Transformation Optics, Generalized Cloaking and Superlenses
Andre Nicolet, Frederic Zolla, Christophe Geuzaine
备注：
7 pages (two columns), 9 figures, to appear in IEEE Trans. Mag., invited paper in Compumag 2009 (Florianopolis, Brasil), corresponding slides available on http://www.fresnel.fr/perso/nicolet/
In this paper, transformation optics is presented together with a generalization of invisibility cloaking: instead of an empty region of space, an inhomogeneous structure is transformed via Pendry's map in order to give, to any object hidden in the central hole of the cloak, a completely arbitrary appearance. Other illusion devices based on superlenses considered from the point of view of transformation optics are also discussed.
In this paper, a generalization of cloaking is presented: instead of an empty region of space, an inhomogeneous structure is transformed via Pendry's map in order to give, to any object hidden in the central hole of the cloak, a completely arbitrary appearance.
Transformation optics is a design tool that connects geometry of space and propagation of light. Invisibility cloaking is a corresponding benchmark example. Recent experiments at optical frequencies have demonstrated cloaking for the light amplitude ("ray cloaking"). In this Letter, we demonstrate far-field cloaking of the light phase ("wave cloaking") by interferometric microscope-imaging experiments on the previously introduced three-dimensional carpet cloak at 700-nm wavelength and for arbitrary polarization of light.
Despite much interest and progress in optical spatial cloaking, a three-dimensional (3D), transmitting, continuously multidirectional cloak in the visible regime has not yet been demonstrated. Here we experimentally demonstrate such a cloak using ray optics, albeit with some edge effects. Our device requires no new materials, uses isotropic off-the-shelf optics, scales easily to cloak arbitrarily large objects, and is as broadband as the choice of optical material, all of which have been challenges for current cloaking schemes. In addition, we provide a concise formalism that quantifies and pr…
Transformation optics, a recent geometrical design strategy of controlling light by combining Maxwell's principles of electromagnetism with Einstein's general relativity, promises without precedent an invisibility cloaking device that can render a macroscopic object invisible in three dimensions. However, most previous proof-of-concept transformation-optics cloaking devices focused predominantly on two dimensions, whereas detection of a macroscopic object along its third dimension was always unfailing. Here, we report the first experimental demonstration of transformation-optics macroscopic vi…
We investigate two-dimensional invisibility cloaking via transformation optics approach. The cloaking media possess much more singular parameters than those having been considered for three-dimensional cloaking in literature. Finite energy solutions for these cloaking devices are studied in appropriate weighted Sobolev spaces. We derive some crucial properties of the singularly weighted Sobolev spaces. The invisibility cloaking is then justified by decoupling the underlying singular PDEs into one problem in the cloaked region and the other one in the cloaking layer. We derive some completely n…
We show that it is possible to design an invisible wavelength-sized metal-dielectric metamaterial object without evoking cloaking. Our approach is an extension of the neutral inclusion concept by Zhou and Hu [Phys.Rev.E 74, 026607 (2006)] to Mie scatterers. We demonstrate that an increase of metal fraction in the metamaterial leads to a transition from dielectric-like to metal-like scattering, which proceeds through invisibility or optical neutrality of the scatterer. Formally this is due to cancellation of multiple scattering orders, similarly to plasmonic cloaking introduced by Alu and Enghe…
The advent of transformation optics has lead to the initiation of designing devices and applications associated to electromagnetic wave propagation in anisotropic media. Here, a method is suggested using a coordinate transformation with spherical coordinates for the purpose of designing a three dimensional cloak for a body having an arbitrary convex geometry. For the purpose of verification of the algorithm, a ray tracing process is carried out for an ellipsoid having axial symmetry.
Non-Euclidean geometry combined with transformation optics has recently led to the proposal of an invisibility cloak that avoids optical singularities and therefore can work, in principle, in a broad band of the spectrum [U. Leonhardt and T. Tyc, Science 323, 110 (2009)]. Such a cloak is perfect in the limit of geometrical optics, but not in wave optics. Here we analyze, both analytically and numerically, full wave propagation in non-Euclidean cloaking. We show that the cloaking device performs remarkably well even in a regime beyond geometrical optics where the device is comparable in size wi…
Conventional cloaking based on Euclidean transformation optics requires that the speed of light should tend to infinity on the inner surface of the cloak. Non-Euclidean cloaking still needed media with superluminal propagation. Here we show by giving an example that this is no longer necessary.
