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Transformation optics, a path to
invisibility cloaks, concentrators and other devices**

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D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, D. R. Smith

In the transformation design method one imagines a fictitious space with some desired topological property, like a hole. The properties of this space are recorded in a coordinate transformation, in a manner quite familiar to General Relativists. Though the transformation properties of the electromagnetic constitutive tensors are well known in the literature on the formal structure of electromagnetics, the interpretation of the components of the permeability and permittivity tensors in the transformed coordinate system is new. The invariance of Maxwell’s equations under the transformation yields an alternative to the view that these components represent free space in an alternative topology. The tensor components can be viewed as a complex material in flat, Cartesian space. Thus a set of material properties are obtained that electromagnetically mimic the interesting topology in our own boring space. Using this method one can straightforwardly design a variety of reflectionless devices. To implement the material designs requires precise control over spatial variance and anisotropy. Metamaterials can provide this control. Recently, we have demonstrated this by constructing a 2D invisibility cloak at microwave frequencies using metamaterials. A variety of other devices are also possible.