# High-Gain Waveguide-Fed Circularly Polarized Spidron Fractal Aperture Antenna
## 2 Antenna Design
### Design of the Rectangular Waveguide-Fed CP Spidron Fractal Aperture Antenna  
Figure 2a presents the design process of the rectangular waveguide-fed antennas, i.e., without a superstrate. First, Antenna-1 was designed by simply covering an open-ended waveguide with a single dielectric layer. Subsequently, instead of using the open-ended waveguide, fractal apertures were applied, forming Antenna-2 and Antenna-3. In Antenna-2, the fractal aperture is realized with only one Spidron fractal slot. Meanwhile, in Antenna-3, two Spidron fractal slots are merged to form the fractal aperture. The simulated results of the reflection coefficients and axial ratios (ARs) of all three antennas are plotted in Figure 2b,c. Clearly, Antenna-1 resonates at a frequency of approximately 11.35 GHz with a very high reflection coefficient of \(-10.7\) dB, as Antenna-1 is basically an open-ended waveguide antenna which is covered by a single dielectric layer. In addition, Antenna-1 is a linearly polarized antenna. Given that it uses a fractal aperture, Antenna-2 has a single resonance at 11 GHz with a minimum reflection coefficient of \(-23\) dB and a narrow bandwidth (see Figure 2b). However, as indicated in Figure 2c, Antenna-2 does not exhibit circular polarization operation. By properly merging two Spidron fractal slots to form the proposed Spidron fractal aperture, Antenna-3 generates two resonances at the frequencies of 10.35 GHz and 11.65 GHz. The two resonances are combined to realize a wide \(-10\) dB reflection bandwidth of 10.00-11.94 GHz. Furthermore, Antenna-3 yields circular polarization operation with a 3 dB AR bandwidth of 10.91-11.26 GHz (see Figure 2c). This 3 dB AR bandwidth is entirely covered by the \(-10\) dB reflection bandwidth. It is important to note that additional resonances can be realized to form a wider \(-10\) dB reflection bandwidth by adding additional Spidron fractal slots and merging them. However, considering the given aperture areas of the rectangular waveguide, the aperture consisting of only two Spidron fractal slots is effectively excited by the rectangular waveguide. Therefore, two Spidron fractal slots were finally used to realize the proposed Spidron fractal aperture.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(l_{sub}\) & 0.51 mm & \(d_{x}\) & 6.79 mm \\ \(l_{sup}\) & 0.64 mm & \(d_{y}\) & 4.226 mm \\ \(S\) & 15.5 mm & \(\beta_{1}\) & 34.94\({}^{\circ}\) \\ \(h\) & 7.0 mm & \(\beta_{2}\) & 32.96\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Optimized dimensional parameters of the proposed antenna.  
In order to demonstrate how circular polarization operation is realized, we investigated the time-varying magnetic current distributions on the proposed Spidron fractal aperture at 11.1 GHz. Figure 3 depicts the simulated magnetic current distributions observed from the \(+z\)-direction for \(t=0\) and \(t=T/4\), where \(T\) is the period. At \(t=0\), the major currents are on Spidron fractal slot #1, and their vector sum (\(M_{total}\)) is from the right-upper corner to the left-lower corner. Meanwhile, at \(t=T/4\), the currents on Spidron fractal slot #2 dominate the radiation, exhibiting a vector sum (\(M_{total}\)) from the left-upper corner to the right-lower corner. This vector is perpendicular to that at \(t=0\) and revolves in the counter-clockwise direction as the time \(t\) changes, hence generating RHCP in the \(+z\)-direction.  
Figure 2: (**a**) Design process; simulated results of (**b**) reflection coefficients and (**c**) simulated axial ratios (ARs).