# Metalens Antenna Based on an Ultrathin Dual-Polarized Double-Layer Huygens' Metasurface
## 3 Design and Discussion of a Dual-Polarized Metalens Antenna  
To validate the applicability and practical performance of the proposed meta-atoms, a dual-polarized metalens antenna was designed. As analyzed in Section 2, when \(g_{x}=g_{y}\), the meta-atom can produce identical responses to incident waves with different polarization directions, realizing the dual-polarized function. The dual-polarized metalens is designed to transform the spherical wavefront generated by a feed source into a planar wavefront, thereby achieving high-gain and highly directional radiation beams. The directional radiation metalens can be regarded as the inverse of the focusing metalens. By placing the feed antenna at the focal point, the emitted spherical wave is transformed into a highly directional plane wave by the metalens. A 25 GHz horn antenna with 14.8 dBi gain is vertically placed at the focal point of the metalens with a distance of \(F_{h}\). Then, the discretized phase distribution for the metalens can be calculated as follows:  
\[\phi_{1}(m,n)=\frac{2\pi f_{c}}{c}\bigg{(}\sqrt{(mp)^{2}+(np)^{2}+F_{h}^{2}}-F_ {h}\bigg{)} \tag{3}\]  
where \(p\) is the period of the meta-atoms, \((m,n)\) represents the position of the unit cell on the metalens. The center coordinates of the unit cell can be expressed as \((mp,np,0)\), with the corresponding phase \(\phi_{1}(m,n)\). \(f_{c}\) is the operating frequency and \(c\) is light speed in vacuum. \(F_{h}\) is the focus length. The metalens antenna contains \(33\times 33\) meta-atoms with an aperture size of \(158.4\times 158.4\) mm\({}^{2}\). The parameters chosen in this work are: operating frequency \(f_{c}=25\) GHz, focus length \(F_{h}=150\) mm, focal-diameter ratio \(F/D=0.95\). Figure 5a shows the theoretically calculated transmission phase distribution of the metalens, obtained through Equation (3). The proposed meta-atoms are mapped onto the theoretical phase, with the actual phase shown in Figure 5b. Due to the discrete phase approximation of meta-atoms, phase errors arise between the implemented and theoretical designs, as plotted in Figure 5c. Notably, the phase errors are very small, with the majority of them approaching zero, and the maximum deviation being lower than \(15^{\circ}\). Meanwhile, the gain is determined by the transmission amplitude. As seen in Figure 5d, the amplitude distribution across the entire metalens aperture remains above \(-2\) dB, demonstrating high transmittance. Thus, the amplitude and phase of the implemented meta-atoms mapping satisfy the theoretical requirements. In order to validate the electromagnetic properties of the designed metalens, simulations are performed in CST Microwave Studio. The simulation domain was set to \(160\times 160\times 300\) mm\({}^{3}\). The open boundary conditions were applied in all boundaries, and the phase center of the horn antenna feed source was positioned at \((0,0,-150)\) mm. The configuration of the designed metalens antenna is illustrated in Figure 6a, and the results of \(Ey\) are shown in Figure 6b. It can be seen that the spherical wave generated by the feed source is converted into a directional radiation plane wave after propagating through the metalens. To further demonstrate the directional radiation capability of the metalens, the far-field radiation patterns of \(E\)-plane and \(H\)-plane are plotted in Figure 7a,b. The simulation results show that a highly directional beam is generated by the designed metalens with a maximum gain of 30.4 dBi. The 3 dB gain bandwidth in the \(E\)- and \(H\)-plane are \(4.3^{\circ}\) and \(4.4^{\circ}\), respectively, and the sidelobe levels are 8.16 dBi and 9.23 dBi. In addition, the cross-polarization level is below \(-28.3\) dBi and \(-30.8\) dBi for the \(E\)- and \(H\)-plane, respectively, which is significantly lower than the co-polarization levels. These results demonstrate that the designed metalens antenna exhibits outstanding far-field radiation directivity and low cross-polarization levels.