## 3 Results
### Simulated Results  
To illustrate the operational mechanism of the element antennas, we performed the surface current distributions of two elements at specific time instances (e.g., phase = 0\({}^{\circ}\) and 90\({}^{\circ}\)) within a period, as shown in Figure 6. As shown in Figure 6a, the surface current direction of the S-band antenna element rotates in the anticlockwise direction, achieving RHCP radiation. On the other hand, the surface current direction of the C-band antenna element will rotate in the clockwise direction, and an LHCP radiation is thus achieved, as shown in Figure 6b.  
For the purpose of elucidating the operational mechanism of the offset of excitation, the surface electric field distributions of the S- and C-band antenna elements were investigated, as depicted in Figure 7. It is a well-established principle in the field of electromagnetics that a diminished electric field intensity correlates with a relatively reduced impedance value. Consequently, by positioning the probe in the vicinity of points characterized by lower electric field intensity, the attainment of favorable impedance matching conditions can be ensured. This approach is predicated on the fundamental understanding of the relationship between electric field characteristics and impedance behavior, thereby facilitating the optimization of antenna performance through precise manipulation of the probe location with respect to the electric field distribution. In Figure 7, it can be seen that the electric field intensities at the positions where the two probes are located are relatively weak, indicating that the antenna has a relatively good impedance matching at this time. For the S-band element antenna, the offset of the probe relative to the \(y\)-axis is 1.4 mm (millimeter); on the other hand, on the patch of the C-band element, the probe offset is about 2.3 mm.  
The simulated S\({}_{11}\) and the gain of the elements are shown in Figure 8. As shown in Figure 8a, the simulated \(-\)10 dB impedance bandwidth of the S-band antenna is about 6.6% from 1.91 GHz to 2.04 GHz. A simulated maximum gain of 6.76 dB is attained at the center frequency of 1.97 GHz. The peak gain does not take into account the mismatch caused by reflection. The gain variation of the antenna is less than 0.1 dBi over the whole operation band. The simulated results of the C-band element are depicted in Figure 8b; the simulated S\({}_{11}\) shows that the impedance bandwidth is about 10% from 3.37 to 3.73 GHz. A simulated  
Figure 6: Simulated current distributions of (**a**) the S-band element at 1.975 GHz; (**b**) the C-band element at 3.55 GHz.  
maximum gain of 6.84 dBi is achieved at a center frequency of 3.55 GHz. The peak gain is higher than 6.5 dBi with a variation of less than 0.2 dBi over the whole operation band. Notably, the reason that the impedance bandwidth in the C-band is higher than that in the S-band is its relatively greater thickness (the element in the C-band is 0.071 \(\lambda_{c}\), while that in the S-band is 0.04 \(\lambda_{s}\)).  
The simulated AR of the proposed shared-aperture array is shown in Figure 9; one can see that a good CP performance with AR less than 0.5 dB is obtained in the whole operating bands of S-/C-bands. For the proposed array, such excellent circular polarization performance within the two frequency bands benefits from the application of the sequential rotation technique.  
Figure 8: Simulated S\({}_{11}\) and gains (**a**) the S-band antenna element; and (**b**) the C-band antenna element.  
Figure 7: Simulated electric field distributions of (**a**) the S-band element at 1.975 GHz; and (**b**) the C-band element at 3.55 GHz.