Negative index materials: some mathematical perspectives

TL;DR

This paper explores mathematical properties and applications of negative index materials, including superlensing, cloaking, and wave propagation, highlighting recent theoretical advances and simplified proofs.

Contribution

It provides new mathematical insights and refined proofs on negative index materials, expanding understanding of their properties and potential applications.

Findings

Superlensing achieved using complementary media

Cloaking via anomalous localized resonance demonstrated

Well-posedness and finite speed propagation established in dispersive media

Abstract

Negative index materials are artificial structures whose refractive index has a negative value over some frequency range. These materials were postulated and investigated theoretically by Veselago in 1964 and were confirmed experimentally by Shelby, Smith, and Schultz in 2001. New fabrication techniques now allow for the construction of negative index materials at scales that are interesting for applications, which has made them a very active topic of investigation. In this paper, we report various mathematical results on the properties of negative index materials and their applications. The topics discussed herein include superlensing using complementary media, cloaking using complementary media, cloaking an object via anomalous localized resonance, and the well-posedness and the finite speed propagation in media consisting of dispersive metamaterials. Some of the results have been refined and have simpler proofs than the original ones.