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Research Activities > Programs > Electromagnetic Metamaterials

Electromagnetic Metamaterials and their Approximations:
Practical and Theoretical Aspects

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Alternative Derivation of Electromagnetic Cloaks and Concentrators

Professor Arthur Yaghjian

Air Force Research Laboratory

Abstract:   To complement the 'transformation optics' approach of Pendry, Schurig, and Smith and the ‘general relativity’ approach of Leonhardt and Philbin, we formulate electromagnetic cloaking as a boundary-value problem involving a single Maxwell first-order differential equation. The boundary value formulation, which does not involve eigenfunctions or separation of variables, is based on the requirements that the cloaking occurs for all possible incident fields and that the cloaks with frequency omega > 0 have continuous tangential components of E and H fields across their outer surfaces, and zero normal components of D and B fields at their inner material surfaces.

The tangential field boundary conditions at the outer surface of the cloak ensure zero scattered fields, and the normal-field boundary conditions at the inner surface of the cloak are compatible with zero total fields inside the interior cavity of the cloak. For spherical cloaks, unlike cylindrical cloaks, these boundary conditions lead to all the tangential components of the E and H fields being continuously zero across their inner surfaces?cylindrical cloaks having delta functions in polarization densities at their inner surfaces (a discovery first made by Greenleaf, Kurylev, Lassas, and Uhlmann). For bodies with no interior free-space cavities, the formulation is used to derive nonscattering spherical and cylindrical 'concentrators' that magnify the incident fields near their centers. For static fields (omega = 0), the boundary-value formulation is appropriately modified to obtain a relative permeability dyadic that will cloak magnetostatic fields. Causality-energy conditions imply that, unlike magnetostatic cloaking, electrostatic cloaking as well as low-frequency cloaking for omega > 0 is not realizable.

It is also confirmed that perfect cloaking over any nonzero bandwidth violates causality-energy conditions and thus the cloaking of realistic time dependent fields must be approximate.

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