## 3 Element Design
### Full-Wave Results  
The aforementioned antenna, that is shown in Figure 5a, consists of a _dual-polarized aperture-coupled stacked patch_ made of three dielectric substrates. On the bottom of the lower substrate (Rogers Kappa438) two printed microstrip lines are used to excite two slots on the top of the same substrate. The plane where the slots are located is also used as a ground plane. On the lower part of the upper substrate there is a parasite patch, slightly smaller  
Figure 4: The beamwidths along the principal planes \(\Theta_{\rm h}\) (in black) and \(\Psi_{\rm h}\) (in gray) vs. \(f\) in the range \(f_{\rm min}\)–\(f_{max}\). Numerical (theoretical) results are reported with solid (dashed) lines. Figure 3: (**a**) Beam squint \(\Delta\theta\) and (**b**) gain loss vs. \(f\) in the range \(f_{\rm min}=0.95f_{0}\), \(f_{\rm max}=1.05f_{0}\). In (**a**) numerical (theoretical) results are reported with solid black (dashed gray) lines. than the main patch, printed on the top of the same layer. Both upper and middle dielectric layers are realized with a Taconic TLX-8 laminate. The radiating element was simulated in CST [24] in a 2-D periodic environment, in order to take into account the coupling effects that occur in a 2-D array. Coaxial feeders, excited in their fundamental TEM mode, were simulated to properly account for their effect in the antenna design. Two wave ports are necessary to properly excite both horizontal and vertical polarization, referred to, respectively, as the H port and V port from now on. The S-parameters results obtained from the simulation of the optimized antenna are shown in Figure 5b. The isolation between ports is rather satisfactory, with values below \(-30\) dB, as well as a reflection coefficient that is well below \(-10\) dB in the frequency range of interest, showing double-resonance behavior related to the presence of the main and parasitic patches of the proposed antenna structure. In Figure 6, the radiation patterns are shown on the principal planes, and as expected from the reflection coefficients a low cross-polarization level and a symmetric co-polar pattern are obtained for both the H- and V-port excitations. To complete the picture, full-wave 3-D radiation patterns for the co-polar and cross-polar components of both H and V port are shown in Figure 7. A detailed view of the resulting antenna is also shown in Figure 8, whereas in Table 1 a list of the various design parameters is reported. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Substrates/Patch/Connectors** & \multicolumn{2}{c}{**Slots**} & \multicolumn{2}{c}{**Strips**} \\ \hline
**Parameter** & **Value [mm]** & **Parameter** & **Value [mm]** & **Parameter** & **Value [mm]** \\ \hline \(p\) & 26.98 & \(d_{x\text{Hslot}}\) & 12.42 & \(d_{x\text{Hstrip}}\) & 4.80 \\ \(h_{1}\) & 0.51 & \(d_{y\text{Hslot}}\) & 10.00 & \(d_{y\text{Hstrip}}\) & 13.05 \\ \(h_{2}\) & 0.79 & \(d_{x\text{Vslot}}\) & 6.02 & \(d_{x\text{Vstrip}}\) & 8.55 \\ \(h_{3}\) & 2.36 & \(d_{y\text{Vslot}}\) & 12.56 & \(d_{y\text{Vstrip}}\) & 4.80 \\ \(w_{\text{p1}}\) & 12.9 & \(w_{\text{Hslot}}\) & 1.84 & \(w_{\text{Hstrip}}\) & 0.9 \\ \(h_{\text{p1}}\) & 12.9 & \(h_{\text{Hslot}}\) & 1.84 & \(l_{\text{Hstrip}}\) & 8.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Design parameters for the radiating element. Figure 5: (a) Proposed antenna, (b) S-parameters of the optimized radiating element.