# Wideband Circularly Polarized Antenna Based on a Non-Uniform Metasurface
## Antenna Design  
### Antenna with Uniform MS  
In order to achieve wideband operation for both reflection coefficient (S\({}_{11}\)) and axial ratio (AR) BWs, the driven patch and the MS are designed to operate at adjacent frequency bands. Here, the driven patch is designed so that it can radiate CP waves. First, a square patch with dimensions of \(W_{p}\times W_{p}\) is  
Figure 1: Geometry of the proposed wideband circularly polarized (CP) antenna. The optimized dimensions are as follows: \(W_{s}\) = 40, \(H_{s}\) = 1.52, \(W_{p}\) = 11, \(d\) = 6.8, \(L_{f}\) = 8.5, \(W_{f}\) = 3, \(p\) = 10, \(W_{i}\) = 9.0, \(W_{o}\) = 8.1 (unit: mm). chosen to work at the fundamental TM\({}_{01}\) mode (\(f_{r}\)). \(W_{p}\) can be approximately calculated based on the following equation:  
\[W_{p}=\frac{c}{2f_{r}\sqrt{\varepsilon_{eff}}}=\frac{c}{2f_{r}\sqrt{\frac{ \varepsilon_{r}+1}{2}}} \tag{1}\]  
where \(c\) is the speed of light and \(\varepsilon_{eff}\) is the effective dielectric constant of the substrate. Then, two opposite corners are truncated to produce two orthogonal modes. By tuning \(d\), the magnitudes and the phases of these orthogonal modes can be adjusted so that they have an equal magnitude and are \(90^{\circ}\) out of phase for CP radiation. \(W_{p}\) is optimized around the predicted value according to Equation (1), while \(d\) only has a significant effect on the AR value. The optimal values of \(W_{p}\) and \(d\) can be obtained through the simulation. To broaden the operating BW of the square patch antenna, the MS is designed to allow operation in a higher frequency band. This phenomenon has been extensively investigated in [17; 26]. According to these studies, the resonances of the surface waves propagating on the MS can be qualitatively calculated by  
\[\beta_{sw}=\frac{m\pi}{N\times P}\ ;m=1,\ 2,\ \ldots \tag{2}\]  
where \(\beta_{sw}\) is the propagation constant and \(N\) and \(P\) are the unit cell number and its periodicity, respectively. Figure 2 presents the dispersion diagram, which shows the phase shift of the single unit cell at a given frequency at the first two eigenmodes, TM (transverse magnetic) and TE (transverse electric). Here, when the phase shift is \(90^{\circ}\), the surface wave resonant frequencies of the MS, which are defined by the intersection between the vertical lines (\(\beta_{SW}P=90^{\circ}\)) and the dispersion curves, are around 5.7 and 6.2 GHz. According to Equation (2), the number of unit cells is \(2\times 2\) with \(m=1\) and \(4\times 4\) with \(m=2\). Since the MS is the radiating aperture of the antenna, a larger MS will have a larger aperture, leading to higher gain radiation. Thus, we choose \(m=2\) to obtain high gain radiation for the proposed design. It is noted that the number of unit cells can be increased; however, the drawback is large antenna dimensions. The simulated performance of the antenna without an MS and with a uniform MS (\(W_{i}=W_{o}\)) is compared and depicted in Figure 3. As observed, significant improvements in both \(-10\) dB \(|S_{11}|\) and \(3\) dB AR BWs can be obtained with the presence of MS. In the \(|S_{11}|\) profile, besides the lower resonances at 4.7 and 5.1 GHz produced by the driven patch, there are also two additional resonances at 5.8 and 6.3 GHz. These resonances are generated by the MS and are quite well matched with the prediction based on the dispersion diagram in Figure 2. This phenomenon has been thoroughly investigated in [26]. In terms of AR, there are two CP bands at around 5.1 and 5.7 GHz, which are respectively produced by the driven patch and the MS. For better demonstration, Figure 4 presents the simulated AR of the antenna for different sizes of the patch (\(W_{p}\)) and the unit cell (\(W_{i}\)). It can be observed that tuning  
Figure 2: Dispersion diagram of the metasurface (MS) unit cell. TM: transverse magnetic; TE: transverse electric. \(W_{p}\) has a strong impact on the lower CP resonance, which shifts to a higher band as \(W_{p}\) decreases.