Unidirectional Reflectionless Transmission for Two-Dimensional $\mathcal{PT}$-symmetric Periodic Structures

TL;DR

This paper rigorously analyzes unidirectional reflectionless transmission in 2D $ ext{PT}$-symmetric periodic structures, providing precise conditions and demonstrating robustness and tunability of the phenomenon through analytical and numerical methods.

Contribution

It offers a rigorous scattering matrix and perturbation analysis of unidirectional reflectionless transmission in 2D $ ext{PT}$-symmetric structures, surpassing approximate coupled-mode models.

Findings

Real zero-reflection frequencies are robust under $ ext{PT}$-symmetric perturbations.

Unidirectional reflectionless transmission occurs when the dielectric perturbation satisfies a simple condition.

Numerical examples confirm analytical predictions and demonstrate tunable unidirectional invisibility.

Abstract

Unidirectional reflectionless propagation (or transmission) is an interesting wave phenomenon observed in many $\mathcal{PT}$-symmetric optical structures. Theoretical studies on unidirectional reflectionless transmission often use simple coupled-mode models. The coupled-mode theory can reveal the most important physical mechanism for this wave phenomenon, but it is only an approximate theory, and it does not provide accurate quantitative predictions with respect to geometric and material parameters of the structure. In this paper, we rigorously study unidirectional reflectionless transmission for two-dimensional (2D) $\mathcal{PT}$-symmetric periodic structures sandwiched between two homogeneous media. Using a scattering matrix formalism and a perturbation method, we show that real zero-reflection frequencies are robust under $\mathcal{PT}$-symmetric perturbations, and unidirectional reflectionless transmission is guaranteed to occur if the perturbation (of the dielectric function) satisfies a simple condition. Numerical examples are presented to validate the analytical results, and to demonstrate unidirectional invisibility by tuning the amplitude of balanced gain and loss.