Unidirectional reflectionless transmission for two-dimensional PT-symmetric periodic structures

Unidirectional reflectionless propagation (or transmission) is an interesting wave phenomenon observed in many 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 PT-symmetric structures (with one-dimensional periodicity) sandwiched between two homogeneous media. Using a scattering matrix formalism and a perturbation method for the case where only one diffraction channel is open, we show that real zero-reflection frequencies are robust under 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.