Nonlocal homogenization of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetric multilayered structures

Unique and highly tunable optical properties of $\mathcal{PT}$-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 $\mathcal{PT}$ 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 $\mathcal{PT}$-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 $\mathcal{PT}$ 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 $\mathcal{PT}$-symmetric systems and advance the development of auxiliary tools for analyzing their peculiar optical response.

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