Solutions in folded geometries, and associated cloaking due to anomalous resonance

TL;DR

This paper explores how folded geometries and their unfolded equivalents can produce cloaking effects through anomalous resonance, with implications for hyperlens design and cloaking technology.

Contribution

It introduces a novel interpretation of unphysical solutions in coated cylinders via geometry unfolding, revealing cloaking due to anomalous resonance in hyperlens-like structures.

Findings

Cloaking occurs in both folded and unfolded geometries.

Anomalous resonance cancels external fields on dipoles.

Hyperlens can be impedance matched with zero loss.

Abstract

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.