Superlensing using complementary media

TL;DR

This paper provides the first rigorous proof of superlensing and magnification of arbitrary inhomogeneous objects using complementary media, overcoming mathematical challenges related to sign-changing coefficients and localized resonances.

Contribution

It introduces a novel analytical technique combining removal of localized singularities and reflecting methods to prove superlensing with complementary media.

Findings

Established a rigorous proof of superlensing for a class of lenses.

Demonstrated magnification of arbitrary inhomogeneous objects.

Overcame mathematical difficulties due to sign-changing coefficients and resonances.

Abstract

This paper studies magnifying superlens using complementary media. Superlensing using complementary media was suggested by Veselago in [16] and innovated by Nicorovici et al. in [9] and Pendry in [10]. The study of this problem is difficult due to two facts. Firstly, this problem is unstable since the equations describing the phenomena have sign changing coefficients; hence the ellipticity is lost. Secondly, the phenomena associated are localized resonant, i.e., the field explodes in some regions and remains bounded in some others. This makes the problem difficult to analyse. In this paper, we develop the technique of removing of localized singularity introduced in [6] and make use of the reflecting technique in [5] to overcome these two difficulties. More precisely, we suggest a class of lenses which has root from [9] and [14] and inspired from [6] and give a proof of superlensing for this class. To our knowledge, this is the first rigorous proof on the magnification of an arbitrary inhomogeneous object using complementary media.