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 Ac are reconstructed from those of Am 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.