The suggestive idea of "cloaking" an electromagnetic sensor, i.e., strongly reducing its visibility (scattering) while maintaining its field-sensing (absorption) capabilities, has recently been proposed in the literature, based on scattering-cancellation, Fano-resonance, or transformation-optics approaches. In this paper, we explore an alternative, transformation-optics-based route, which relies on the recently-introduced concept of "anti-cloaking." More specifically, our proposed approach relies on a suitable tailoring of the competing cloaking and anti-cloaking mechanisms, interacting in a t…
It is generally believed that transformation optics based cloaking, besides rendering the cloaked region invisible to detection by scattering of incident waves, also shields the region from those same waves. We demonstrate a coupling between the cloaked and uncloaked regions, exposing a difference between cloaking for rays and waves. Interior resonances allow this coupling to be amplified, and careful choice of parameters leads to effective cloaks with degraded shielding. As one application, we describe how to use transformation optics to hide sensors in the cloaked region and yet enable the s…
In this paper, we present the design of cylindrical and spherical electromagnetic cloaks working at visible frequencies. The cloak design is based on the employment of layered structures consisting of alternating plasmonic and non-plasmonic materials and exhibiting the collective behavior of an effective epsilon-near-zero material at optical frequencies. The design of a cylindrical cloak to hide cylindrical objects is firstly presented. Two alternative layouts are proposed and both magnetic and non-magnetic objects are considered. Then, the design of spherical cloaks is also presented. The ful…
Invariant transformation for quantum mechanical systems is proposed. A cloaking of matter wave can be realized at given energy by designing the potential and effective mass of the matter waves in the cloaking region. The general conditions required for such a cloaking are determined and confirmed by both the wave and particle (classical) approaches. We show that it may be possible to construct such a cloaking system for cold atoms using optical lattices.
We give a comprehensive study on regularized approximate electromagnetic cloaking via the transformation optics approach. The following aspects are investigated: (i) near-invisibility cloaking of passive media as well as active/radiating sources; (ii) the existence of cloak- busting inclusions without lossy medium lining; (iii) overcoming the cloaking-busts by employing a lossy layer outside the cloaked region; (iv) the frequency dependence of the cloaking performances. We address these issues and connect the obtained asymptotic results to singular ideal cloaking. Numerical verifications and d…
Transformation optics constructions have allowed the design of electromagnetic, acoustic and quantum parameters that steer waves around a region without penetrating it, so that the region is hidden from external observations. The material parameters are anisotropic, and singular at the interface between the cloaked and uncloaked regions, making physical realization a challenge. We address this problem by showing how to construct {\sl isotropic and nonsingular} parameters that give {\sl approximate} cloaking to any desired degree of accuracy for electrostatic, acoustic and quantum waves. The te…
In recent years a remarkable progress was made in the construction of spatial cloaks using the methods of transformation optics and metamaterials. The temporal cloaking, i.e. the cloaking of an event in spacetime, was also widely studied by using transformations on spacetime domains. We propose a simple and general method for the construction of temporal cloaking using the change of time variables only.
