Complementary Electromagnetic Metasurfaces in a Dual Dielectric Half-Space

In this letter, we study the boundary conditions of complementary metasurfaces whose theoretical basis is the Babinet's principle. Nevertheless, the metasurface is usually fabricated on the substrate interface, whereas the standard Babinet's principle requests the metasurface to be in a homogenized space. In order to solve complementary metasurfaces, they are placed on dual substrate interfaces. By introducing the effective permittivity and dual effective permeability, the problem can be converted into complementary metasurfaces in the dual effective substrates, which exactly corresponds to the existing Babinet's principle. Finally, an intrinsic equation can be established for complementary metasurfaces on the dual substrate interfaces, in which the effective permittivity and dual effective permeability can be exactly offset with each other. Thus, the proposed model provides a fresh and insightful perspective about the electromagnetic mechanism of complementary metasurfaces on the substrate interface.