## 2 Compact Dual-Polarized Pillbox Feeding Structure with High Isolation  
The dual-polarization characteristic requires that polarizations in a single aperture should operate independently of each other. To achieve this requirement, conventional antennas implementing dual polarization use dipoles in different directions; however, the problem is that dipoles for different polarizations cannot share the same position, thereby halving the actual usable aperture [16]. Conversely, HA is well suited for implementing dual polarization because the appropriate behavior of each polarization can be ensured regardless of the different patterns being superimposed. To design a dual-polarized HA, we need unit cells that can behave independently but also share a single structure. Figure 1 shows a schematic of the proposed dual-polarized HA for three-dimensional full-wave simulation operated by two orthogonally polarized reference waves propagating along the \(x\)- and \(y\)-axes. To achieve the desired HA radiation characteristics, the feeding system should produce a surface wave with low phase distortion. In particular, frequency beam scanning HAs require a plane wave as the reference wave. Conventional beam scanning dual-polarized HAs use dividing networks and feed antenna arrays to generate plane waves in a wide aperture [10]. However, this approach requires a large area that should be comparable to the aperture size and the location of the feeding structures for orthogonal polarizations in the same plane leads to high coupling effects between the polarizations. It also introduces phase distortion, resulting in high cross-polarization levels, which significantly degrade the radiation efficiency when the beam is scanned across the broadside. Furthermore, to achieve continuous scanning without gain degradation, it is necessary to design a structure that can minimize the radiation of unwanted cross-polarized radiation fields. Therefore, to overcome these problems, we propose a novel dual-polarized three-layer pillbox feeding structure that can effectively solve the increased size, low isolation, and gain degradation at the broadside encountered in conventional dual-polarized HAs. Figure 2 shows the conventional single-polarized HA using the pillbox feeding structure [17]. It is shown that the pillbox feeding structure consists of two layers of the same height Taconic RF-60 TC (\(\epsilon_{r}=6.15\), \(\tan\delta=0.002\)) substrate. In the bottom layer, the SIW H-plane sectoral horn is integrated as a feeder. As shown in Figure 2a, the SIW horn is excited by the edge end launcher to send a cylindrical guided wave into the bottom substrate. Subsequently, the guided wave is reflected by an integrated parabolic reflecting surface consisting of metal via connecting the bottom and top coppers. In addition, the coupling slot connects the bottom and top layers; it is positioned in front of the reflecting surface at \(\lambda_{\mathrm{g}}/2\), and has the same length as the reflecting surface. Therefore, the reflecting surface acts as a 180\({}^{\circ}\) coupler between the bottom and top substrates and also converts the cylindrical wave into a plane wave. In addition, Figure 2b shows the upper view of the single-polarized pillbox feeding structure. However, as mentioned previously, the conventional pillbox feeding structure is designed only for single-polarization antennas. Thus, it needs to be modified to a novel design to satisfy dual polarization. Figure 1: Configuration of the proposed dual-polarized HA. Figure 2: Conventional single-polarized HA using a pillbox feeding structure: (**a**) schematic of the pillbox feeding structure and (**b**) upper view of the pillbox feeding structure. Figure 3 shows the field distribution of the pillbox feeding structure on the bottom and top substrates. Figure 3a shows the cylindrical wave fed from the SIW horn antenna on the bottom substrate. Figure 3b shows the converted plane wave by the parabolic reflecting surface on the top substrate.