Invisibility cloaking not only catches the human imagination, but also promises fascinating applications in optics and photonics. By manipulating electromagnetic waves with metamaterials, researchers have been able to realize electromagnetic cloaking in the microwave, terahertz and optical regimes. Nevertheless, the complex design and fabrication process, narrow bandwidth, and high intrinsic losses in the metamaterial-based cloaks have imposed intractable limitations on their realistic applications. Seeking new approaches to overcome these perceived disadvantages is in progress. Here by using …
Invisibility cloaking imposes strict conditions on the refractive index profiles of cloaking media that must be satisfied to successfully hide an object. The first experimental demonstrations of cloaking used artificial metamaterials to respond to this challenge. In this work we show how a much simpler technique of electromagnetically induced transparency can be used to achieve a partial, {\it carpet} cloaking at optical frequencies in atomic vapours or solids. To generate a desired combination of low absorption with strong modifications of the refractive index, we use chiral media with an ind…
The invisibility cloak has been a long-standing dream for many researchers over the decades. By transforming space and light propagation, a three-dimensional (3D) object can be perceived as having reduced number of dimensions, in the form of points, lines, and thin sheets, making it "undetectable" judging from scattered field. Although a variety of cloaking devices have been reported at microwave and optical frequencies, the Terahertz (THz) domain remains unexplored. Moreover, it should be noted that all the previous experimental demonstrations are performed in a two-dimensional (2D) waveguide…
Is it possible to actually make Harry's invisibility cloaks? The most promising approach for realizing such magical cloaking in our real world would be to use transformation optics, where an empty space with a distorted geometry is imitated with a non-distorted space but filled with transformation medium having appropriate permittivity and permeability. An important requirement for true invisibility cloaks is nonreciprocity; that is, a person in the cloak should not be seen from the outside but should be able to see the outside. This invisibility cloak, or a nonreciprocal shield, cannot be cre…
Coordinate-transformation approaches to invisibility cloaking rely on the design of an anisotropic, spatially inhomogeneous "transformation medium" capable of suitably re-routing the energy flux around the region to conceal without causing any scattering in the exterior region. It is well known that the inherently magnetic properties of such medium limit the high-frequency scaling of practical "metamaterial" implementations based on subwavelength inclusions (e.g., split-ring resonators). Thus, for the optical range, non-magnetic implementations, based on approximate reductions of the constitut…
The straightforward method of transformation optics implies that one starts from the coordinate transformation, determines the Jacobian matrix, the fields and material parameters of the cloak. However, the coordinate transformation appears as an optional function: it is not necessary to know it. We offer the solution of some sort of the inverse problem: starting from the fields in the invisibility cloak we directly derive the permittivity and permeability tensors of the cloaking shell. The approach can be useful for finding material parameters for the specified electromagnetic fields in the cl…
Invisibility cloaks of light, which used to be confined to the imagination, have now been turned into a scientific reality, thanks to the enabling theoretical tools of transformation optics and conformal mapping. Inspired by those theoretical works, the experimental realisation of electromagnetic invisibility cloaks has been reported at various electromagnetic frequencies. All the invisibility cloaks demonstrated thus far, however, have relied on nano- or micro-fabricated artificial composite materials with spatially varying electromagnetic properties, which limit the size of the cloaked regio…
Invisibility or cloaking has captured human's imagination for many years. With the recent advancement of metamaterials, several theoretical proposals show cloaking of objects is possible, however, so far there is a lack of an experimental demonstration at optical frequencies. Here, we report the first experimental realization of a dielectric optical cloak. The cloak is designed using quasi-conformal mapping to conceal an object that is placed under a curved reflecting surface which imitates the reflection of a flat surface. Our cloak consists only of isotropic dielectric materials which enable…
We demonstrate in this letter a unique approach for watching outside while hiding in a carpet cloaking based on transformation optics. Unlike conventional carpet cloaking, which screens all the incident electromagnetic waves, we break the cloak and allow incident light get into the carpet. Hence outside information is detected inside the cloak. To recover the invisible cloaking, complementary techniques are applied in the broken space. Consequently, a hiding-inside-and-watching-outside (HIWO) carpet cloak is sewed, which works as a perfectly invisible cloaking and allows surveillance of the ou…
Subwavelength structures demonstrate many unusual optical properties which can be employed for engineering functional metadevices, as well as scattering of light and invisibility cloaking. Here we demonstrate that the suppression of light scattering for any direction of observation can be achieved for an uniform dielectric object with high refractive index, in a sharp contrast to the cloaking with multilayered plasmonic structures suggested previously. Our finding is based on the novel physics of cascades of Fano resonances observed in the Mie scattering from a homogeneous dielectric rod. We o…
Here we theoretically show, by designing and manipulating spatially inhomogeneous, non-uniform conductivity patterns across a single flake of graphene, that this single-atom-layered material can serve as a "one-atom-thick" platform for infrared metamaterials and transformation optical devices. It is known that by varying the chemical potential using gate electric and/or magnetic fields, the graphene conductivity in the THz and IR frequencies can be changed. This versatility provides the possibility that different "patches" on a single flake of graphene possess different conductivities, suggest…
Based on transformation optics (TO), we present and experimentally realize a new thermal carpet cloak. The device, which we call a "thermal carpet", provides a considerable cloaking effect. The device is designed, fabricated and measured to verify the thermal cloaking performance. In comparison with previous experimental work, the advantage of this design is that the required medium parameter is inherently isotropic and thus easier to fabricate.
