Abstract
Unique and highly tunable optical properties of PT-symmetric systems and metamaterials enable a plenty of entirely new linear and nonlinear optical phenomena with numerous applications, e.g., for designing subdiffraction lenses, nonreciprocal devices, etc. Therefore, the artificial media with the PT symmetry attract ever-increasing attention and are now a subject for intensive investigations. One of the commonly used methods providing information about the optical response of artificial nanostructural media is a so-called effective medium theory. Here we examine the possibility of utilizing the effective medium theory for a comprehensive analysis of PT-symmetric multilayered systems composed of alternating loss and gain slabs. We show that applicability of local effective material parameters (or Maxwell Garnett approximation) is very limited and cannot be exploited for a prediction of exceptional points marking a PT symmetry breaking. On the other hand, nonlocal bianisotropic effective medium parameters can be reliably used, if the thickness of a unit cell is much smaller than the radiation wavelength. In the case of obliquely incident plane waves, we reveal the limitation on the loss-gain coefficient, which should not be too large compared with the real part of the permittivity. We believe that our findings can improve the fundamental understanding of physics behind PT-symmetric systems and advance the development of auxiliary tools for analyzing their peculiar optical response.
Highlights
PT symmetry entered physics as a realization of the nonHermitian quantum mechanics keeping eigenvalues real [1,2]
We show that applicability of local effective material parameters is very limited and cannot be exploited for a prediction of exceptional points marking a PT symmetry breaking
In Ref. [34] the nonlocal homogenization theory is exploited to prove that the Maxwell Garnett approach is more applicable for the unit cells with inversion symmetry compared to the unit cells without it
Summary
PT symmetry entered physics as a realization of the nonHermitian quantum mechanics keeping eigenvalues real [1,2]. The accurate transfer-matrix solution is available for multilayered systems, it is instructive to have a homogenized solution too It may simplify the description, and unveil novel regularities. [34] the nonlocal homogenization theory is exploited to prove that the Maxwell Garnett approach is more applicable for the unit cells with inversion symmetry compared to the unit cells without it. We employ the operator effective medium approximation (OEMA) [29,31] to investigate its area of validity in description of PT -symmetric multilayered systems. OEMA juxtaposes a homogeneous nonlocal bianisotropic effective medium to the multilayer, allowing us to accurately find the transmission and reflection spectra [31] and surface-wave propagation [34].
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