dB bandwidth of 51 nm, and accurate central wavelength of 1553.1 nm. And we also fabricated it on the commercial SOI wafer. The measured maximum efficiency is -3.10 dB, the 3 dB bandwidth is 55 nm, and the central wavelength is 1551.5 nm.

Asymmetric universal invisible gateway.

Previous invisible gateways are mainly based on super-scattering effect, which can only work for the perfect electric conductor (PEC) wall, while no further exploration is conducted for the walls made of other materials (i.e., the actual wall is not PEC). In this study, we design an asymmetric universal invisible gateway by transformation optics, which is versatile for applying arbitrary materials as wall materials. In addition, its unique asymmetric structure leads to the difference of the detection results when the relative position of the detection source and the invisible gateway changes: one side can only see a complete wall (no gateway) and the other side can detect the gateway in the middle of the wall. This research advances a new step for the specific application of invisible gateway.

Modes computation in arbitrarily shaped waveguides by a transformation optics approach

Modes computation in arbitrarily shaped waveguides by a transformation optics approach

Numerical analysis of a finite element method for the electromagnetic concentrator model

In this paper, we consider the electromagnetic concentrator model obtained through transformation optics. This model is formed by a system of coupled time-dependent Maxwell’s equations with three unknowns, which makes the analysis and simulation much more challenging compared to the standard Maxwell equations. In our previous work (W. Yang, J. Li, Y. Huang, and B. He, Commun. Comput. Phys., 25(1), pp. 135–154, 2019), we proposed a finite element time-domain (FETD) method with edge elements for solving this model efficiently without any theoretical analysis. Here, we provide a rigorous analysis for the mathematical modelling equations and the FETD method proposed there.

Design of continuously variant metasurfaces for conformal transformation optics.

Metasurfaces optics and structured light represent two emerging paradigms which are revolutionizing optics in a wide range of fields, from imaging to telecommunications, both in the classical and single-photon regimes. In this work, we present and describe a method for the design of high-resolution geometric-phase metasurfaces in the form of continuously variant sub-wavelength gratings, and we demonstrate how this technique is suitable for harmonic phase masks implementing conformal optical transformations. In this framework, we revisit the metasurface design of blazed gratings and spiral phase plates, the so-called q-plates, and we extend the method to the metasurface implementation of two conformal mappings, the log-pol and the circular-sector transformation, which have been exploited successfully to perform the generation, sorting and manipulation of structured light beams carrying orbital angular momentum.

Design and finite element simulation of information-open cloaking devices

In this paper, based on the transformation optics theory as well as the complementary media ideas, we design a novel type of information-open (IO) cloaking devices by using nonlinear coordinate transformations. Finite element methods are used to design layered IO cylindrical cloaking devices. The equidistant and hierarchical layered designs of the IO cloaking devices are considered, and their cloaking performances are verified. Finally, by comparing the finite element numerical results, we find that satisfactory IO cloaking performances can be obtained with fewer layers by the hierarchical layered design. As far as we know, this is the first work on the hierarchical design of IO cloaking devices via nonlinear transformations.

Photonic Fractal Metamaterials: A Metal–Semiconductor Platform with Enhanced Volatile‐Compound Sensing Performance

Advance of photonics media is restrained by the lack of structuring techniques for the 3D fabrication of active materials with long-range periodicity. A methodology is reported for the engineering of tunable resonant photonic media with thickness exceeding the plasmonic near-field enhancement region by more than two orders of magnitude. The media architecture consists of a stochastically ordered distribution of plasmonic nanocrystals in a fractal scaffold of high-index semiconductors. This plasmonic-semiconductor fractal media supports the propagation of surface plasmons with drastically enhanced intensity over multiple length scales, overcoming the 2D limitations of established metasurface technologies. The fractal media are used for the fabrication of plasmonic optical gas sensors, achieving a limit of detection of 0.01 vol% at room temperature and sensitivity up to 1.9nm vol%-1 , demonstrating almost a fivefold increase with respect to an optimized planar geometry. Beneficially to their implementation, the self-assembly mechanism of this fractal architecture allows fabrication of micrometer-thick media over surfaces of several square centimeters in a few seconds. The designable optical features and intrinsic scalability of these photonic fractal metamaterials provide ample opportunities for applications, bridging across transformation optics, sensing, and light harvesting.

