Concept Of Transformation Optics Research Articles

Temporary Singularities and Axions: An Analytic Solution that Challenges Charge Conservation

AbstractAn analytic solution for electromagnetic fields interacting with an axion field that violates global charge conservation is constructed. Despite providing a specific example where “physics breaks down” at a singularity, it nevertheless demonstrates that the physical laws on the surrounding spacetime still impose constraints on what is allowed to happen. The construction is valid for a spacetime containing a temporary singularity and a Maxwellian electrodynamics containing a proposed “topological” axion field. Further, the concepts of transformation optics can be applied to show that our specific mathematical solution has a much wider applicability.

A Phased Array Antenna with New Elements Designed Using Source Transformations

Transformation electromagnetics/optics (TE/TO) has been shown to be a useful technique in designing electromagnetic devices with very unique properties. Here, the concepts of transformation optics for single elements is extended to an array of “pinwheel” shaped elements for the first time. Through full-wave finite element analysis (FEA), it is shown that a transformed “pinwheel” linear array can be designed to operate identically to a uniformly spaced linear dipole array. Thus, the “pinwheel” antenna array will maintain all the advantages of array processing of a simple dipole antenna array. The proposed method has applications in structurally integrated and conformal phased arrays for wireless communications, radars, and sensing where structural and mechanical constrains do not align with antenna performance.

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.

Assembled medium: A route to the generation of vortex waves carrying orbital angular momentum with different modes

In this letter, a method for the generation of multimodal vortex waves carrying orbital angular momentum (OAM) is proposed based on the transformation optics concept. The device is equally divided into eight sectors assigned by transformed material parameters, which are determined by solving Laplace’s equation. Sectors with different phase variations from 0 to 2π can be judiciously shuffled to generate vortex beams with different modes. Full wave numerical simulations are performed to validate multimodal OAM beam generation functionality and broadband performance of the proposed device. Such an implementation method opens the door to the application of vortex waves carrying OAM in communication systems.

Compacted dimensions and singular plasmonic surfaces

In advanced field theories, there can be more than four dimensions to space, the excess dimensions described as compacted and unobservable on everyday length scales. We report a simple model, unconnected to field theory, for a compacted dimension realized in a metallic metasurface periodically structured in the form of a grating comprising a series of singularities. An extra dimension of the grating is hidden, and the surface plasmon excitations, though localized at the surface, are characterized by three wave vectors rather than the two of typical two-dimensional metal grating. We propose an experimental realization in a doped graphene layer.

How to hide a dimension from view

Transformation Optics Compacted dimensions are essential ingredients of advanced string theories; the extra dimensions used to describe the world are hidden from view, or compacted. Pendry et al. used concepts of transformation optics, in which metamaterials are designed to produce specific optical properties, to show theoretically that compacted dimensions could be possible in plasmonic structures. For example, simulations with a metallic grating and periodically doped graphene revealed that two-dimensional structures exhibit optical properties of a bulk material. To all intents and purposes, it looks as if one of the dimensions is compacted. The results could have practical application in designing broadband optical absorbers. Science , this issue p. [915][1] [1]: /lookup/doi/10.1126/science.aap7939

Electromagnetic field tapering using all-dielectric gradient index materials.

The concept of transformation optics (TO) is applied to control the flow of electromagnetic fields between two sections of different dimensions through a tapering device. The broadband performance of the field taper is numerically and experimentally validated. The taper device presents a graded permittivity profile and is fabricated through three-dimensional (3D) polyjet printing technology using low-cost all-dielectric materials. Calculated and measured near-field mappings are presented in order to validate the proposed taper. A good qualitative agreement is obtained between full-wave simulations and experimental tests. Such all-dielectric taper paves the way to novel types of microwave devices that can be easily fabricated through low-cost additive manufacturing processes.

