Transmission through stacked 2D periodic distributions of square conducting patches

Abstract

In this paper, we study the transmissivity of electromagnetic waves through stacked two-dimensional printed periodic arrays of square conducting patches. An analytical circuit-like model is used for the analysis. The model accounts for the details of the transmission spectrum provided that the period of the unit cell of each patterned layer is well below the wavelength in the dielectric slabs separating the printed surfaces. In particular, we analyze the low-pass band and rejection band behavior of the multilayer structure, and the results are validated by comparison with a computationally intensive finite element commercial electromagnetic solver. The limiting case of an infinite periodic structure is analytically solved and the corresponding band structure is used to explain the passband/stopband behavior of finite structures. In addition, we study in depth the elementary unit cell consisting of a single dielectric slab coated by two metal patch arrays, and its resonance behavior is explained in terms of Fabry-Pérot resonances when the electrical thickness of the slab is large enough. In such case, the concept of equivalent thickness of the equivalent ideal Fabry-Pérot resonator is introduced. For electrically thinner slabs it is also shown that the analytical model is still valid, and its corresponding first transmission peak is explained in terms of a lumped-circuit LC resonance.