Circuit model for metallic gratings with tapered and stepped slits

The study of the transmission of electromagnetic waves through periodically perforated opaque screens, even though being a very classical topic, has received a renewed attention along the last fifteen years because of the discovery of the exciting phenomenon so-called extraordinary optical transmission [1]. The transmission spectrum of structures consisting on periodic arrays of holes or slits made in electrically thick metal plates has been explained in terms of the surface waves supported by the perforated screens (spoof surface plasmon polaritons). However, some of the authors of this paper have reported simple circuit models accounting for the transmission spectra of a variety of periodically perforated structures. In this paper we apply the circuit model methodology to explain the details of the transmission spectra of periodic gratings of slits made in thick conducting screens when the slits are geometrically nonuniform. In particular, we study slits with unsymmetrically placed bumps and cuts and tapered slits. The results provided by simple analytical circuit-like models are shown to agree very well with data obtained with a commercial finite elements solver. The availability of analytical models reports obvious advantages over numerical approaches, specially for design purposes.