In this article, we propose a 4-D characteristic matrix theory for the electromagnetic coupling of the multilayer metasurface system. The multilayer metasurface system is generally composed of periodic sub-wavelength metallic elements printed on the substrates. In the system, not only the coupling between multilayer metallic elements but also the coupling between different polarized waves can exist. In order to analyze the couplings and determine the total transmission (reflection) characteristic, a series of 4-D characteristic matrices are established for the substrates and metallic elements to relate the total tangential fields (two electrical components and two magnetic components) at adjacent interfaces. Finally, a four-layer metasurface system is designed to verify the theory whose results agree well with the simulated ones at arbitrary incidence angle. Unlike the existing methods, the four-dimensional characteristic matrix theory is not only independent of the anisotropy of the metallic elements, but also insensitive to the layer number of the metasurface. Thus, the proposed theory holds valid for arbitrary multilayer metasurface system, regardless of the layer number and the metallic elements.

中文翻译：

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多层亚波长超表面系统电磁耦合的四维特征矩阵

在本文中，我们提出了用于多层超表面系统电磁耦合的 4-D 特征矩阵理论。多层超表面系统通常由印刷在基板上的周期性亚波长金属元素组成。在系统中，不仅可以存在多层金属元件之间的耦合，还可以存在不同极化波之间的耦合。为了分析耦合并确定总传输（反射）特性，为基板和金属元素建立了一系列 4-D 特性矩阵，以关联相邻界面处的总切向场（两个电分量和两个磁分量） . 最后，设计了一个四层超表面系统来验证理论，其结果与任意入射角的模拟结果非常吻合。与现有方法不同，四维特征矩阵理论不仅与金属元素的各向异性无关，而且对超表面层数不敏感。因此，无论层数和金属元素如何，所提出的理论都适用于任意多层超表面系统。