scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics

01 Feb 2009-Siam Review (Society for Industrial and Applied Mathematics)-Vol. 51, Iss: 1, pp 3-33
TL;DR: Recent theoretical and experimental progress on making objects invisible to detection by electromagnetic waves is described and ideas for devices that would once have seemed fanciful may now be at least approximately implemented physically using a new class of artificially structured materials called metamaterials.
Abstract: We describe recent theoretical and experimental progress on making objects invisible to detection by electromagnetic waves. Ideas for devices that would once have seemed fanciful may now be at least approximately implemented physically using a new class of artificially structured materials called metamaterials. Maxwell's equations have transformation laws that allow for the design of electromagnetic material parameters that steer light around a hidden region, returning it to its original path on the far side. Not only would observers be unaware of the contents of the hidden region, they would not even be aware that something was being hidden. An object contained in the hidden region, which would have no shadow, is said to be cloaked. Proposals for, and even experimental implementations of, such cloaking devices have received the most attention, but other designs having striking effects on wave propagation are possible. All of these designs are initially based on the transformation laws of the equations that govern wave propagation but, due to the singular parameters that give rise to the desired effects, care needs to be taken in formulating and analyzing physically meaningful solutions. We recount the recent history of the subject and discuss some of the mathematical and physical issues involved.
Citations
More filters
Journal ArticleDOI
TL;DR: In this paper, the authors survey mathematical developments in the inverse method of electrical impedance tomography which consists in determining the electrical properties of a medium by making voltage and current measurements at the boundary of the medium.
Abstract: We survey mathematical developments in the inverse method of electrical impedance tomography which consists in determining the electrical properties of a medium by making voltage and current measurements at the boundary of the medium. In the mathematical literature, this is also known as Calderon's problem from Calderon's pioneer contribution (Calderon 1980 Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro, 1980) p 65 (Soc. Brasil. Mat.)). We concentrate this review around the topic of complex geometrical optics solutions that have led to many advances in the field. In the last section, we review some counterexamples to Calderon's problems that have attracted a lot of interest because of connections with cloaking and invisibility.

473 citations


Cites background from "Cloaking Devices, Electromagnetic W..."

  • ..., see the review papers [39], [40] and the references given there....

    [...]

Journal ArticleDOI
TL;DR: In this article, the authors give a brief introduction to the application of the new technique of transformation acoustics, which draws on a correspondence between coordinate transformation and material properties and is formulated for both acoustic waves and linear liquid surface waves.
Abstract: In this review, we give a brief introduction to the application of the new technique of transformation acoustics, which draws on a correspondence between coordinate transformation and material properties The technique is formulated for both acoustic waves and linear liquid surface waves Some interesting conceptual devices can be designed for manipulating acoustic waves For example, we can design acoustic cloaks that make an object invisible to acoustic waves, and the cloak can either encompass or lie outside the object to be concealed Transformation acoustics, as an analog of transformation optics, can go beyond invisibility cloaking As an illustration for manipulating linear liquid surface waves, we show that a liquid wave rotator can be designed and fabricated to rotate the wave front The acoustic transformation media require acoustic materials which are anisotropic and inhomogeneous Such materials are difficult to find in nature However, composite materials with embedded sub-wavelength resonators can in principle be made and such 'acoustic metamaterials' can exhibit nearly arbitrary values of effective density and modulus tensors to satisfy the demanding material requirements in transformation acoustics We introduce resonant sonic materials and Helmholtz resonators as examples of acoustic metamaterials that exhibit resonant behaviour in effective density and effective modulus

350 citations

Journal ArticleDOI
TL;DR: In this article, a strategy for regularizing the inversion procedure for the two-dimensional D-bar reconstruction algorithm based on the global uniqueness proof of Nachman [Ann. Math. 143] for the ill-posed inverse conductivity problem is presented.
Abstract: A strategy for regularizing the inversion procedure for the two-dimensional D-bar reconstruction algorithm based on the global uniqueness proof of Nachman [Ann. Math. 143 (1996)] for the ill-posed inverse conductivity problem is presented. The strategy utilizes truncation of the boundary integral equation and the scattering transform. It is shown that this leads to a bound on the error in the scattering transform and a stable reconstruction of the conductivity; an explicit rate of convergence in appropriate Banach spaces is derived as well. Numerical results are also included, demonstrating the convergence of the reconstructed conductivity to the true conductivity as the noise level tends to zero. The results provide a link between two traditions of inverse problems research: theory of regularization and inversion methods based on complex geometrical optics. Also, the procedure is a novel regularized imaging method for electrical impedance tomography.

