# Metalens Antenna Based on an Ultrathin Dual-Polarized Double-Layer Huygens' Metasurface
## 4 Design and Discussion of a Two-Channel Focusing Metalens  
Dual- or multi-channel devices based on different polarization excitations have been widely applied, facilitating the realization of polarization multiplexing and multifunctional integration [35]. We applied the proposed Huygens' meta-atom on the two-channel focusing metalens, which generates different focal points for different polarizations. According to the meta-atom analyzed in Section 2, tuning \(g_{x}\) and \(g_{y}\) allows independent control of the phase responses by the corresponding polarizations. Thus, utilizing this characteristic, the phase distributions for the \(x\)-polarized and \(y\)-polarized incident waves are independently designed to achieve two-channel focusing. To realize the designed function, the spherical wave excitation is converted into a plane wave by introducing the phase compensation \(\phi_{1}\) as Equation (3), and then the resulting \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Reference**} & \multirow{2}{*}{\begin{tabular}{c} **Frequency** \\ **(GHz)** \\ \end{tabular} } & \
\begin{tabular}{c} **Layer** \\ **Number and** \\ **Principle** \\ \end{tabular} & \multirow{2}{*}{**Thickness**} & \multirow{2}{*}{**Max. Gain** **(dBi)**} & \multirow{2}{*}{
\begin{tabular}{c} **Aperture** \\ **(G\%)** \\ \end{tabular} } & \multicolumn{2}{c}{**3 dB**} \\  & & & & & **Efficiency** & **Bandwidth** \\ \hline
[21] & 11.7 & 4-FSS & 0.65 \(\lambda\) & 26.2 & 62 & 17 \\
[22] & 13.3 & 3-FSS & 0.2 \(\lambda\) & 26.2 & 29.3 & 6.7 \\
[27] & 30 & 2-Huygens & 0.12 \(\lambda\) & 24.4 & 7 & 15 \\
[29] & 13 & 2-Huygens & 0.033 \(\lambda\) & 31.9 & 61.04 & 3 \\
[23] & 12.8 & 2-Huygens & 0.14 \(\lambda\) & 18.4 & 20.2 & 9.4 \\
[28] & 9.1 & 2-Huygens & 0.045 \(\lambda\) & 18.9 & 27.8 & / \\
[19] & 26.2 & 2-Huygens & 0.087 \(\lambda\) & 30.5 & 41.9 & 17.9 \\ This work & 25 & 2-Huygens & 0.067 \(\lambda\) & 30.4 & 47.8 & 8.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparisons of the proposed metalens antenna with the references. Figure 7: Far-field radiation patterns on (**a**) \(E\)-plane, (**b**) \(H\)-plane of the designed metalens at 25 GHz. (**c**) Spectrum of gain for the proposed metalens antenna and the horn antenna. (**d**) Aperture efficiency as a function of the frequency. plane wave is focused using a focus phase \(\phi_{2}\). Assuming the focal point is located at \((x_{0},y_{0},F)\), \(\phi_{2}\) is given by:  
\[\phi_{2}(m,n)=\frac{2\pi f_{c}}{c}\bigg{(}\sqrt{(mp-x_{0})^{2}+(np-y_{0})^{2}+F ^{2}}-F\bigg{)} \tag{4}\]  
The total phase \(\phi_{total}\) of the metalens in this Section is the sum of Equation (3) and (4), which is expressed as:  
\[ \begin{split}\phi_{total}(m,n)=&\frac{2\pi f_{c}} {c}\bigg{(}\sqrt{(mp)^{2}+(np)^{2}+F_{h}^{2}}-F_{h}\bigg{)}\\ &+\frac{2\pi f_{c}}{c}\bigg{(}\sqrt{(mp-x_{0})^{2}+(np-y_{0})^{2 }+F^{2}}-F\bigg{)}\end{split}  \tag{5}\]  
The designed metalens shares the same dimensions and operating frequency as those in Section 3. With \(F_{h}=150\) mm, the horn antenna feed source is located at \((0,0,-150)\) mm, whose azimuth angle is set to \(45^{\circ}\) to simultaneously excite both \(x\)- and \(y\)-polarized spherical waves. The different channels of waves are focused at \(F_{1}\)\((0,0,100)\) mm and \(F_{2}\)\((0,50,75)\) mm. Based on Equation (5), the calculated phase compensation distributions for the \(x\)- and \(y\)-polarized channels are shown in Figure 8.  
According to the discrete phase distributions, the designed meta-atoms are mapped and assembled into the metalens. The two-channel functionality of the implemented metalens is then verified using CST. Figure 9a shows the normalized electric field distribution of \(\mathbf{E}\). It can be seen that the spherical incident waves, including both \(x\)- and \(y\)-polarized components, generate two different focus points after propagating through the metalens.