Natural granular pile as electromagnetic ground cloak

Rendering an object invisible through a cloaking device is an ongoing dream of human beings and material scientists. Recently, intensive theories and experiments have predicted and demonstrated that such a cloaking device can be realized based on transformation optics and metamaterials, in fields of electromagnetics, optics acoustics, or even heat transfer. Metamaterials enable precise control over the propagation of waves due to their delicate micro-structures and spatially tailorable properties. However, a simple and natural way to achieve cloaking without a delicate micro-structure remains unattainable. Here, we report that an electromagnetic quasi-cloaking device can be readily achieved by a granular pile, formed by the falling-off and cumulation of particles on the object to be cloaked. We show that natural particle size segregation during the formation of the granular pile imparts the pile with a spatially variable filling ratio and resultant gradient-distributed permittivity, which enables the realization of the electromagnetic cloaking device. This work may open the possibility that a complicated electromagnetic device may be alternately achieved from manipulation of particle movement or arrangement.

Limitations and potentials of generalized Veselago-Pendry lenses

We study the imaging performance of anisotropic generalized Veselago–Pendry (GVP) lenses derived via complex transformation optics technique. The derived material tensors of such generalized lenses can be controlled via a complex coordinate transformation parameter resulting in an anisotropic constitutive tensor with loss/gain characteristics. We discuss their limitations and potentials based on the parametric analysis of material properties. We show that, although GVP lenses are not affected by the loss/gain level, akin to conventional VP lenses, their subwavelength imaging performance is also susceptible to material deviations from their original values. We also discuss that the resolution of GVP lenses can be significantly improved by tuning the real part of the transformation parameter. The proposed GVP lenses could be realized using, for instance, a metal-dielectric structure, with improved subwavelength imaging characteristics.

Angularly Dispersionless Scattering Patterns for Impenetrable Surfaces: A straightforward design based on transformation optics

Utilizing transformation optics (TO) methodology, we propose a feasible and straightforward approach to control the scattering pattern of impenetrable surfaces in the desired manner. As a great advantage not reported in previous studies, the presented coating layer can scatter multiple arbitrarily oriented beams whose directions are not affected by the frequency variation, namely as angularly dispersionless scattering. We benefit from the simplicity of classic geometrical optics (GO) as a design tool to avoid the complex procedure of the material derivation resulting from TO. Inspired by irregularities in rough surfaces, we propose a coating layer mimicking the scattering behavior of rough surfaces with high abilities to generate different far-field patterns with arbitrary beam numbers along the desired directions. Moreover, two interesting functionalities, i.e., anomalous reflection and retroreflection, are designed using the proposed coating layer. The material parameters of the proposed coating layer are numerically derived by solving the inverse Laplace equation. Our idea is further extended to design a scattering diffusion device with the quasi-isotropic pattern, which is applicable in radar cross-section reduction. As a demonstration, an anomalous reflector is implemented with an all-dielectric, lossless, and broadband coating layer. The experimental results are in good agreement with the numerical simulations.

Hybrid nonsingular mappings in the multi-objective design of a transverse-magnetic reduced cloak

This paper describes the integrated use of two design strategies for controlling the permittivity and permeability of a transformation electromagnetics two-dimensional cloak. This hybrid process permits more freedom in the choice of the constitutive properties, which could simplify the implementation with metamaterials. Because simplicity of materials and scattering performance are inherently conflicting characteristics, a multi-objective genetic algorithm is applied to optimize them. According to the presented results for a transverse-magnetic layered cloak, it is possible to have a good performance in terms of scattering even with an approximated reduced set of parameters with unitary axial permeability.

Glide-Symmetric Metallic Structures With Elliptical Holes for Lens Compression

In this article, we study the wave propagation in a metallic parallel-plate structure with glide-symmetric elliptical holes. To perform this study, we derived a mode-matching technique based on the generalized Floquet theorem for glide-symmetric structures. This mode-matching technique benefits from a lower computational cost since it takes advantage of the glide symmetry in the structure. It also provides physical insight into the specific properties of Floquet modes propagating in these specific structures. With our analysis, we demonstrate that glide-symmetric structures with periodic elliptical holes exhibit an anisotropic refractive index over a wide range of frequencies. The equivalent refractive index can be controlled by tuning the dimensions of the holes. Finally, by combining the anisotropy related to the elliptical holes and transformation optics, a Maxwell fish-eye (MFL) lens with a 33.33% size compression is designed. This lens operates in a wideband frequency range from 2.5 to 10 GHz.