188 citations

Journal ArticleDOI
TL;DR: In this paper, the authors examined a natural regularization, obtained by blowing up a ball of radius ρ rather than a point, and including a well-chosen lossy layer at the inner edge of the cloak.
Abstract: The transformation optics approach to cloaking uses a singular change of coordinates, which blows up a point to the region being cloaked. This paper examines a natural regularization, obtained by (1) blowing up a ball of radius ρ rather than a point, and (2) including a well-chosen lossy layer at the inner edge of the cloak. We assess the performance of the resulting near-cloak as the regularization parameter ρ tends to 0, in the context of (Dirichlet and Neumann) boundary measurements for the time-harmonic Helmholtz equation. Since the goal is to achieve cloaking regardless of the content of the cloaked region, we focus on estimates that are uniform with respect to the physical properties of this region. In three space dimensions our regularized construction performs relatively well: the deviation from perfect cloaking is of order ρ. In two space dimensions it does much worse: the deviation is of order 1/|log ρ|. In addition to proving these estimates, we give numerical examples demonstrating their sharpness. Some authors have argued that perfect cloaking can be achieved without losses by using the singular change-of-variable-based construction. In our regularized setting the analogous statement is false: without the lossy layer, there are certain resonant inclusions (depending in general on ρ) that have a huge effect on the boundary measurements. © 2010 Wiley Periodicals, Inc.

179 citations


Cites background from "Cloaking Devices, Electromagnetic W..."

  • ...In three space dimensions our regularized construction performs relatively well: the deviation from perfect cloaking is of orderρ....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a necessary and sufficient condition on the fixed source term for electromagnetic power dissipation to blow up as the loss parameter of the plasmonic material goes to zero is given.
Abstract: The aim of this paper is to give a mathematical justification of cloaking due to anomalous localized resonance (CALR). We consider the dielectric problem with a source term in a structure with a layer of plasmonic material. Using layer potentials and symmetrization techniques, we give a necessary and sufficient condition on the fixed source term for electromagnetic power dissipation to blow up as the loss parameter of the plasmonic material goes to zero. This condition is written in terms of the Newtonian potential of the source term. In the case of concentric disks, we make the condition even more explicit. Using the condition, we are able to show that for any source supported outside a critical radius, CALR does not take place, and for sources located inside the critical radius satisfying certain conditions, CALR does take place as the loss parameter goes to zero.

170 citations

References
More filters
Book
01 Jan 1941
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Abstract: Introduction Part I: Representation formulas for solutions: Four important linear partial differential equations Nonlinear first-order PDE Other ways to represent solutions Part II: Theory for linear partial differential equations: Sobolev spaces Second-order elliptic equations Linear evolution equations Part III: Theory for nonlinear partial differential equations: The calculus of variations Nonvariational techniques Hamilton-Jacobi equations Systems of conservation laws Appendices Bibliography Index.

25,734 citations

Journal ArticleDOI
TL;DR: The authors' simulations show that a version of the lens operating at the frequency of visible light can be realized in the form of a thin slab of silver, which resolves objects only a few nanometers across.
Abstract: Optical lenses have for centuries been one of scientists’ prime tools. Their operation is well understood on the basis of classical optics: curved surfaces focus light by virtue of the refractive index contrast. Equally their limitations are dictated by wave optics: no lens can focus light onto an area smaller than a square wavelength. What is there new to say other than to polish the lens more perfectly and to invent slightly better dielectrics? In this Letter I want to challenge the traditional limitation on lens performance and propose a class of “superlenses,” and to suggest a practical scheme for implementing such a lens. Let us look more closely at the reasons for limitation in performance. Consider an infinitesimal dipole of frequency v in front of a lens. The electric component of the field will be given by some 2D Fourier expansion,

10,974 citations


"Cloaking Devices, Electromagnetic W..." refers background in this paper

  • ...On the other hand, Pendry, Schurig, and Smith [80] gave a prescription for values of ε and µ giving a cloaking device for electromagnetic waves, based on the fact that ε and µ transform in the same way (2.7) as the conductivity tensor in electrostatics....

