Analytical model for TM scattering of 1-D narrow slit gratings loaded with dielectric slabs

This work presents an improved version of a previously proposed equivalent circuit model for the study of transmissivity of TM polarized waves through lamellar metal gratings loaded with dielectric slabs. The model makes use of lumped elements and transmission lines. The use of an impedance-matching rationale explains the onset of narrow band transmission peaks induced by the presence of dielectric slabs. The finite thickness of the metal screen also yields transmission peaks even in the absence of dielectric layers. Our approach takes into account the behavior of the grating in the sub-diffraction regime, in the region of the Rayleigh-Wood anomalies, and above the onset of the first grating lobes. In contrast with previous implementations of the equivalent circuit model, all the parameters of the model are now obtained in a fully analytical manner. Qualitative and quantitative account of the most fine details of transmission/reflection spectra is possible using this technique provided the slits are narrow enough. The limits of validity of the model are also discussed.