# Invisibility Regions and Regular Metamaterials

## Abstract

For more than half a century people are trying to develop effective methods of remote sensing. RADAR and SONAR systems are the most advertised techniques toward this end, and the contemporary level of sophistication of both of these modalities is really amazing. In fact, so many things have been achieved with these identification methods that the inverse question has been naturally raised: Is it possible to isolate a region of space where nothing can be detected via scattering techniques? Much to our surprise the answer to this question is “yes” and the way to achieve it is knowing as “cloaking.” This is possible through the construction of a material, called “metamaterial” surrounding the cloaked region, which has particular preassigned properties. Cloaking has a history of less than a decade and almost all realistic cloaking regions share the shape of a sphere. However, spherically cloaked regions demand metamaterials with singular conductivity tensors, a consequence of the highly focusing effects of the spherical system as it collapses down to its center. We will demonstrate an ellipsoidal cloaking region, which, as a consequence of the fact that the ellipsoidal system springs from its characteristic focal ellipse, the necessary metamaterial that creates the invisibility region is regular throughout, leaving this way its realization at the level of engineering construction.

## Keywords

Electric Impedance Tomography Spherical Geometry Spherical System Material Tensor Reference Ellipsoid## References

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