    [...]

  • ...(i) Negative index of refraction material (NIM) has also received a great deal of publicity due to its role in the perfect lens, an idea introduced by Pendry [82], building on the earlier work of Veselago [100] where NIMs were first discussed....

    [...]

  • ...This point of view has been advocated by J. Pendry and his collaborators and given the name transformation optics [102]....

    [...]

Journal ArticleDOI
23 Jun 2006-Science
TL;DR: This work shows how electromagnetic fields can be redirected at will and proposes a design strategy that has relevance to exotic lens design and to the cloaking of objects from electromagnetic fields.
Abstract: Using the freedom of design that metamaterials provide, we show how electromagnetic fields can be redirected at will and propose a design strategy. The conserved fields-electric displacement field D, magnetic induction field B, and Poynting vector B-are all displaced in a consistent manner. A simple illustration is given of the cloaking of a proscribed volume of space to exclude completely all electromagnetic fields. Our work has relevance to exotic lens design and to the cloaking of objects from electromagnetic fields.

7,811 citations


"Cloaking Devices, Electromagnetic W..." refers background or methods in this paper

  • ...This brings us to the transformation-optics– based proposals of [65, 80] for cloaking from observation by electromagnetic waves at positive frequency....

    [...]

  • ...This is referred to in [32] as the single coating construction and is the same “spherical cloak” as described in [38, 39, 80]....

    [...]

  • ...2005 there has been a wave of serious theoretical proposals [1, 72, 69, 65, 80] in the physics literature, as well as a widely reported experiment by Schurig et al....

    [...]

  • ...) On the other hand, Pendry, Schurig, and Smith [80] gave a prescription for values of ε and μ giving a cloaking device for electromagnetic waves, based on the fact that ε and μ transform in the same way (2....

    [...]

  • ...On the other hand, Pendry, Schurig, and Smith [80] gave a prescription for values of ε and µ giving a cloaking device for electromagnetic waves, based on the fact that ε and µ transform in the same way (2.7) as the conductivity tensor in electrostatics....

    [...]

Journal ArticleDOI
10 Nov 2006-Science
TL;DR: This work describes here the first practical realization of a cloak of invisibility, constructed with the use of artificially structured metamaterials, designed for operation over a band of microwave frequencies.
Abstract: A recently published theory has suggested that a cloak of invisibility is in principle possible, at least over a narrow frequency band. We describe here the first practical realization of such a cloak; in our demonstration, a copper cylinder was "hidden" inside a cloak constructed according to the previous theoretical prescription. The cloak was constructed with the use of artificially structured metamaterials, designed for operation over a band of microwave frequencies. The cloak decreased scattering from the hidden object while at the same time reducing its shadow, so that the cloak and object combined began to resemble empty space.

6,830 citations


"Cloaking Devices, Electromagnetic W..." refers background or methods in this paper

  • ...On the other hand, [108] described the scattering characteristics of the simplified “reduced cylindrical parameters,” which the experiment [88] was designed to implement, and showed that in fact cloaking with the reduced parameters (which do not arise from transformation optics, but were proposed to replicate the ray behavior of the ideal cloak while using material parameters easier to physically realize) fails even for passive objects....

    [...]

  • ...In section 4 we consider the case of cloaking an infinite cylinder for Maxwell’s equations; the experiment [88] was designed to implement a “reduced” set of material parameters, easier to construct but replicating a two-dimensional slice of the ray geometry of the mathematical ideal....

    [...]

  • ...[88], for cloaking devices—structures that would render an object not only invisible but also undetectable to electromagnetic waves....

    [...]