The refractive index of reciprocal electromagnetic media

Abstract

We study the electromagnetics of media described by identical inhomogeneous relative dielectric and magnetic tensors, Such media occur generically as spatial transformation media, i.e. electromagnetic media that are defined by a deformation of space. We show that such media are completely described by a refractive index that depends on position and direction but is independent of polarization. The phase surface is always ellipsoidal, and is therefore represented by the radius vector to the surface of the ellipsoid. We apply our method to calculate the angular dependence of the refractive index in the well-studied cylindrical cloak and to a new kind of structurally chiral medium induced by a twist deformation. By way of a simple example we also show that media for which do not in general preserve the impedance properties of vacuum. The implications of this somewhat surprising conclusion for the field of transformation optics are discussed.