Wideband analytical equivalent circuit for one-dimensional periodic stacked arrays

Abstract

A wideband equivalent circuit is proposed for the accurate analysis of scattering from a set of stacked slit gratings illuminated by a plane wave with transverse magnetic or electric polarization that impinges normally or obliquely along one of the principal planes of the structure. The slit gratings are printed on dielectric slabs of arbitrary thickness, including the case of closely spaced gratings that interact by higher-order modes. A Π-circuit topology is obtained for a pair of coupled arrays, with fully analytical expressions for all the circuit elements. This equivalent Π circuit is employed as the basis to derive the equivalent circuit of finite stacks with any given number of gratings. Analytical expressions for the Brillouin diagram and the Bloch impedance are also obtained for infinite periodic stacks.