Analysis of Complementary Metasurfaces Based on the Babinet Principle

Abstract

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.