Extension of Babinet's principle for plasmonic metasurfaces

Babinet's principle is widely applied in optics and has been useful for designing metasurfaces with dual behavior. Although this principle can be rigorously demonstrated for infinitely thin perfect conducting screens, it is not exact for any real screen. In fact, metals used in plasmonic metasurfaces are far from good conductors, and the thickness of samples is not negligible in comparison with the typical size of the patterned structure. In this paper, we propose an extension of Babinet's principle valid for plasmonic metasurfaces by redefining the concept of complementary screens and finding impedance relations between such screens that ultimately leads to a simple relation between the transmission matrices of two complementary plasmonic metasurfaces. The theory is valid under the assumptions of the electroquasistatic approximation and plane waves in the far field. It may find applications in the design of optical plasmonic metasurfaces, nanocircuits, and nanoantennas.