## 2 Proposed Antenna Design  
### Proposed Unit-Cell Structure  
Figure 1 depicts the geometry of the proposed antenna unit-cell. The proposed antenna unit-cell has one S-band antenna on the upper layer and nine X-band antennas on the lower layers, as shown in Figure 1a. To achieve broadband matching characteristics with a low-profile structure, the simple E-shaped geometry is employed for both the X- and S-band array elements. Since the X-band and S-band elements must share a limited size aperture in the stacked configuration, lower-layer elements, especially those in the center, are inevitably blocked by upper-layer elements. To reduce this blockage effect, the S-band element is arranged to rotate 90 degrees with respect to X-band elements so that the polarizations between the S- and X-band elements are perpendicular to each other. Moreover, to minimize performance degradation due to the blockage effect, a mesh structure is also applied to the S-band element for EM transparent characteristics, as depicted in Figure 1b. Then, the thin mesh line structure of the upper-layer S-band element is optimized so that the  
S-band element has polarization-selective EM transparent characteristics in the X-band. The top view of the X-band element is illustrated in Figure 1c. To block the mutual coupling effect among X-band elements, an extended cavity structure is added outside the nine X-band elements We propose using a via cavity structure instead of a normal cavity wall, for a more stable manufacturing process. The red dot presents the feed pin location of the antenna, where the ports of the S-band and X-band antennas are optimized to minimize the reflection coefficient characteristics of the antenna. The heights of the lower (X-band) and upper (S-band) layers are \(h_{1}\) and \(h_{2}\), respectively, as indicated in Figure 1d. The thickness of the E-shaped antenna on the top layer is \(h_{3}\) = 0.035 mm. The radiating patch of the antenna is made of copper with a conductivity of 5.87 \(\times\) 10\({}^{7}\) S/m and is printed on the substrate, RF-35 (\(\epsilon_{r}\) = 3.5, tan \(\delta\) = 0.0018), using an etching process. The optimal parameters are derived from parametric studies using the FEKO electromagnetic simulator [26] and the detailed geometrical parameters are listed in Table 1. In this configuration, as the S-band element with a larger size radiator is stacked on top, the performance of the X-band element deteriorates due to the blockage effect. The blockage of the E-shaped antenna, which is related to optical transparency (OT), can be defined as the ratio between its open area to the total area. Herein, the OT has a value between zero and one, and the value of one means the total transmission. The OT of the S-band E-shaped antenna without the mesh structure can be calculated as follows [27]:  
\[\text{OT}=\frac{2\times(w_{2}\times l_{5})}{w_{1}\times l_{1}} \tag{1}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Values (mm)** & **Parameters** & **Values (mm)** \\ \hline \(h_{1}\) & 1.52 & \(l_{0}\) & 51 \\ \(h_{2}\) & 4.56 & \(l_{1}\) & 48 \\ \(h_{3}\) & 0.035 & \(l_{2}\) & 7.5 \\ \(w_{0}\) & 51 & \(l_{3}\) & 10 \\ \(w_{1}\) & 20 & \(l_{4}\) & 0.5 \\ \(w_{2}\) & 18 & \(l_{5}\) & 0.5 \\ \(w_{3}\) & 13 & \(l_{6}\) & 8.5 \\ \(w_{4}\) & 6.5 & \(l_{7}\) & 7 \\ \(w_{5}\) & 4.55 & \(l_{8}\) & 0.2 \\ \(f_{ps}\) & 8.9 & \(l_{9}\) & 2.8 \\ \(f_{psx}\) & 2.9 & \(d\) & 17 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Geometrical parameters of the proposed antenna. Figure 1: _Cont._  
Through this equation, the OT of the S-band E-shaped antenna is 0.019, which is significantly low, and may therefore lead to the performance degradation of the center X-band element. In order to lower the OT and improve the performance of the X-band element, the physical area of the S-band element must be minimized. However, since the area of the S-band element is related to various radiation characteristics, it is important to note that the S-band element is not a good indicator of the S-band element.