Journal ArticleDOI
Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics
TLDR
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.read more
Citations
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Journal ArticleDOI
Electrical impedance tomography and Calderón's problem
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.
Journal ArticleDOI
Acoustic cloaking and transformation acoustics
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.
Journal ArticleDOI
Regularized d-bar method for the inverse conductivity problem
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.
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Cloaking via change of variables for the Helmholtz equation
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.
Journal ArticleDOI
Spectral Theory of a Neumann–Poincaré-Type Operator and Analysis of Cloaking Due to Anomalous Localized Resonance
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.
References
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Journal ArticleDOI
Determining conductivity by boundary measurements
Robert V. Kohn,Michael Vogelius +1 more
TL;DR: In this article, Calderon poses the question: "Is it possible to determine the conductivite thermique of an object by means of mesures statiques de la temperature and du flux de chaleur a la limite?"
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General relativity in electrical engineering
Ulf Leonhardt,Thomas G. Philbin +1 more
TL;DR: In this article, the authors show that general relativity provides the theoretical tools for designing devices made of metamaterials, such as perfect invisibility devices, perfect lenses, the optical Aharonov-Bohm effect and electromagnetic analogues of the event horizon.
Journal ArticleDOI
Calderon's inverse conductivity problem in the plane
Kari Astala,Lassi Päivärinta +1 more
TL;DR: In this paper, it was shown that the Dirichlet to Neumann map for the equation ∇·σ∇u = 0 in a two-dimensional domain uniquely determines the bounded measurable constant.
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Homogenization of metamaterials by field averaging (invited paper)
David R. Smith,John B. Pendry +1 more
TL;DR: In this paper, the authors present a homogenization technique in which macroscopic fields are determined via averaging the local fields obtained from a full-wave electromagnetic simulation or analytical calculation.
Journal ArticleDOI
On the cloaking effects associated with anomalous localized resonance
TL;DR: In this paper, it was shown that the resonant field generated by a polarizable line or point dipole acts back on the polarizable lines or points and effectively cancels the field acting on it from outside sources.