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Four-Dimensional Characteristic Matrix for Electromagnetic Coupling of Multilayer Sub-Wavelength Metasurface System

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.