Analytical model for the transmission of electromagnetic waves through arrays of slits in perfect conductors and lossy metal screens

Abstract

This paper presents a very simple analytical model for the analysis of the resonant transmission of microwaves or millimeter waves through periodically distributed slits in a thick metal screen. The model is based on equivalent circuits consisting of transmission line elements of known characteristic admittances and propagation constants loaded by capacitors. Closed-form analytical expressions are provided for all the circuit parameters. Alternatively, the circuit parameters can be quickly computed from numerical simulations carried out at a few frequency points. The proposed analytical model accounts for all the details of the observed transmission spectrum, including conventional Fabry-Pérot (FP) resonances, which are controlled by the thickness of the screen, as well as extraordinary transmission peaks, which are related to the periodicity. The range of validity of the model as a function of dimensional parameters is discussed. The experimentally observed and numerically predicted redshift of the Fabry-Pérot transmission peaks with respect to the ideal Fabry-Pérot resonance condition is accurately accounted for by the capacitors of the model. For narrow slits, the extraordinary transmission peak is linked to the singular behavior of the capacitances at the Rayleigh-Wood anomaly frequency point. Finally, the effect of the lossy nature of the metal screens is included in the model, providing accurate predictions of the transmission losses. Additionally, for lossy screens the model adequately predicts the anomalous behavior of the above mentioned redshift when the slit width becomes comparable to the skin depth in the metal, which is in good agreement with experimental and theoretical data previously reported for a single slit.