An angle on invisibility

TL;DR

This paper analyzes PT-symmetric optical gratings embedded on substrates, extending previous models to include arbitrary angles of incidence and exploring their potential for invisibility and lasing applications.

Contribution

It provides an analytic solution for PT-symmetric gratings on substrates with different refractive indices and generalizes the incidence angle, enhancing understanding of their optical properties.

Findings

Invisibility from one side at specific wavelengths

Enhanced reflection at particular angles of incidence

Potential for lasing applications

Abstract

The $PT$-symmetric optical grating with index profile $e^{i\beta z}$ has been shown to have the interesting property of being essentially invisible for light incident from one side, while possessing greatly enhanced reflection at a particular wavelength for light incident from the other side. We extend a previous analysis of this grating to obtain an analytic solution for the case when the grating is embedded on a substrate, with different refractive indices on either side. We also generalize the previous case of normal incidence to incidence at an arbitrary angle. In that case the enhanced reflection occurs at a particular angle of incidence for a given wavelength. Finally we discuss how the grating may be used to give lasing.