Exploring the Potentials of the Multi-modal Equivalent Circuit Approach for Stacks of 2-D Aperture Arrays

Many frequency selective surface (FSS) structures are based on the use of a single periodic array of slot/apertures in a conducting sheet embedded in a layered medium. However, it is well known that stacking several conducting sheets and breaking the alignment of the stack can bring multiple benefits to the structure. In this paper, the analysis and design of stacks of 2-D aperture arrays are carried out by exploiting as much as possible all the potentialities of a rigorous and systematic formulation based on the multi-modal equivalent circuit approach (ECA). A key feature of the formulation is that linear transformations between the apertures of adjacent plates (rotation, translation, and scaling) can be dealt with from a purely analytical perspective. This fact is of potential interest for many practical applications, such as the design of polarization converters, absorbers, filters, and thin matching layers. When the apertures have an arbitrary geometry, it can be applied a hybrid approach that combines the ability of commercial simulators to handle arbitrary geometries with the fast computation times and physical insight of the ECA. In general, either the purely analytical or the hybrid approach can be applied in those many practical scenarios where the spatial profile of the electric field on the considered apertures hardly changes with frequency. As an additional feature of the approach, the dispersion properties (phase/attenuation constants and Bloch impedance) of infinite periodic stacks can be derived and, in particular, analytical expressions for mirror- and glide-symmetric configurations are provided.