Transformation optics for the validation of a time-domain full-wave model of linear complex media

Complex media have gained interest in microwave and millimeter-wave devices. They display some interesting characteristics such as, for instance, tunability and controlled filtering capacity. However, such media are generally very complex as they can be fully nonhomogeneous; frequency dependent, anisotropic, time dependent, or chiral. This requires simulation techniques capable of solving Maxwell’s equations accounting for such media. Also, apart comparison with rather difficult measurement, canonical solutions are not available for validation. In this paper, the concept of transformation optics (TO) is presented as a systematic tool to construct computational problems involving complex media for which the analytical solution is known. Several examples are shown for validation of a new transmission-line matrix (TLM) cell that model complex media.

Surface Wave Cloak from Graded Refractive Index Nanocomposites.

Recently, a great deal of interest has been re-emerged on the possibility to manipulate surface waves, in particular, towards the THz and optical regime. Both concepts of Transformation Optics (TO) and metamaterials have been regarded as one of key enablers for such applications in applied electromagnetics. In this paper, we experimentally demonstrate for the first time a dielectric surface wave cloak from engineered gradient index materials to illustrate the possibility of using nanocomposites to control surface wave propagation through advanced additive manufacturing. The device is designed analytically and validated through numerical simulations and measurements, showing good agreement and performance as an effective surface wave cloak. The underlying design approach has much wider applications, which span from microwave to optics for the control of surface plasmon polaritons (SPPs) and radiation of nanoantennas.

Distant and wide range wireless power transfer from metamedia

Based on electromagnetic scattering theory, a model of superscatterer enhanced distant wireless power transfer (WPT) device has designed and analyzed with the concept of transformation optics. The numerical results obtained through a series expansion method reveal that a properly designed ss-WPT has high efficiency for long transfer distances as well as a wide transfer range. The transfer distance can be further enlarged by fine tuning of the design. These effects can be explained qualitatively through the study of magnetic flux.

Restoring in-phase emissions from non-planar radiating elements using a transformation optics based lens

The broadband directive in-phase emission from an array of sources conformed cylindrically is numerically and experimentally reported. Such manipulation is achieved through the use of a lens designed by transformation optics concept. The all-dielectric lens prototype is realized through three-dimensional (3D) polyjet printing and presents a graded refractive index. A microstrip antenna array fabricated using standard lithography techniques and conformed on a cylindrical surface is used as TE-polarized wave launcher for the lens. To experimentally demonstrate the broadband focusing properties and in-phase directive emissions, both the far-field radiation patterns and the near-field distributions have been measured. Experimental measurements agreeing qualitatively with numerical simulations validate the proposed lens and open the way to inexpensive all-dielectric microwave lenses for beam forming and collimation.

Photonic skin-depth engineering

Recently we proposed a paradigm shift in light confinement strategy showing how relaxed total internal reflection and photonic skin-depth engineering can lead to sub-diffraction waveguides without metal (S. Jahani and Z. Jacob, "Transparent sub-diffraction optics: nanoscale light confinement without metal," Optica 1, 96-100 (2014)). Here, we show that such extreme-skin-depth (e-skid) waveguides can counter-intuitively confine light better than the best-case all-dielectric design of high index silicon waveguides surrounded by vacuum. We also analytically establish that figures of merit related to light confinement in dielectric waveguides are fundamentally tied to the skin depth of waves in the cladding, a quantity surprisingly overlooked in dielectric photonics. We contrast the propagation characteristics of the fundamental mode of e-skid waveguides and conventional waveguides to show that the decay constant in the cladding is dramatically larger in e-skid waveguides, which is the origin of sub-diffraction confinement. We also propose an approach to verify the reduced photonic skin depth in experiment using the decrease in the Goos-Hanschen phase shift. Finally, we provide a generalization of our work using concepts of transformation optics where the photonic-skin depth engineering can be interpreted as a transformation on the momentum of evanescent waves.

Realization of deep subwavelength resolution with singular media.

The record of imaging resolution has kept being refreshed in the past decades and the best resolution of hyperlenses and superlenses so far is about one out of tens in terms of wavelength. In this paper, by adopting a hybrid concept of transformation optics and singular media, we report a broadband meta-lens design methodology with ultra-high resolution. The meta-lens is made of subwavelength metal/air layers, which exhibit singular medium property over a broad band. As a proof of concept, the subwavelength imaging ability is demonstrated over a broad frequency band from 1.5–10 GHz with the resolution varying from 1/117 to 1/17 wavelength experimentally.

