Analysis of unidirectional non-paraxial invisibility of purely reflective PT-symmetric volume gratings

TL;DR

This paper analytically investigates the unidirectional invisibility of a purely reflective PT-symmetric volume grating, considering full Maxwell equations to accurately account for boundary reflections and diffraction behaviors.

Contribution

It provides an exact analytical solution for the diffraction in PT-symmetric gratings beyond the paraxial approximation, enabling precise analysis of unidirectional invisibility.

Findings

Unidirectional invisibility occurs in specific configurations of the PT-symmetric grating.

Full Maxwell equations reveal boundary reflection effects overlooked by paraxial models.

Analytic solutions facilitate design of non-paraxial reflective invisibility devices.

Abstract

We study the diffraction produced by a slab of purely reflective PT-symmetric volume Bragg grating that combines modulations of refractive index and gain/loss of the same periodicity with a quarter-period shift between them. Such a complex grating has a directional coupling between the different diffraction orders, which allows us to find an analytic solution for the first three orders of the full Maxwell equations without resorting to the paraxial approximation. This is important, because only with the full equations can the boundary conditions, allowing for the reflections, be properly implemented. Using our solution we analyze unidirectional invisibility of such a grating in a wide variety of configurations.