Multiscale Modeling &Simulation, Volume 18, Issue 2, Page 758-797, January 2020.
We study the anomalous electromagnetic scattering in the homogenization regime, by a subwavelength thin layer consisting of periodically distributed plasmonic nanoparticles on a perfectly conducting plane. By using quasi-periodic layer potential techniques, we derive the asymptotic expansion of the electromagnetic field away from the thin layer and quantitatively analyze the field enhancement induced by the excitation of the mixed collective plasmonic resonances, which can be characterized by the spectra of two types of periodic Neumann--Poincaré operators. Based on the asymptotic behavior of the scattered field in the macroscopic scale, characterize the reflection scattering matrix for the thin layer and demonstrate that the optical effect of this metasurface can be effectively approximated by a Leontovich impedance boundary condition, which is uniformly valid no matter whether the incident frequency is near the resonant range. The quantitative approximation clearly shows the blow-up of the field energy and the conversion of the field polarization when the resonance occurs, resulting in a significant change of the reflection property of the conducting plane. These results confirm essential physical changes of electromagnetic metasurface at resonances mathematically, whose occurrence was verified earlier for the acoustic case and the transverse magnetic case.

中文翻译：

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电磁等离子超表面的数学分析

2020年1月，《多尺度建模与仿真》，第18卷，第2期，第758-797页。
我们研究了由均匀导电平面上周期性分布的等离子体纳米粒子组成的亚波长薄层在均质化机制中的异常电磁散射。通过使用准周期层势技术，我们推导出了电磁场从薄层开始的渐近扩展，并定量分析了混合集体等离激元共振的激发所引起的场增强，这可以通过两种类型的光谱来表征Neumann-Poincaré周​​期算子的形式。基于宏观尺度上散射场的渐近行为，表征薄层的反射散射矩阵，并证明通过Leontovich阻抗边界条件可以有效地近似该超表面的光学效应，无论入射频率是否在谐振范围附近，这都是一致有效的。定量近似清楚地显示出发生共振时场能量的爆炸和场极化的转换，从而导致导电平面的反射特性发生重大变化。这些结果从数学上证实了电磁超表面的基本物理变化，这种现象的发生早在声学情况和横向磁场情况下得到了验证。