Maxwell's equations in curved space time are invariant under electromagnetic duality transformations. We exploit this property to constrain the design parameters of metamaterials used for transformation electromagnetics. We show that a general transformation must be implemented using a dual-symmetric metamaterial. We also show that the spatial part of the coordinate transformation has the same action for both helicity components of the electromagnetic field, while the spatiotemporal part has a helicity dependent effect. Dual-symmetric metamaterials can be designed by constraining the polarizability tensors of their individual constituents, i.e., the meta atoms. We obtain explicit expressions for these constraints. Two families of realistically implementable dual-symmetric meta atoms are discussed, one that exhibits electric-magnetic cross polarizability and one that does not. In simple three-dimensional periodical arrangements of the meta atoms (Bravais lattices), the helicity dependent effect can only be achieved if the meta atoms exhibit nonzero electric-magnetic cross polarizabilities. In our derivations, we find that two dipoles located at the same point, one electric (p) and one magnetic (m), are needed to produce a total field with well-defined helicity equal to +1 or -1 and that they must be related as p=icm or -icm, respectively.
|Number of pages||7|
|Journal||Physical Review B: Condensed Matter and Materials Physics|
|Publication status||Published - 12 Aug 2013|