Modified Babinet Principle for Complementary Antennas in a Dielectric Half-Space

In this letter, the modified Babinet principle is applied to complementary antennas on the substrate interface. First, it is verified that the existing Babinet principle only holds for complementary metallic elements in the homogenized substrate. Then, the effective relative permittivity is introduced into the substrate interface through the zero-thickness effective substrate, which can keep the electromagnetic behavior (such as total electrical field and surface current density) of metallic element unchanged. Thereby, the modified Babinet principle can be established for arbitrary complementary metallic elements on the substrate interface. Finally, the proposed theory is applied to input impedances of complementary antennas on the substrate interface. The simulation strongly supports the proposed theory, regardless of the substrates and antenna sizes. The study not only establishes the modified Babinet principle for complementary metallic elements on the substrate interface, but also clarifies the electromagnetic influence of effective relative permittivity for the metallic element at the substrate interface.