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 techniques used here may be applicable to a wider range of transformation optics designs.
For the Helmholtz equation, cloaking is possible outside a discrete set of frequencies or energies, namely the Neumann eigenvalues of the cloaked region. For the frequencies or energies corresponding to the Neumann eigenvalues of the cloaked region, the ideal cloak supports trapped states; near these energies, an approximate cloak supports {\sl almost trapped states}. This is in fact a useful feature, and we conclude by giving several quantum mechanical applications.
Two novel classes of spherical invisibility cloaks based on nonlinear transformation have been studied. The cloaking characteristics are presented by segmenting the nonlinear transformation based spherical cloak into concentric isotropic homogeneous coatings. Detailed investigations of the optimal discretization (e.g., thickness control of each layer, nonlinear factor, etc.) are presented for both linear and nonlinear spherical cloaks and their effects on invisibility performance are also discussed. The cloaking properties and our choice of optimal segmentation are verified by the numerical si…
Electromagnetic invisibility cloak requires material with anisotropic distribution of the constitutive parameters deduced from a geometrical transformation as first proposed by Pendry et al. [Science 312, 1780 (2006)]. In this paper, we proposed a useful method to realize the required radius-dependent, anisotropic material parameters and to construct an electromagnetic cloak through concentric layered structure of thin, alternating layers of homogeneous isotropic materials. With proper design of the permittivity or the thickness ratio of the alternating layers, we demonstrated the low-reflecti…
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…
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…
Cloaking techniques conceal objects by controlling the flow of electromagnetic waves to minimize scattering. Herein, the effectiveness of homogenized anisotropic materials in non-resonant dielectric multilayer cloaking is studied. Because existing multilayer cloaking by isotropic materials can be regarded as homogenous anisotropic cloaking from a macroscopic view, anisotropic materials can be efficiently designed through optimization of their physical properties. Anisotropic properties can be realized in two-phase composites if the physical properties of the material are within appropriate bou…
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.
A new type of cloak is discussed: one that gives all cloaked objects the appearance of a flat conducting sheet. It has the advantage that none of the parameters of the cloak is singular and can in fact be made isotropic. It makes broadband cloaking in the optical frequencies one step closer.
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.
Recently, researchers have proposed several carpet cloaking designs that are able to hide a real object under a bump in a way that it is perceived as a flat ground plane. Here, we present a method to design two-dimensional isotropic carpet cloaking devices using Laplace transformation. We show that each functional form of a Laplace transformation corresponds to a different carpet cloaking design. Therefore, our approach allows us to systematically design a rich variety of cloaking devices. Our analysis includes several examples containing different bump geometries that illustrate the proposed …
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…
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.
In this contribution, we present the design of cylindrical electromagnetic cloaks working at optical frequencies, making use of layered structures of plasmonic and non-plasmonic materials. The simulated results confirm the validity of the proposed approach and show a rather broad-band behavior of the cloaking device.
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…
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…
There is currently a great deal of interest in the theoretical and practical possibility of cloaking objects from the observation by electromagnetic waves. The basic idea of these invisibility devices \cite{glu1, glu2, le},\cite{pss1} is to use anisotropic {\it transformation media} whose permittivity and permeability $\var^{λν}, μ^{λν}$, are obtained from the ones, $\var_0^{λν}, μ^{λν}_0$, of isotropic media, by singular transformations of coordinates. In this paper we study electromagnetic cloaking in the time-domain using the formalism of time-dependent scattering theory. This formalism all…
We demonstrate three simple cloaking devices that can hide very large spatial objects over the entire visible spectrum using only passive, off-the-shelf optics. The cloaked region for all of the devices exceeds 10^6 mm3 with the largest exceeding 10^8 mm3. Although uni-directional, these cloaks can hide the cloaked object, even if the object is transversely or self-illuminated. Owing to the small usable solid angle, but simple scaling, these cloaks may be of value in hiding small field-of-view objects such as mid- to high-earth orbit satellites.
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.
