Babinet’s principle for optical frequency metamaterials and nanoantennas

We consider Babinet’s principle for metamaterials at optical frequencies and include realistic conditions which deviate from the theoretical assumptions of the classic principle such as an infinitely thin and perfectly conducting metal layer. It is shown that Babinet’s principle associates not only transmission and reflection between a structure and its complement but also the field modal profiles of the electromagnetic resonances as well as effective material parameters—a critical concept for metamaterials. Also playing an important role in antenna design, Babinet’s principle is particularly interesting to consider in this case where the metasurfaces and their complements can be regarded as variations on a folded dipole antenna array and patch antenna array, respectively.