# A Circularly Polarized Non-Resonant Slotted Waveguide Antenna Array for Wide-Angle Scanning
## 3 Design of Antenna Array
### Planar Array  
In this section, the parallel waveguide linear array described in Section 3.1 is arranged into a two-dimensional array, and the structure of the planar array is shown in Figure 12. To reduce the width of the linear array, we adopted the staggered arrangement method to position adjacent linear arrays. However, this staggered arrangement results in an asymmetric planar array, leading to high axial ratio levels and elevated, far side-lobe levels. To address this issue, we staggered the placement of the eight-element and nine-element linear arrays. However, the staggered non-resonant array exhibits a less-than-optimal phase distribution. As depicted in Figure 13a, the phase distribution of the eight-element array does not align with that of the nine-element array. This mismatched phase distribution exacerbates the grating lobe performance during phase scanning, as indicated by the red line in Figure 14. To remedy this, we increase the excitation phase of the eight-element arrays to compensate for the phase offset induced by the staggered arrangement (Figure 13b). The magnitude of the increased phase is determined by the waveguide wavelength \(\lambda_{g}\) and the slot distance \(d\). The precise expression for the compensated phase is given by  
\[Phase_{comp}=(\frac{d}{\lambda}-\frac{1}{2})\pi \tag{5}\]  
As shown in Figure 13, the phase compensation can be achieved by increasing the distance between the excite port and the first element. Figure 13a shows the situation without phase compensation; the neighboring elements exhibit non-uniform phase excitation, and the red arrow indicates the direction of the electromagnetic wave transmission. In Figure 13b, we introduce an additional distance between the first element and the feed port, as highlighted by the yellow rectangular marker; subsequently, the first element's working phase is compensated for to achieve the correct value. The compensated result is depicted by the blue line in Figure 14, and the grating lobe was suppressed effectively by applying this method.  
Figure 11: Configuration of an eight-element linear array.  
of the nine-element array are defined using the pattern synthesis method, and the initial near field curve is extracted and compared with that of the eight-element array. Based on the discrepancy between the two curves, adjustments are made to the cylinder height and slot length of the nine-element array to ensure that its curve matches the standard curve. This iterative process is repeated several times throughout the design phase, resulting in the final curves depicted in Figure 15. The results demonstrate the good alignment between the two curves.  
As discussed earlier, the staggered arrangement results in a complex near field distribution, exacerbated by the excitation of traveling waves, leading to the intricate phase distribution of the near field. Additionally, the compact arrangement of the radiating cavities exacerbates the coupling effects compared to normal conditions. In such scenarios, the planar array's leakage wave on the radiating surface exhibits a complex phase and field distribution, adversely affecting the axial ratio level. To mitigate the influence of the leakage wave, isolation gaps are introduced on the radiating surface. These gaps serve as channels into which the leakage wave can be transmitted, subsequently being reflected at the bottom of the gaps. By adjusting the depth of the gap, the reflected wave and transmitted wave can be neutralized within it. The configuration of the isolation gaps is illustrated in Figure 12.  
With the above analyses and designs, we can obtain the final configuration of the planar array antenna. The detailed parameters are presented in Table 2.