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…
Ground-plane cloak designs are presented, which minimize scattering of electromagnetic radiation from metallic objects in the visible spectrum. It is showed that simplified ground-plane cloaks made from only a few blocks of all-dielectric isotropic materials, either embedded in a background medium or in free space, can provide considerable cloaking performance while maintaining their broadband nature. A design which operates isolated in free space that cloaks radiation originating from a specified direction is also analyzed. These schemes should be much easier to be demonstrated experimentally…
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…
We describe families of potentials which act as approximate cloaks for matter waves, i.e., for solutions of the time-independent Schrödinger equation at energy $E$, with applications to the design of ion traps. These are derived from perfect cloaks for the conductivity and Helmholtz equations, by a procedure we refer to as isotropic transformation optics. If $W$ is a potential which is surrounded by a sequence $\{V_n^E\}_{n=1}^\infty$ of approximate cloaks, then for generic $E$, asymptotically in $n$ (i) $W$ is both undetectable and unaltered by matter waves originating externally to the cloak…
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.
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…
Carpets under consideration here, in the context of pressure acoustic waves propagating in a compressible fluid, do not touch the ground: they levitate in mid-air (or float in mid-water), which leads to approximate cloaking for an object hidden underneath, or touching either sides of a square cylinder on, or over, the ground. The tentlike carpets attached to the sides of a square cylinder illustrate how the notion of a carpet on a wall naturally generalizes to sides of other small compact objects. We then extend the concept of flying carpets to circular cylinders. However, instead of reducing …
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…
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.
Recent theoretical advances applied to metamaterials have opened new avenues to design a coating that hides objects from electromagnetic radiation and even the sight. Here, we propose a new design of cloaking devices that creates perfect invisibility in isotropic media. A combination of positive and negative refractive indices, called plus-minus construction, is essential to achieve perfect invisibility (i.e., no time delay and total absence of reflection). Contrary to the common understanding that between two isotropic materials having different refractive indices the electromagnetic reflecti…
In this manuscript, we demonstrate the design and experimental proof of an optical cloaking structure which multi-directionally conceals a perfectly electric conductor (PEC) object from an incident plane wave. The dielectric modulation around the highly reflective scattering PEC object is determined by an optimization process for multi-directional cloaking purposes. And to obtain the multi-directional effect of the cloaking structure, an optimized slice is mirror symmetrized through a radial perimeter. Three-dimensional (3D) finite-difference time-domain method is integrated with genetic optim…
In the past few years, carpet cloaking attracted interests because of its feasibility at optical frequencies and potential in stealth technologies. Metasurfaces have been proposed as a method to engineer ultra-thin carpet cloaking surfaces due to their abilities to manipulate wavefronts, polarization, and phase at subwavelength scale. However, achieving broadband carpet cloaking with a significant bandwidth is one of the key remaining challenges for metasurface designs. To date, broadband carpet cloaking based on metasurfaces has not been achieved and cloaking is limited to discrete wavelength…
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…
A study of ray trajectories was undertaken for the Tamm medium which represents the spacetime of a cosmic spinning string, under the geometric-optics approximation. Our numerical studies revealed that: (i) rays never cross the string's boundary; (ii) the Tamm medium supports evanescent waves in regions of phase space that correspond to those regions of the string's spacetime which could support closed timelike curves; and (iii) a spinning string can be slightly visible while a non-spinning string is almost perfectly invisible.
