Analytical modeling of structured 1D diffraction gratings using a microwave engineering approach

The study of the transmission of electromagnetic waves through sub-wavelength apertures has been a very popular topic since the discovery of the phenomenon so-called extraordinary transmission. Some of the authors have recently presented useful models to deal with this phenomenon in a very simple manner. Following this research line, in this contribution an analytical circuit-like model is proposed to characterize the transmission of electromagnetic waves through electrically thick conducting diffraction gratings having internal structure. This means that the slits conforming the grating are not internally uniform. The analysis of this kind of structures has been recently carried out using full-wave solvers, which demand lengthy calculations and provide poor physical insight. Our circuit-based approach, previously demonstrated for other uniform structures, is adapted here to account for 1D arrays of slits having width steps. It is shown that a closed-form expression for the transmissivity can be found. The consequences of the internal structure are studied making use of our simplified model.