## 3 Dual-Polarized Hologram Pattern with Anisotropic Surface Impedance  
The top layer of the antenna consists of the hologram pattern, which is composed of an impedance surface using subwavelength metasurfaces. Equation (1) defines the surface impedance of the hologram pattern [1]:  
\[Z_{surf}=j\eta_{0}X^{\prime}\Big{[}1+M\cdot\text{Re}\Big{\{}\psi_{ref}\psi_{ obj}^{*}\Big{\}}\Big{]}, \tag{1}\]  
where \(\psi_{ref}\) and \(\psi_{obj}\) represent the reference and the desired objective wave, respectively, and \(X^{\prime}\) and \(M\) reflect the normalized average surface impedance and modulation index, respectively. We chose a commercial dielectric substrate (Taconic RF-60 TC, \(\epsilon_{r}\) = 6.15, \(\tan\delta\) = 0.002, \(h\) = 1.28 mm) to satisfy the range of surface impedance. In addition, we selected appropriate values for the hologram pattern parameters, namely \(X^{\prime}\) = 1.3 and \(M\) = 0.15, to achieve high directivity and appropriate impedance matching characteristics in a compact size. By using the selected values on a commercial substrate, the size of the antenna can be reduced without using a metasurface matching structure, which is a prerequisite in conventional HAs [14]. Figure 10 illustrates the unit cells for the dual-polarized hologram pattern. The unit cell has a shape in which two strips are arranged crosswise. The surface impedance varies  
Figure 9: Field distribution of the proposed pillbox feeding structure: (**a**) field distribution on the travel path of mode 1 (\(x\)-pol. ), (**b**) phase distribution of the \(x\)-pol. surface wave, and (**c**) phase distribution of the \(y\)-pol. surface wave. with the length of the dimension of the unit cell. The red and yellow strips represent the \(x\)- and \(y\)-polarized hologram patterns, respectively. Each of these cells is assembled in the top layer of the proposed HA and forms a dual-polarized hologram pattern. To suppress the OSB phenomenon, it is effective to use a unit cell with anisotropic properties to suppress the radiation field from unwanted cross polarization [8; 12]. For the same purpose, in accordance with [12], we used a cross-shaped anisotropic unit cell, which is very stable due to the absence of any surface impedance changes in cross polarization that could independently adjust surface impedance in both polarizations. In addition, the stable cross-polarized surface impedance does not represent a modulating surface, which can prevent unwanted cross-polarized radiation. Figure 11 shows the shape and characteristics of the unit cell. Figure 11a shows the length of each element of the unit cell. Figure 11b shows the variation in the surface impedance of the co-polarized and cross-polarized waves with varying lengths of \(S_{x}\) and \(S_{y}\) for the Jerusalem cross-unit cell. Also, the black and red curves represent the surface impedance at co- and cross-polarization, respectively. The cross-polarized surface impedance maintains a constant impedance with changing co-polarized surface impedance. This in turn represents an unmodulated impedance surface in cross-polarization, which suppresses radiation from cross-polarized fields, similar to OSB in conventional HA [8]. Figure 12 shows the field distribution in the XZ plane when the proposed antenna radiates forward, broadside, and backward. Figure 12a shows the field distribution when  
Figure 11: Variation in surface impedance for the Jerusalem Cross unit cells with changing geometry. (**a**) Geometry of the proposed unit cell and (**b**) surface impedance variation curve in terms of changing geometry. Figure 10: Jerusalem cross-shaped unit cells for the dual-polarized hologram pattern. radiating forward +14 degrees at 22 GHz. Also, as shown in Figure 12b, the proposed antenna radiates broadside at 23.5 GHz. Finally, the proposed antenna radiates in the backward direction \(-24^{\circ}\) at 27 GHz as shown in Figure 12c. Figure 13 shows the simulated radiation patterns in the XZ (\(x\)-polarization) and YZ (\(y\)-polarization) planes.