Analytic Solution for $PT$-Symmetric Volume Gratings

TL;DR

This paper derives an exact analytic solution for the diffraction properties of a PT-symmetric volume grating, enabling comprehensive analysis of its behavior including boundary reflections, beyond approximate methods.

Contribution

It provides the first full Maxwell equation solution for PT-symmetric volume gratings with boundary conditions, advancing understanding of their diffraction characteristics.

Findings

Analytic expressions for the first three diffraction orders.

Insights into boundary reflection effects.

Versatile analysis of different grating configurations.

Abstract

We study the diffraction produced by a $PT$-symmetric volume Bragg grating that combines modulation 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 reflections, be properly implemented. Using our solution we analyze the properties of such a grating in a wide variety of configurations.