# A Circularly Polarized Non-Resonant Slotted Waveguide Antenna Array for Wide-Angle Scanning
## 2 Configuration of the Antenna Element
### Design of Circular Polarizer  
The circular polarizer is implemented using an open-ended four-ridge waveguide. Excited by the slot, the circular polarizer reflects linearly polarized waves fully from the cavity walls, generating two orthogonal electric field components: the \(TE_{10}\) mode and the \(TE_{01}\) mode. In properly adjusting the polarizer's profile, an equal amplitude and a 90\({}^{\circ}\) phase gradient between these two propagating modes can be achieved. Consequently, upon reaching the radiating aperture interface, the combination of these two modes yields circularly polarized waves. The primary objective of the waveguide circular polarizer is to propagate the \(TE_{10}\) and \(TE_{01}\) modes while suppressing the \(TE_{11}\) mode within the operating frequency band. A cross-section of the circular polarizer is depicted in Figure 3. The outer shape of the polarizer is a square, with four ridges positioned inside, where the opposite ridges are of equal size. The parameters of the ridges significantly impact the propagation characteristics of the electromagnetic wave modes. Specifically, the lower ridges primarily affect the \(TE_{10}\) mode, while the higher ridges influence the \(TE_{01}\) mode. Moreover, due to their close proximity, the \(TE_{11}\) mode is susceptible to influence from both the \(TE_{01}\) and \(TE_{10}\) modes. The electric field distributions of these three modes in the polarizer cross-section are shown in Figure 4.  
The parameter values are subject to several conditions. The outer size of the polarizer is determined by the dimensions of the element radiator, which, ideally, should be minimized. The width of the ridges is contingent upon the fabrication accuracy requirements and had a negligible influence on the cutoff frequencies in this study. Consequently, the analysis focused on the ridge parameters to ascertain specific changes in the cutoff frequency. As depicted in Figure 5, \(d1\) and \(d2\) exert significant effects on the cutoff frequencies of the three modes. The simulated results align with the prior analysis; Figure 5a illustrates that \(d1\) can alter the cutoff frequencies of the \(TE_{10}\) and \(TE_{11}\) modes, with their curves exhibiting similar trends, whereas the performance of the \(TE_{01}\) mode is minimally affected by changes in \(d1\). Similarly, Figure 5b demonstrates that variations in \(d2\) have a similar effect than those in \(d1\), albeit with an emphasis on the \(TE_{10}\) and \(TE_{11}\) modes. Our objective is to preserve the \(TE_{01}\) and \(TE_{11}\) modes while suppressing the \(TE_{11}\) mode within the operating  
Figure 3: Top view of the circular polarizer. Figure 2: Configuration of the proposed antenna element. frequency band. The available bandwidth is indicated by the black arrow in Figure 5b. By finely adjusting these parameters, we can effectively control the propagating modes of the polarizer. The cutoff frequencies of each mode, as well as the waveguide wavelength, are obtained according to the parameters of the ridges. In order to satisfy the phase difference between the two modes, the height of the polarizer satisfies the following:  
\[\frac{2\pi h}{\lambda_{g10}}-\frac{2\pi h}{\lambda_{g01}}=\frac{\pi}{4} \tag{2}\]  
where \(\lambda_{g10}\) is the waveguide wavelength of the \(TE_{10}\) mode, \(\lambda_{g01}\) refers to the waveguide wavelength of the \(TE_{01}\) mode, and \(h\) is the height of the polarizer. With the aforementioned analysis, the dimensional parameters of the polarizer are established. The accepted design parameters are listed in Table 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **s1** & **s2** & **d1** & **d2** & **h** \\ \hline Value (mm) & 7.5 & 7.5 & 2.9 & 5.3 & 31.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameter values of the four-ridge cavity design. Figure 4: Electric field distributions of the three modes in a circular polarization cavity at 6.6 GHz.