Invisibility and PT-symmetry

TL;DR

This paper explores the relationship between PT-symmetry and invisibility in complex scattering potentials, identifying conditions for invisibility and discovering reflectionless configurations in a two-layer optical model.

Contribution

It demonstrates that PT-symmetry is not essential for invisibility but helps characterize invisible configurations, and provides exactly solvable models with practical reflectionless properties.

Findings

PT-symmetry invariance in invisibility equations

Identification of PT-symmetric and non-PT-symmetric invisible configurations

Discovery of reflectionless configurations over broad spectral ranges

Abstract

For a general complex scattering potential defined on a real line, we show that the equations governing invisibility of the potential are invariant under the combined action of parity and time-reversal (PT) transformation. We determine the PT-symmetric an well as non-PT-symmetric invisible configurations of an easily realizable exactly solvable model that consists of a two-layer planar slab consisting of optically active material. Our analysis shows that although PT-symmetry is neither necessary nor sufficient for the invisibility of a scattering potential, it plays an important role in the characterization of the invisible configurations. A byproduct of our investigation is the discovery of certain configurations of our model that are effectively reflectionless in a spectral range as wide as several hundred nanometers.