Form Invariance of Maxwell´s Equations: The Pathway to Novel Metamaterial Specifications for Electromagnetic Reshaping

We present spatial-coordinate transformation techniques to control the propagation of electromagnetic fields in several surprising and useful applications. The implementation of this approach is based on the fact that Maxwell´s equations are form-invariant under coordinate transformations. Specifically, the effect of a general coordinate transformation can be realized by means of an equivalent anisotropic material, in which the original forms of Maxwell´s equations are still preserved in the transformed space. Constitutive parameters of the anisotropic material are determined to appropriately reflect the consequences of the coordinate transformation on the electromagnetic fields. In this paper, we introduce novel implementations and interpretations of the coordinate-transformation approach for the purpose of “reshaping” objects in electromagnetic scattering, and for reshaping and miniaturizing waveguides. We demonstrate the applications of the proposed techniques via several finite-element simulations.