## 2 Design of Antenna Element and Feed Networks  
The system diagram of the Ku-band satellite communication is given in Figure 1, in which two active phased arrays are utilized for beam scanning. Figure 2 shows the configuration of the proposed antenna element, which consists of four dielectric substrates, two Bonding films, two Air gap layers, and seven metal layers. An RS300 dielectric substrate (\(\epsilon_{\rm r1}=2.94\), \(\tan\delta_{1}=0.001\)) is employed as Substrates 1-4, due to its performances of low gas output, low dielectric constant thermal stability coefficient, and low thermal expansion coefficient, applying to the space SATCOM application. The dielectric material of the foam layer is ROHACELL\({}^{5}\)HF51 (\(\epsilon_{\rm r3}=1.08\), \(\tan\delta_{3}=0.0021\) at 10 GHz), serving as the Air layer. A metal Reflector is proposed to provide support and protection. In addition, a bonding pre-prey layer (PP) RLP30 (\(\epsilon_{\rm r2}=3\), \(\tan\delta_{2}=0.002\)) with a thickness of 0.1 mm is adopted to bond Substrates 2-4. The thickness of the metal layers--including Ground 1, Ground 2, Feed 1, Feed 2, and Driven patch--is uniformly designed as 0.5 oz (17.5 \(\upmu\)m). The detailed dimensions of the proposed element are listed in Table 1.  
Figure 1: System diagram of the Ku-band satellite communication. Specifically, the dual-polarized dual-band antenna element spacing is designed as \(0.665\lambda_{01}\times 0.77\lambda_{02}\) (\(\lambda_{01}\) is the free space wavelength at 14.25 GHz and \(\lambda_{02}\) is the free space wavelength at 12.5 GHz). The seven metal layers from bottom to top are Feed 2, Ground 2, Ground 1, Feed 1, Driven patch, Parasitic patch, and Via-loaded ring. The first four layers are located on Substrates 2-4, and the last two layers are printed in Substrate 1. In detail, Feed 1 and Feed 2 are employed as the feed-line for dual-polarization operation at the Tx and Rx bands, respectively. The I-shaped slot is introduced for the slot-coupling excitation with broad bandwidth performance. Furthermore, Ground 1 and Ground 2 between the two above feed networks are introduced to reduce the coupling between two dual-polarized ports and then to enhance the port-to-port isolation. The slot-coupled octagonal Driven patch is located on the top layer of Substrate 2. The patch is symmetric along the \(x\)- and \(y\)-directions, which guarantees the shared-aperture radiation of the dual-polarized waves. An Air gap is added between Substrate 1 and Substrate 2 to enhance the broadband characteristic. In addition, an octagonal Parasitic patch on the bottom layer of Substrate 1 is placed on the top layer of Substrate 2. The \(y\)-direction is located on the top layer of Substrate 2. Substrate 1 and the Via-loaded ring embedded in Substrate 1 is utilized to increase the gain performance and decrease the coupling between the antenna elements. The electric field distributions in Substrate 1 of the antenna element with and without the Via-loaded ring are shown in Figure 3 for comparison. It can be seen from Figure 3a that the electromagnetic wave of the element is restrained by the Via-loaded ring as compared with that in Figure 3b, leading to weak coupling between the adjacent elements. In addition, the low cross-polarization performance is enhanced due to the octagonal patch. The electric vector of the element in Figure 3c shows that the radiations around the edges on the _yoz_-plane are out of phase. Therefore, the cross-polarization component is suppressed around the corners of the patch antenna. In addition, the simulated S-parameters of the element are plotted in Figure 4. The impedance bandwidth for \(\,\left|\,S_{11}\,\right|<-15\,\)dB is 14.7 % (from 13 GHz to 15.1 GHz) for Port 1 and 10.8 % (from 11.9 GHz to 13.25 GHz) for Port 2, and the isolation results are above 17 dB in the operating bands.