Solutions in folded geometries and associated cloaking due to anomalous resonance

Solutions for the fields in a coated cylinder where the core radius is bigger than the shell radius are seemingly unphysical, but can be given a physical meaning if one transforms to an equivalent problem by unfolding the geometry. In particular, the unfolded material can act as an impedance matched hyperlens, and as the loss in the lens goes to zero finite collections of polarizable line dipoles lying within a critical region surrounding the hyperlens are shown to be cloaked having vanishingly small dipole moments. This cloaking, which occurs both in the folded geometry and the equivalent unfolded one, is due to anomalous resonance, where the collection of dipoles generates an anomalously resonant field, which acts back on the dipoles to essentially cancel the external fields acting on them.