Circuit Models for Stacked Planar Periodic Structures - Mesa, Francisco; Rodriguez-Berral, Raul; Medina, Francisco (2019 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2019)
The study of periodically structured metalo-dielectric devices has been a very popular research topic for decades. This research activity has been stimulated by the interesting electromagnetic properties exhibited by such kind of structures. They provide mechanisms to control the transmission, reflection, absorption or polarization of the electromagnetic waves interacting with them. Diffraction gratings, polarizers, frequency selective surfaces and, more recently, metasurfaces and metamaterials, are good examples of this class of electromagnetic systems. One of the simplest implementations of this type of structures, specially when dealing with microwave or millimeter wave signals, makes use of one-dimensional/two-dimensional distributions of planar strips/patches printed on dielectric substrates, as well as their complementary versions, consisting of periodic distributions of apertures in planar thin metal screens. Although modern electromagnetic full-wave simulators are routinely used to analyze and design electromagnetic periodic structures, the availability of approximate analytical models provides clear advantages to the designer. Analytical models are usually based on equivalent circuit representations whose electrical components can readily be computed or estimated without too much computational effort. A recent review on this subject can be found in [1]. An interesting problem related to the derivation of circuit models for periodic structures arises when several planar periodic configurations are stacked on a pile with relatively small separation between adjacent grids. If the separation is large, the problem is quite simple, since the individual two-port circuit models accounting for the response of each of the stacked grids can be obtained as if they were uncoupled to the adjacent grids. These two-port circuits are then trivially interconnected by means of transmission line sections representing the propagation of the fundamental Floquet harmonic of the periodic structure. For small separation between grids, interactions due to higher-order Floquet modes are essential both from a quantitative and a qualitative point of view.