Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics

Greenleaf, Allan; Kurylev, Yaroslav; Lassas, Matti; Uhlmann, Günther

doi:10.1137/080716827

Cited by 239 publications

(190 citation statements)

References 101 publications

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“…Since the pioneer works [11], [14], and [19], extensive research has been done on cloaking in electromagnetic scattering. We refer to [10], [9], and [21] for recent development on electromagnetic cloaking. One of the main tools to obtain cloaking is to use a change of variables scheme (also called transformation optics).…”

Section: Introductionmentioning

confidence: 99%

Enhancement of Near-Cloaking. Part II: The Helmholtz Equation

Ammari¹,

Kang

Lee

et al. 2012

Commun. Math. Phys.

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The aim of this paper is to extend the method of [6] to scattering problems. We construct very effective near-cloaking structures for the scattering problem at a fixed frequency. These new structures are, before using the transformation optics, layered structures and are designed so that their first scattering coefficients vanish. Inside the cloaking region, any target has near-zero scattering cross section for a band of frequencies. We analytically show that our new construction significantly enhances the cloaking effect for the Helmholtz equation.

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Section: Introductionmentioning

confidence: 99%

Enhancement of Near-Cloaking. Part II: The Helmholtz Equation

Ammari¹,

Kang

Lee

et al. 2012

Commun. Math. Phys.

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“…For similar results for electromagnetic waves, acoustic waves, quantum waves, etc., see the review papers [61,62] and the references given there. The fact that the boundary measurements do not change, when a conductivity is pushed forward by a smooth diffeomorphism leaving the boundary fixed (see Sect.…”

Section: Invisibility For Electrostaticsmentioning

confidence: 99%

Inverse problems: seeing the unseen

2014

Self Cite

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This survey article deals mainly with two inverse problems and the relation between them. The first inverse problem we consider is whether one can determine the electrical conductivity of a medium by making voltage and current measurements at the boundary. This is called electrical impedance tomography and also Calderón's problem since the famous analyst proposed it in the mathematical literature (Calderón in On an inverse boundary value problem. Seminar on numerical analysis and its applications to continuum physics (Rio de Janeiro, 1980), Soc Brasil Mat. Rio de Janeiro, pp. [65][66][67][68][69][70][71][72][73] 1980). The second is on travel time tomography. The question is whether one can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as a geometry problem, the boundary rigidity problem. Can we determine a Riemannian metric of a compact Riemannian manifold with boundary by measuring the distance function between boundary points? These two inverse problems concern visibility, that is whether we can determine the internal properties of a medium by making measurements at the boundary. The last topic of this paper considers the opposite issue: invisibility: Can one make objects invisible to different types of waves, including light?Communicated by Ari Laptev.

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“…For similar results for electromagnetic waves, acoustic waves, quantum waves, etc., see the review papers [62], [63] and the references given there. The fact that the boundary measurements do not change, when a conductivity is pushed forward by a smooth diffeomorphism leaving the boundary fixed (see section 1.7), can already be considered as a weak form of invisibility.…”

Section: Invisibility For Electrostaticsmentioning

confidence: 99%