We propose a generalization of the two-dimensional eikonal-limit cloak derived from a conformal transformation to three dimensions. The proposed cloak is a spherical shell composed of only isotropic media; it operates in the transmission mode and requires no mirror or ground plane. Unlike the well-known omnidirectional spherical cloaks, it may reduce visibility of an arbitrary object only for a very limited range of observation angles. In the short-wavelength limit, this cloaking structure restores not only the trajectories of incident rays, but also their phase, which is a necessary ingredien…
We show that dielectric or even perfectly conducting cylinders can be cloaked by a uniform or a layered dielectric cladding, without the need of any exotic or magnetic material parameters. In particular, we start by presenting a simple analytical concept that can accurately describe the cloaking effect obtained with conical silver plates in the visible spectrum. The modeled structure has been originally presented in [S. A. Tretyakov, P. Alitalo, O. Luukkonen, C. R. Simovski, Phys. Rev. Lett., vol. 103, p. 103905, 2009], where its operation as a cloak in the optical frequencies was studied only…
Light emitters are bound to strongly interact with light through enhanced absorption and scattering, which imposes limitations on the design and performance of photonic devices such as solar cells, nanoantennas, and (nano) lasers. Overcoming these limitations forces the use of ineffective nonreciprocity approaches or separation of radiation and scattering in the frequency or time domain. A design that combines the properties of an efficient emitter in one state and the property of being invisible in another state is vital for various applications. In this work, we propose a nanolaser design ba…
In this study, the design of a directional cloaking based on the Luneburg lens system is proposed and its operating principle is experimentally verified. The cloaking concept is analytically investigated via geometrical optics and numerically realized with the help of the finite-difference time-domain method. In order to benefit from its unique focusing and/or collimating characteristics of light, the Luneburg lens is used. We show that by the proper combination of Luneburg lenses in an array form, incident light bypasses the region between junctions of the lenses, i.e., the "dark zone." Hence…
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.
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…
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…
Coordinate transformations are a versatile tool to mould the flow of light, enabling a host of astonishing phenomena such as optical cloaking with metamaterials. Moving away from the usual restriction that links isotropic materials with conformal transformations, we show how non-conformal distortions of optical space are intimately connected to the complex refractive index distribution of an isotropic non-Hermitian medium. Remarkably, this insight can be used to circumvent the material requirement of working with refractive indices below unity, which limits the applications of transformation o…
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 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.
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…
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 geometrical interpretation of electromagnetism in transparent media (transformation optics) is extended to include media with isotropic, inhomogeneous, chirality. It is found that such media may be described through introducing the non-Riemannian geometrical property of torsion into the Maxwell equations, and shown how such an interpretation may be applied to the design of optical devices.
Surface waves can propagate on the planar interface of a linear electro-optic (EO) material and an isotropic dielectric material, for restricted ranges of the orientation angles of the EO material and the refractive index of the isotropic material. These ranges can be controlled by the application of a dc electric field, and depend on both the magnitude and the direction of the dc field. Thus, surface-wave propagation can be electrically controlled by exploiting the Pockels effect.
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 present an experimental study of the nonlinear optical absorption of the eutectic mixture E7 at the nematic-isotropic phase transition by the Z-scan technique, under a continuos wave excitation at 532 nm. In the nematic region, the effective nonlinear optical coefficient βfor an extraordinary beam is negative and for an ordinary beam is positive, being null in the isotropic phase. The parameter S_{NL} defined in terms of the nonlinear absorption coefficients in a similar way than the optical order parameter from the linear dichoic ratio behavies like an order parameter with a critical expon…
Semi-analytical model for calculating acoustic response to a line-focused laser pulse in an optically absorptive isotropic cylinder is proposed and implemented. It is assumed that the laser input is absorbed over the volume and thus creates a radially distributed thermoelastic source. Closed-form solution is obtained in the Fourier domain. Two inverse Fourier transforms in frequency and circumferential wave number yield the sought waveforms of acoustic response in the time-space domain. Numerical simulation is compared to the calculation based on a surface dipole source. The two signals have e…
Motivated by the theoretical observation that isotropic chirality can exist even in completely random systems, we design a dielectric metamaterial consisting of a random colloid of meta-atoms, which exhibits unprecedentedly high isotropic optical activity. Each meta-atom is composed of a helically arranged cluster of silicon nanospheres. Such clusters can be fabricated by large-scale DNA self-assembly techniques. It is demonstrated that the use of a high concentration of the meta-atoms in the colloid provides significant suppressions of incoherent scattering losses. As a result, the proposed s…
