Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors
arXiv:1001.2761 · doi:10.1088/1367-2630/12/3/033035
Abstract
We show that any pair of real symmetric tensors $\BGve$ and $\BGm$ can be realized as the effective electric permittivity and effective magnetic permeability of a metamaterial at a given fixed frequency. The construction starts with two extremely low loss metamaterials, with arbitrarily small microstructure, whose existence is ensured by the work of Bouchitt{é} and Bourel and Bouchitté and Schweizer, one having at the given frequency a permittivity tensor with exactly one negative eigenvalue, and a positive permeability tensor, and the other having a positive permittivity tensor, and a permeability tensor having exactly one negative eigenvalue. To achieve the desired effective properties these materials are laminated together in a hierarchical multiple rank laminate structure, with widely separated length scales, and varying directions of lamination, but with the largest length scale still much shorter than the wavelengths and attenuation lengths in the macroscopic effective medium.
12 pages, no figures
References in corpus (15)
- Hiding Under the Carpet: a New Strategy for Cloaking
- Dielectric Optical Cloak
- Design of Electromagnetic Cloaks and Concentrators Using Form-Invariant Coordinate Transformations of Maxwell's Equations
- Circuit elements at optical frequencies: nano-inductors, nano-capacitors and nano-resistors
- A complementary media invisibility cloak that can cloak objects at a distance outside the cloaking shell
- Transformation media that rotate electromagnetic fields
- Electromagnetic wormholes and virtual magnetic monopoles
- Full-wave invisibility of active devices at all frequencies
- Impedance-matched Hyperlens
- Magnifying perfect lens and superlens design by coordinate transformation
- Cylindrical Superlens by a Coordinate Transformation
- Solutions in folded geometries, and associated cloaking due to anomalous resonance
- A rigorous analysis of high order electromagnetic invisibility cloaks
- Opaque perfect lenses
- Far field imaging by a planar lens: diffraction versus superresolution