Circuit-Model Analysis of Frequency Selective Surfaces With Scatterers of Arbitrary Geometry

Abstract

Abstract-An equivalent-network model is here proposed to characterize two-dimensional planar periodic arrays of arbitrary scatterers/apertures embedded in a layered environment. The model is an extension of the approach previously developed by some of the authors, which only considered simple rectangular scatterers. A key underlying assumption in the present approach is that the current/field distribution in the scatterer can be factorized so that the spatial profile is independent of the frequency in the considered range of interest. This approximation is proven to work properly for a great variety of useful planar scatterer/aperture patterns, even at frequencies within the diffraction regime. The spatial current/field profile is determined from a full-wave simulation at a single and low frequency value. Our numerical results are validated through comparison to commercial simulators for very wide frequency ranges as well as with previously proposed circuit-model approaches.

Evaluation of the Electric Polarizability for Planar Frequency-Selective Arrays

“…Assume we have obtained the current profile J x (x, y) for a given patch element using e.g. a fullwave solver [16]. For the family of shapes, obtained from the original shape under local stretching and scaling of the shapes parts, the obtained J x (x, y), modified with the corresponding local stretching and scaling, is expected to remain a good approximation for a current profile, as indicated by numerical examinations.…”

“…A validation and further details of MNA can be found in [15], [16]. It is computationally effective and provides a deep insight in the physics of the problem.…”

Pseudo-analytical circuits for dual-polarized FSS

“…This FSS consists of a thin conducting wall perforated with arbitrarily-shaped dualpolarized apertures that can be embedded/printed in a layered environment. To develop the circuit model, here we base on the formulation presented in [8] and [9], that presented the complete formulation and were limited to considering a single current profile on the scatterer. For the sake of simplicity, in the following we clarify the modifications to consider in previous formulations in order to extend it to account for two field profiles.…”

“…These spatial profiles are obtained from the eigenmode analysis (2-D problem) of a hollow metallic waveguide whose cross section is given by the geometry of the periodic element, as described in [9]. This expression for the electric field in the aperture is considered as the new Eq.…”

Equivalent Circuit Model for Coupled Complementary Metasurfaces

“…A hybrid approach under the assumption that the current is independent of the frequency is employed to extend this circuit modelling to periodic layers with arbitrary shaped scatterers. The initial current distribution is imported from a full-wave analysis and subsequently used to extract the circuit parameters [19]. An equivalent circuit model of fish-net type negative index materials in its closed form has been shown [20].…”