# Metalens Antenna Based on an Ultrathin Dual-Polarized Double-Layer Huygens' Metasurface
## 2 Theoretical Analysis and Design of Huygens' Meta-Atoms
The dielectric substrate has a thickness of \(d=0.8\) mm and is made of Rogers RT5880 material with a relative permittivity of \(2.2\) and a loss tangent of \(0.0009\). The side length of the proposed Huygens' meta-atom is \(p=4.8\) mm. In order to investigate the resonance modes and physics mechanisms of the proposed meta-atom, full-wave simulations were performed in commercial software CST Microwave Studio 2020, considering the dual-polarized scenario, i.e., \(g=g_{x}=g_{y}=0.2\) mm. Because of the symmetrical structure in this situation, the meta-atom exhibits identical responses to both \(x\)- and \(y\)-polarized incident waves. The following analysis is performed based on the \(y\)-polarized normal incident wave. Figure 3a illustrates the transmission amplitude and phase of the proposed meta-atom on the frequency range from \(20\) GHz to \(35\) GHz. A transmission peak is observed with an amplitude of \(-0.55\) dB, indicating the near-unity transmission amplitudes at frequency \(f=25.2\) GHz. More importantly, the proposed meta-atom maintains high transmission \((|T|\geq-3\) dB) and full-phase coverage over a  
Figure 1: Schematic diagram of the Huygens’ metasurface. broad frequency range from 24 GHz to 31 GHz, which facilitates the subsequent meta-lens antenna design and the high-gain requirement. Furthermore, the Huygens' resonance is explained by analyzing the frequency response of the normalized electric surface admittance \(Y_{\text{e}}\) and magnetic surface impedance \(Z_{\text{m}}\). As shown in Figure 3b, three Huygens' resonance points are identified, which are characterized by the phenomena that the imaginary parts of \(Y_{\text{e}}\) and \(Z_{\text{m}}\) are equal, while the real parts are nearly zero. According to Equation (2), the electric and magnetic resonances are balanced at these frequencies, generating nearly full transmission over a broad frequency band. Figure 3c demonstrates the electric current distribution and the magnetic field distribution on the top and bottom surfaces of the meta-atom at 25.2 GHz, in which the transmission amplitude has a peak value. It can be seen that when the meta-atom is excited by the \(y\)-polarized wave, the surface currents are induced in the corner-ring-shaped patches of the top and bottom layers, which are denoted as \(J_{\text{top}}\) and \(J_{\text{bot}}\). The \(J_{\text{top}}\) flows along the \(+y\) direction while the \(J_{\text{bot}}\) flows along the \(-y\) direction. Such oppositely directed currents form a closed current loop, generating an orthogonal magnetic field. In contrast, the double-cross-shaped patches support relatively weak surface currents, which only contribute to providing electric resonance. Therefore, the Huygens' metasurface simultaneously controls both electric and magnetic resonances, and a balance of these is achieved at 25.2 GHz, which results in Huygens' resonance. In order to ensure that the desired high transmission and wide phase coverage can be achieved by varying the structural parameter at the Huygens' resonance point, the relationship between the transmission coefficient and the gap widths of the corner-ring-shaped patches \(g\) at 25 GHz is plotted, as shown in Figure 3d. As \(g\) varies from 0.1 mm to 1 mm, the transmission amplitude of the meta-atom remains above -1.9 dB, with a maximum transmission amplitude of -0.3 dB. Meanwhile, the transmission phase covers a range of 320\({}^{\circ}\), which is nearly full phase coverage and sufficient for the design of the metalens. Thus, both the amplitude and phase coverage meet the design requirements for the metalens. Moreover, the dependence of the polarization excitation is investigated by controlling \(g_{x}\) and \(g_{y}\) separately. Figure 4 shows the transmission coefficients under \(y\)-polarized excitation at 25 GHz. It can be seen that the meta-atom maintains high transmission in most situations as \(g_{x}\) and \(g_{y}\) vary.