## 2 Compact Dual-Polarized Pillbox Feeding Structure with High Isolation
This shows that a plane wave with a constant phase is realized over a wide aperture. Figure 4 shows the newly designed three-layer pillbox feeding structure for dual polarization. To generate two orthogonal surface waves while maintaining a compact size, two pillbox structures are stacked orthogonally. It is constructed by stacking one more dielectric substrate underneath the structure shown in Figure 2b. However, by simply overlapping the pillboxes of the two polarizations, the field of the \(y\)-polarization can also be transferred to the middle layer (Sub 2), where port 1 is located, as shown in Figure 4b, causing coupling effects between the ports and rendering it difficult to achieve the high isolation required to realize a full-duplex system. In addition, field components with overlapping feeding paths add to each other, resulting in plane wave polarization distortion and low cross-polarization levels, thereby confirming the necessity of a new feeding structure design to avoid these problems. As shown in Figure 4b, the \(x\)- and \(y\)-polarized fields are fed from the lower layers (Sub 1, Sub 2). As described earlier, the field fed from the lower and middle layers is initially converted into a cylindrical wave by the proposed pillbox structure and then into a plane wave by the parabolic reflecting surface realized by the vias. The field is also coupled to the top layer (Sub 3) through a coupling slot located at \(\lambda_{g}/2\) away from the tube wavelength. The converted plane wave then travels along the dielectric substrate. Figure 4: Three-layered pillbox feeding structure for dual-polarization: (**a**) overall configuration and (**b**) simplified model of the propagation path of each polarization. Figure 3: Field distribution in the pillbox feeding structures: (**a**) on the bottom substrate and (**b**) on the top substrate. Figure 5 shows the proposed pillbox feeding structure for high isolation using blocking vias. As shown in Figure 5, the blocking vias are located on the opposite side of the parabolic reflecting surface for preventing field propagation onto the middle layer (Sub 2); the distance between the blocking via and the reflecting surface is \(1\lambda_{g}\). Furthermore, Figure 5 demonstrates that the blocking vias allow the two polarization fields to be physically separated by different layers. Therefore, the path of the field propagating to the middle layer is blocked by the additional blocking via. Consequently, the newly proposed pillbox feeding structure with additional blocking vias can achieve high isolation in a compact size without increasing the size. Figure 6 shows the detailed configuration and effects of the added blocking via. As shown in Figure 6, the blocking via is placed on the opposite side of the \(y\)-polarized parabolic reflecting surface to avoid interference with the formation of the implemented plane wave. In addition, since reflected and propagating fields should have the same phase and be transmitted to the upper dielectric, they are placed in the coupling slot at a distance of \(\lambda_{g}/2\). The diameter of the via (\(d_{via}\)) was set to 1 mm and the spacing between the vias (\(g_{via}\)) was 1.3 mm. On the left side of the blocking via, vias were placed to avoid field propagation in the middle layer. In contrast, the right side of the blocking via was arranged asymmetrically because the \(x\)-polarized reflecting surface not only affects the via arrangement but also suppresses the field flow in the reflecting surface itself. Figure 6 shows the simulated results of the field distribution by the blocking vias. The fields of the lower layers cannot be coupled to the second layer where the \(x\)-polarized feed horn is located. The blocking vias physically separate the fields. Figure 5: Proposed pillbox feeding structure for high isolation using blocking vias: (**a**) simplified model of the propagation path of each polarization and the effect of blocking vias and (**b**) overall configuration.