Alternative derivation of electromagnetic cloaks and concentrators

By Arthur D. Yaghjian, Stefano Maci. 2007

142 citations recorded by the source corpus.

Beginning with a straightforward formulation of electromagnetic ‘cloaking’ that reduces to a boundary value problem involving a single Maxwell first-order differential equation, explicit formulae for the relative permittivity–permeability dyadic and fields of spherical and circular cylindrical annular cloaks are derived in terms of general compressed radial coordinate functions. The general formulation is based on the requirements that the cloaking occurs for all possible incident fields and that the cloaks with frequency ω>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. For H-wave incident fields, a nonmagnetic circular cylindrical annulus is found that has nonzero scattered fields but zero total fields within its interior cavity. 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 (ω=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 ω>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.

Subfields: Aerospace Engineering, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials

View Paper: https://www.semanticscholar.org/paper/867eae322de8bc46a68078d9b5a10b69c98c3bb2

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Citations in the corpus

Transformation optics and metamaterials. (2010, background): “This is inevitable because the required effective permittivity and permeability can only be realized by resonances in the building blocks of the metamaterials, and causality requirements dictate that perfect invisibility cannot have wide bandwidt”
Metasurfing: Addressing Waves on Impenetrable Metasurfaces (2011, methodology): “This methodology has been, for instance, applied to design “TO cloaks,” or shells of anisotropic metamaterials capable of rendering any object within their interior cavities invisible to detection from outside (see [2] and references therein).”
Cloaking via change of variables for the Helmholtz equation (2010, background): “Recent reviews with many references to the rapidly growing literatur e on cloaking and other applications of “transformation optics” can be found in [12 , 3, 23, 29]; see also [28] for an enlightening treatment, [14] for information ab out earlier work along similar lines, and [3, 5] for an applicat”