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

Abstract

Unidirectional reflectionless propagation (or transmission) is an interesting wave phenomenon observed in many $\mathcal{P}\mathcal{T}$-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) $\mathcal{P}\mathcal{T}$-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 $\mathcal{P}\mathcal{T}$-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.

10 pages, 5 figures

References in corpus (4)

• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Invisibility and PT-symmetry
• Unidirectional reflectionlessness and invisibility in the TE and TM modes of a PT-symmetric slab system
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• Approximating transmission and reflection spectra near isolated nondegenerate resonances
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• Real transmission and reflection zeros of periodic structures with a bound state in the continuum
• Unidirectional reflectivity in non-Hermitian lossy thin films