  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.