Reducing physical appearance of electromagnetic sources

We propose to use the concept of transformation optics for the design of novel radiating devices. By applying transformations that compress space, and then that match it to the surrounding environment, we show how the electromagnetic appearance of radiating elements can be tailored at will. Our efficient approach allows one to realize a large aperture emission from a small aperture one. We describe transformation of the metric space and the calculation of the material parameters. Full wave simulations are performed to validate the proposed approach on different space compression shapes, factors and impedance matching. The idea paves the way to interesting applications in various domains in microwave and optical regimes, but also in acoustics.

Numerical and experimental demonstration of a coordinate transformation‐based azimuthal directive emission

AbstractThis article deals with the modeling, practical implementation, and characterization of an azimuthal directive antenna around 10 GHz. The design of the antenna is based on transformation optics concept by transforming the radiation of a plane source into an azimuthal radiation. This coordinate transformation procedure is achieved by modifying the electromagnetic properties of the space around the plane source. Metamaterials presenting electric and magnetic resonances are used to produce the effective material parameters necessary for the transformation. S11 parameter and direct far‐field measurements are performed on a fabricated prototype to experimentally demonstrate the narrow beam profile and the beam deflection. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:2536–2540, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27122

Nonlinear transformation optics and engineering of the Kerr effect

The concept of transformation optics is extended to nonlinear electrodynamics. It is shown that transformation optics favors implicit constitutive relations in terms of energy densities D.E and B.H rather than E^2 and H^2. The Kerr nonlinearity is studied in detail and the transformation optics based engineering of self-interaction effects is discussed. As a specific example we introduce transformation optics applied on a self-focusing field configuration.

Coordinate-transformation-based ultra-directive emission

The modelling, practical implementation and characterisation of an ultra-directive antenna around 10 GHz are presented. The design of the antenna is based on the transformation optics concept by transforming a radiating cylindrical space into a rectangular one. Metamaterials presenting electric and magnetic resonances are used to achieve the transformation. Field intensity mappings and direct far-field measurements are performed to experimentally demonstrate the narrow beam profile.

Design of optical cloaks and illusion devices along a circumferential direction in curvilinear coordinates

We propose a cloaking and illusion device of circumferential topology based on the concept of transformation optics. The device is capable to cloak an object and/or simultaneously generate illusion images along a circumferential direction in curvilinear orthogonal coordinates. This feature allows us to construct multiple illusions in different ways, irrespective of the profile and direction of incident wave. Particularly when the device is served as a building brick of a larger device, one can generate a circumferential array of illusions in a periodic or any preferred pattern. We demonstrate the effectiveness of the proposed illusion devices by carrying out full wave simulations based on finite element calculations.

Extreme non-linear elasticity and transformation optics

Transformation optics is a powerful concept for designing novel optical components such as high transmission waveguides and cloaking devices. The selection of specific transformations is a non-unique problem. Here we reveal that transformations which allow for all dielectric and broadband optical realizations correspond to minimizers of elastic energy potentials for extreme values of the mechanical Poisson's ratio ν. For TE (Hz) polarized light an incompressible transformation ν = 1/2 is ideal and for TM (Ez) polarized light one should use a compressible transformation with negative Poissons's ratio ν = -1. For the TM polarization the mechanical analogy corresponds to a modified Liao functional known from the transformation optics literature. Finally, the analogy between ideal transformations and solid mechanical material models automates and broadens the concept of transformation optics.

Transformation Optics for Plasmonics

A new strategy to control the flow of surface plasmon polaritons at metallic surfaces is presented. It is based on the application of the concept of transformation optics to devise the optical parameters of the dielectric medium placed on top of the metal surface. We describe the general methodology for the design of transformation optical devices for surface plasmons and analyze, for proof-of-principle purposes, three representative examples with different functionalities: a beam shifter, a cylindrical cloak, and a ground-plane cloak.