Recovery of Babinet's Principle for Plasmonic Metasurfaces

Babinet's principle is not valid in general for plasmonic complementary metasurfaces because metals are not good conductors and sample thicknesses are not negligible respect to other tiny details of the unit cell. Nevertheless, we demonstrate that it is possible to recover its validity under a suitable choice of materials and sample thickness. Namely, we show numerical results for several complementary designs made of silicon and silver for which the validity of Babinet's principle in infrared is only confirmed when the thickness is about 13 nm.