# Subwavelength-Cavity High-Gain Circularly Polarized Antenna with Planar Metamaterials
## 2 Simulations and Experimental Measurements  
In this study, we investigated a circularly polarized subwavelength cavity metamaterial antenna made of an MNM operating in GHz range. Figure 1 shows a three-dimensional schematic of the proposed antenna operating at 2.80 GHz. The metamaterial antenna consisted of three layers. The top layer was an MNM-PRS reflector composed of a periodic array of metallic crosses and patches on both surfaces of a 1.524 mm thick dielectric Rogers 4003C substrate (Rogers Corporation, Chandler, AZ, USA). Copper, with an electrical conductivity of 5.7 \(\times\) 10\({}^{7}\) S/m, was the selected metal. The MNM-PRS reflector has the characteristics of high reflection and low transmission. The biggest difference between the MNM-PRS reflector and the smooth metal reflector is that the former has a tunable reflection phase from 0\({}^{\circ}\) to 360\({}^{\circ}\). The MNM-PRS reflector as a reflection plate for the cavity structure can reduce the thickness of the cavity. The middle layer was an air-filled subwavelength cavity. The bottom layer was a 1.524 mm thick dielectric (Rogers 4003c) substrate covered with a metallic patch feed on the upper face and a metallic ground plane acting as a perfect electric conductor (PEC) reflector on the other face; a single metallic patch was used as a radiation source on the top surface and a 50 \(\Omega\) input port was provided on the opposite side. The electromagnetic signal radiated by the metal patch feed is reflected in the MNM-PRS reflector and metal ground plane. Multiple reflected electromagnetic waves propagate in the air-filled subwavelength cavity. When the thickness of the cavity meets certain conditions, the standing wave formed by multiple reflections can achieve resonance enhancement. High-directional electromagnetic signals can be radiated through the MNM-PRS reflector. To calculate the radiation capability of the cavity structure, the resonant cavity antenna was simplified as shown in Figure 2. The proposed cavity was analyzed using both the reflection and transmission coefficients of the superstrate, as well as the reflection coefficient of the ground plane. The governing equations for a normally incident wave are given by [1,47]:  
\[a_{1}=e^{-j\varphi}:x-pol \tag{1}\]  
\[b_{1}=e^{-j\varphi}:y-pol \tag{2}\]  
\[a_{n+1}=e^{-j2\varphi}e^{j\pi}\big{(}R_{xx}a_{n}+R_{xy}b_{n}\big{)} \tag{3}\]  
\[b_{n+1}=e^{-j2\varphi}e^{j\pi}\big{(}R_{yy}b_{n}+R_{yx}a_{n}\big{)} \tag{4}\]  
\[E_{x}=\sum_{n=1}^{\infty}\big{(}T_{xx}a_{n+1}+T_{xy}b_{n+1}\big{)} \tag{5}\]  
\[E_{y}=\sum_{n=1}^{\infty}\big{(}T_{yy}b_{n+1}+T_{yx}a_{n+1}\big{)} \tag{6}\]  
where \(\varphi\) is the phase between the ground plane and superstrate; \(n\) indicates the repetition number of the reflection wave inside the cavity; \(\pi\) is the refection phase of the ground; and \(R\) and \(T\) are the reflection and transmission coefficients, respectively, of the superstrate. In addition, the subscripts for \(R\) and \(T\) denote the polarization of the fields and describe the field transition of reflection and transmission. For example, \(T_{xy}\) indicates the amount of field conversion from \(y\)-polarization to \(x\)-polarization for transmission coefficients passing through the superstrate. When \(x\)-polarization was excited in the cavity, the initial value of \(b_{1}\) was set to 0. However, \(a_{1}\) would become zero when the \(y\)-polarization was excited. Equations (5) and (6) show that the electric field strength of the cavity radiation can be calculated using \(R\), \(T\), and the thickness of the cavity. Figure 1: Schematic of the 3D structure of the proposed antenna. The axial ratio (\(AR\)) is the ratio of mutually orthogonal components of an E-field and is often used for antennas, where the desired polarization is circular.