# Subwavelength-Cavity High-Gain Circularly Polarized Antenna with Planar Metamaterials
## 2 Simulations and Experimental Measurements
\(AR\) is calculated using Equations (5) and (6) and is given by the references [1; 47]:  
\[AR=\frac{\left[\frac{1}{2}\bigg{\{}\left|E_{x}\right|^{2}+\left|E_{y}\right|^{2}+ \left|\left|E_{x}\right|^{4}+\left|E_{y}\right|^{4}+\left|E_{x}\right|^{2}\right| E_{y}\right|^{2}\cos(2\phi)\big{|}^{1/2}\bigg{\}}\right]^{1/2}}{\left[\frac{1}{2} \bigg{\{}\left|E_{x}\right|^{2}+\left|E_{y}\right|^{2}-\left|\left|E_{x}\right| ^{4}+\left|E_{y}\right|^{4}+\left|E_{x}\right|^{2}\right|E_{y}\right|^{2}\cos (2\phi)\big{|}^{1/2}\bigg{\}}\right]^{1/2}} \tag{7}\]  
where \(\varphi=\angle E_{x}-\angle E_{y}\). From Equations (5)-(7), it can be seen that the \(AR\) of the electromagnetic waves radiated from the cavity can be calculated from \(R\), \(T\), and the thickness of the cavity. First, we studied the reflection properties of an MNM-PRS unit cell. Figure 3 shows the structure of a square MNM-PRS unit, whose side length (\(p\)) was 24 mm and thickness (\(h\)) was 5 mm. The side length (\(l\)) of the square metallic patch was 14 mm; the width (\(w\)) of the metallic cross was 22.6 mm, and the side length of the corner cut (\(q\)) of the square metallic patch was 1.60 mm. To obtain \(R\) and \(T\) of the superstrate, the plane waves were illuminated from wave port 1 with \(x\)- or \(y\)-polarization to wave port 2, as shown in Figure 3. Additionally, all the lateral sides of the unit cell were enclosed with a periodic boundary condition (PBC), and all the simulations were performed using CST Studio Suite software, where CST Studio Suite is a high-performance 3D EM analysis software package for designing, analyzing, and optimizing electromagnetic (EM) components and systems. \[a_{1}=e^{-j\varphi}:x-pol \tag{1}\]0 The geometry of a unit cell and its boundary conditions; the electromagnetic waves are incident on port 1 and traverse to port 2. \[a_{1}=e^{-j\varphi}:x-pol \tag{1}\]1 Multiple reflections and transmissions between the MNM-PRS and ground plane. Next, we calculated the amplitudes and phase values of \(T_{xx}\), \(T_{yy}\), \(T_{xy}\), \(T_{yx}\), \(R_{xx}\), \(R_{yy}\), \(R_{xy}\), and \(R_{yx}\) for the MNM-PRS unit cells at different polarizations. Figure 4a shows the simulated MNM-PRS reflection and transmission coefficients. The transmission of this structure is mainly in the same polarization mode (\(T_{xx}\), \(T_{yy}\)). The transmission coefficient is greater than 0.6 from 2.40 GHz to 3.20 GHz, with its maximum value being near 2.75 GHz. The values of transmission coefficients with different polarizations (\(T_{xy}\), \(T_{yx}\)) are relatively small, less than 0.1 between 2.40 GHz and 3.20 GHz. The reflection of this structure is mainly in the same polarization mode (\(R_{xx}\), \(R_{yy}\)). The reflection coefficient ranges from 0.7 to 0.8 in the range of 2.40 GHz to 3.20 GHz, with a minimum value of nearly 2.75 GHz. The values of reflection coefficients of different polarizations (\(R_{xy}\), \(R_{yx}\)) are relatively small, less than 0.2 between 2.40 GHz and 3.20 GHz. Figure 4b shows the simulated reflection and transmission phases. In the frequency range of 2.40 GHz to 3.20 GHz, the transmission and reflection phases gradually decrease as the frequency increases. The same polarization reflection phase and transmission phase overlap at about 2.80 GHz. The values and changes of reflection and transmission phases with different polarizations are similar. Based on \(R\) and \(T\) values, the effective refractive index and impedance of the unit cell were calculated, from which \(\mu_{\textit{eff}}\) and \(\varepsilon_{\textit{eff}}\) of the MNM-PRS unit cell can be calculated, as shown in \[a_{1}=e^{-j\varphi}:x-pol \tag{1}\]2 In the figure, the red and black lines denote the real parts of \(\mu_{\textit{eff}}\) and \(\varepsilon_{\textit{eff}}\), respectively, while the magenta and blue lines denote the imaginary parts of \(\mu_{\textit{eff}}\) and \(\varepsilon_{\textit{eff}}\), respectively.