Sum rule for the transmission cross section of apertures in thin opaque screens.

Extraordinary transmission through subwavelength apertures is usually observed in a narrow bandwidth range, and the transmission outside this range is low, in agreement with classical results. The analysis presented here is based on the Babinet's principle and hence scattering by the complementary structure, where the apertures are replaced by finite scatterers. It is shown that the transmission cross section of a set of apertures in an opaque screen satisfies a sum rule that relates the transmission cross section integrated over all wavelengths with the polarizability of the complementary structure as defined by Babinet's principle. The theoretical results are illustrated with numerical examples.