Nearly perfect nonmagnetic invisibility cloaking: Analytic solutions and parametric studies

Coordinate-transformation approaches to invisibility cloaking rely on the design of an anisotropic, spatially inhomogeneous "transformation medium" capable of suitably re-routing the energy flux around the region to conceal without causing any scattering in the exterior region. It is well known that the inherently magnetic properties of such medium limit the high-frequency scaling of practical "metamaterial" implementations based on subwavelength inclusions (e.g., split-ring resonators). Thus, for the optical range, non-magnetic implementations, based on approximate reductions of the constitutive parameters, have been proposed. In this paper, we present an alternative approach to non-magnetic coordinate-transformation cloaking, based on the mapping from a nearly-transparent, anisotropic and spatially inhomogeneous virtual domain. We show that, unlike its counterparts in the literature, our approach is amenable to exact analytic treatment, and that its overall performance is comparable to that of a non-ideal (lossy, dispersive, parameter-truncated) implementation of standard (magnetic) cloaking.