An invisibility cloak that can hide an arbitrary object external to the cloak itself has not been devised before. In this Letter, we introduce a novel way to design a remote cloaking device that makes any object located at a certain distance invisible. This is accomplished using multi-folded transformation optics to remotely generate a hidden region around the object that no field can penetrate and that does not disturb the far-field scattering electromagnetic field. As a result, any object in the hidden region can stay in position or move freely within that region and remain invisible. Our id…
The design rules of transformation optics generally lead to spatially inhomogeneous and anisotropic impedance-matched magneto-dielectric material distributions for, e.g., free-space invisibility cloaks. Recently, simplified anisotropic non-magnetic free-space cloaks made of a locally uniaxial dielectric material (calcite) have been realized experimentally. In a two-dimensional setting and for in-plane polarized light propagating in this plane, the cloaking performance can still be perfect for light rays. However, for general views in three dimensions, various imperfections are expected. In thi…
The invisibility cloak has been a long-standing dream for many researchers over the decades. The introduction of transformational optics has revitalized this field by providing a general method to design material distributions to hide the subject from detection. By transforming space and light propagation, a three-dimensional (3D) object is perceived as having a reduced number of dimensions, in the form of points, lines, and thin sheets, making it "undetectable" judging from the scattered field. Although a variety of cloaking devices have been reported at microwave and optical frequencies, the…
Based on transformation optics theory, we present a new carpet device that can be used to thermally protect a region from the invasion of external heat flux. The designed device is termed 'thermal carpet', which provides considerable cloaking effect. The cloaking performance for heat flux originating from different directions are analyzed. Unlike most thermal cloak designs reported in the literature, the material parameters are constant with position throughout the cloak, indicating that only one type of metamaterial composite to fabricate such a carpet is required.
Recently we have suggested that two-dimensional broadband transformation optics devices based on metamaterial designs may be built using tapered waveguides. Here we review application of this principle to broadband electromagnetic cloaking, trapped rainbow, and novel microscopy devices.
The onset of transformation optics has opened avenues for designing of a plenitude of applications related to propagation of electromagnetic waves in anisotropic media. In this paper, an algorithm is proposed using a coordinate transformation and a piecewise function for the purpose of designing a three dimensional cloak having an arbitrary geometry which could be convex or non-convex in nature. The surfaces of the cloak as well as of the body under consideration are assumed to be conformal to each other. For an arbitrary geometry, the coordinate system needed to model the surface can be a non…
The intriguing concept of "anti-cloaking" has been recently introduced within the framework of transformation optics (TO), first as a "countermeasure" to invisibility-cloaking (i.e., to restore the scattering response of a cloaked target), and more recently in connection with "sensor invisibility" (i.e., to strongly reduce the scattering response while maintaining the field-sensing capabilities). In this paper, we extend our previous studies, which were limited to a two-dimensional cylindrical scenario, to the three-dimensional spherical case. More specifically, via a generalized (coordinate-m…
We propose to use transformation optics to generate a general illusion such that an arbitrary object appears to be like some other object of our choice. This is achieved by using a remote device that transforms the scattered light outside a virtual boundary into that of the object chosen for the illusion, regardless of the profile of the incident wave. This type of illusion device also enables people to see through walls. Our work extends the concept of cloaking as a special form of illusion to the wider realm of illusion optics.
This survey of recent developments in cloaking and transformation optics is an expanded version of the lecture by Gunther Uhlmann at the 2008 Annual Meeting of the American Mathematical Society.
