Extension of Babinet Principle to Complementary Metallic Elements on the Interface of Different Substrates

In this letter, the existing Babinet principle is extended to two-dimensional complementary metallic elements on the interface of different substrates. Specifically, the existing Babinet principle requests homogenized substrate to cover complementary metallic elements. In order to break this restriction, the concept of effective relative permittivity is introduced to keep the original boundary condition unchanged. Further, the extended Babinet principle is expressed as a mathematical equation including vector fields of complementary metallic elements on the substrate interface. Especially, the proposed theory is related to the accuracy of the effective permittivity. In order to verify the proposed theory, the extended Babinet principle is applied to complementary metasurfaces with the approximate effective permittivity. Great consistence exists between theoretical and simulated results. Thus, the extended Babinet principle not only provides a theoretical approach to analyze complementary metallic elements on the substrate interface but also greatly enriches the physical connotation of existing Babinet principle.