Analysis of Complementary Metasurfaces Based on the Babinet Principle

In this letter, we apply the Babinet principle to complementary metasurface with different substrates. For periodic metallic elements A^c, its corresponding magnetic elements and complementary metallic elements are assumed to be A^e and A^m, respectively. First, the relationship between the transmitted fields of A^e and A^m is established based on the generalized Babinet principle. Then, with the same substrates' settings, the fields of A^c are reconstructed from those of A^m based on the impedance condition and the dual boundary condition. Finally, the theory gives the relationship between the tangential transmission matrices of A^c and A^e. The simulated results verify the theoretical ones for the proposed metasurface over a wide range of incidence angle, regardless of the substrate.