Schematics of stacked identical 2D arrays of square conducting patches (dark gray) printed on uniform dielectric slabs of thickness (light pink). (a) Front view of 25 cells of the structure and (b) cross-section along the direction normal to the PRS. The incidence plane is the -plane and two orthogonal polarizations (TE and TM) are considered independently. The lattice parameter is and the gap between the patches is . The thickness of the metal patches is neglected. An elementary unit cell is highlighted with the dashed lines.
(a) Front view and (b) side view of the equivalent transmission lines for TE and TM polarized waves. Periodic boundary conditions are applied in the axis (dotted lines) while electric walls (solid lines; TE polarization) or magnetic walls (dashed lines; TM polarization) are used in the axis. The equivalent circuit proposed in this paper is depicted in (c). The capacitances of the three internal patches (having dielectric slabs at both sides) are different from the first and the last capacitances (see the main text). (d) Unit cell of the periodic structure along the direction for an infinite number of slabs ().
Equivalent circuits for determining the reflection coefficients under (a) even and (b) odd excitation conditions () for the structure in Fig. 1.
(a) Comparison between analytical (blue solid lines) and numerical (finite elements method, FEM—hfss—red dashed lines) results for the transmissivity () of a stacked structure made of 5 PRS separated by 4 dielectric slabs at normal incidence (). Dimensions: mm, mm, mm. Electrical parameters: , , S/m. (b) Analytical predictions over a wider frequency band showing a second passband at around 24–30 GHz (numerical data are not included due to convergence problems with hfss for the high frequency portion of the spectrum).
(a) Transmission spectra obtained for N = 2, 4, and 8 dielectric slabs. Dimensions and electrical parameters are the same as in Fig. 4. (b) Transmission spectra () for three different values of the dielectric constants of the regions separating the PRS (losses have been ignored). The transverse unit cell dimensions are the same as in Fig. 4 and mm, mm, and mm for 10.2, 3.0, and 1.0, respectively.
Brillouin diagram for the first two transmission bands of an infinite periodic structure (1D photonic crystal) with the same unit cell as that used in the curves plotted in Fig. 4. The non-zero transmission region in Fig. 4 matches the first passband in this graph, and the low transmission region in Fig. 4 coincides with the stopband region in this figure. The second passband, which is backward, is consistent with the second set of peaks appearing in Fig. 4(b).
Transmission curves for a single slab structure (1) under oblique TM (a) and TE (b) incidence for several values of . Solid lines are analytical results and circles have been obtained with hfss. The dimensions and the electrical parameters are the same as in Fig. 4.
Longitudinal profile of the -component of the electric field for the frequencies corresponding to the transmission peaks plotted in Fig. 4 ((a) A; (b) B; (c) C; (d) D). Solid green lines, the detailed local field computed by hfss along a center line across the structure; dashed red lines, the corresponding average electric field along every transverse cross-section; solid blue lines, the electric field extracted from the analytical circuit model.
(a) Comparison between circuit model and hfss predictions around the first resonance frequency for three different slab thicknesses (, , and 2.0 mm). (b) The same comparison (case mm) for three different gaps between the patches (, and mm).
(a) Magnetic field color map for the first resonance frequency in the case mm (see Table II). (b) The same plot for mm. (see Table II and Fig. 9).
Upper frequency limit of the low-pass band of the structure with the dimensions and electrical parameters in Fig. 4 as a function of the number of slabs, .
Comparison of the frequencies of total transmission, , calculated by solving the dispersion equation (7), the equivalent thickness formula (8), and using the full-wave hfss solver. The analyzed structure is a two-sided patch array ( mm; mm) printed on a dielectric slab () for different thicknesses under normal incidence conditions.
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