The refractive index of reciprocal electromagnetic media

Abstract

We study the electromagnetics of media described by identical inhomogeneous relative dielectric and magnetic tensors, .  m = 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 n r s , ( ˆ) that depends on position r and direction s, ˆbut is independent of polarization. The phase surface is always ellipsoidal, and n r s , ( ˆ) 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  m = 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.

On spacetime transformation optics: temporal and spatial dispersion

“…From a fundamental (microscopic) perspective, all non-vacuum material properties are dynamic in nature, resulting from the reaction of atoms, molecules, or more complex structures (metamaterials) to the impinging electromagnetic field, and thus changing how that field propagates. It is then an effective-and most likely homogenised [14,15]-version of this dynamic process which we can often simplify into macroscopic permittivity and permeability functions, or perhaps even just a refractive index [16]. The sole remaining symptom of the original dynamics is then the frequency dependence of these constitutive quantities.…”

Generalized transformation design: Metrics, speeds, and diffusion

“…Generalized Transformation Design Dr.Paul.Kinsler@physics.org http://www.kinsler.org/physics/ for an exception. Further, although anisotropic dielectric media are typically birefringent, those generated by transformation from (or to) isotropic media are not [24].…”

Impedance rescaling and scattering from transformation optics devices

“…Although this one axis rescaling has been treated previously [25], I present an abbreviated version here. If the x and y directions are chosen parallel to the interface between two regions in a T-device, whether these have a finite or infinitesimal extent, we can rescale the z axis in the second region by a factor l. Thus the z-direction Figure 1.…”

“…As a start, it was noted that the original radial cloaking conception [1] was impedance matched at the boundary [7]. However, as far as standard impedance calculations are concerned, it was only impedance matched in the radial direction, and not in the angular or axial directions-but it is worth also noting that such naive uses of impedance measures in the anisotropic materials generated by transformation design schemes give misleading results [25,26]. In fact, interfaces between any medium and a transformed version (e.g.…”

“…It is left as a side effect of the constitutive transformation, typically based on a 'kappa medium' assumption where k e m = = (see e.g. [25]), although other choices, such as assuming a dielectric-only response, are made depending on the situation or technological convenience. One notable feature of many reported cloaking results, in either simulation or experiment, is that pictorial reprentations involve the steady state situation with an incident plane wave or other continuous wavefront.…”