The electromagnetic implementation of cloaking, the hiding of objects from sight by diverting and reassembling illuminating electromagnetic fields has now been with us ten years, while the notion of hiding events is now five. Both schemes as initially presented neglected the inevitable dispersion that arises when a designed medium replaces vacuum under transformation. Here we define a transformation design protocol that incorporates both spacetime transformations and dispersive material responses in a natural and rigorous way. We show how this methodology is applied to an event cloak designed …
The application of transformation optics to the development of intriguing electromagnetic devices can produce weakly anisotropic or isotropic media with the assistance of quasi-conformal and/or conformal mapping, as opposed to the strongly anisotropic media produced by general mappings; however, it is typically limited to two-dimensional applications. By addressing the conformal mapping between two manifolds embedded in three-dimensional space, we demonstrate that electromagnetic surface waves can be controlled without introducing singularity and anisotropy into the device parameters. Using fr…
The advances in geometric approaches to optical devices due to transformation optics has led to the development of cloaks, concentrators, and other devices. It has also been shown that transformation optics can be used to gravitational fields from general relativity. However, the technique is currently constrained to linear devices, as a consistent approach to nonlinearity (including both the case of a nonlinear background medium and a nonlinear transformation) remains an open question. Here we show that nonlinearity can be incorporated into transformation optics in a consistent way. We use th…
We consider reshaping a scattering obstacle virtually by using transformation optics in acoustic and electromagnetic scattering. Among the general virtual reshaping results, the virtual minification and virtual magnification are particularly studied. Stability estimates are derived for scattering amplitude in terms of the diameter of a small obstacle, which implies that the limiting case for minification corresponds to a perfect cloaking, i.e., the obstacle is invisible to detection.
The fully covariant formulation of transformation optics is used to find the configuration of a cloaking device operating in an expanding universe modelled by a Friedmann-Lemaître-Robertson-Walker spacetime. This spacetime cloak is used as a platform for probing the covariant formulation of transformation optics, thereby rigorously enhancing the conceptual understanding of the theory. By studying the problem in both comoving and physical coordinates we explicitly demonstrate the preservation of general covariance of electrodynamics under the transformation optics procedure. This platform also …
We consider how transformation optics and invisibility cloaking can be used to construct models in subsets $\mathbb{R}^3$ with a varying metric, where the time-harmonic waves for a given angular wavenumber $k$, are equivalent to the waves in some closed orientable manifold. The obtained models could in principle be physically implemented using a device built from metamaterials. In particular the measurements in the metamaterial device given by the Helmholtz source-to-solution operator are equivalent to Helmholtz source-to-solution measurements in a universe given by $(\mathbb{R}_+\times M, -dt…
In the field of transformation optics, metamaterials mimic the effect of coordinate transformations on electromagnetic waves, creating the illusion that the waves are propagating through a virtual space. Transforming space by appropriately designed materials makes devices possible that have been deemed impossible. In particular, transformation optics has led to the demonstration of invisibility cloaking for microwaves, surface plasmons and infrared light. Here we report the achievement of another "impossible task". We implement, for microwaves, a device that would normally require a dielectric…
In this paper, we apply transformation-based optics to the derivation of a general class of transparent metamaterial slabs. By means of analytical and numerical full-wave studies, we explore their image displacement/formation capabilities, and establish intriguing connections with configurations already known in the literature. Starting from these revisitations, we develop a number of nontrivial extensions, and illustrate their possible applications to the design of perfect radomes, anti-cloaking devices, and focusing devices based on double-positive (possibly nonmagnetic) media. These designs…
Metamaterials are artificially structured media that can focus (lensing) or reroute (cloaking) waves, and typically this is developed for electromagnetic waves at millimetric down to nanometric scales or for acoustics or thin elastic plates at centimeter scales. Extending the concepts of Kadic et al. 2013 we show that the underlying ideas are generic across wave systems and scales by generalizing these concepts to seismic waves at frequencies, and lengthscales of the order of hundreds of meters, relevant to civil engineering. By applying ideas from transformation optics we can manipulate and s…
