## 2 Antenna Design
### Analysis of Radiation Nulls and Axial Ratio Performance  
The radiation null in the lower stopband is inherently produced by the crossed magnetoelectric (ME) dipoles, as established in [25]. To elucidate the operating principles of the two radiation nulls in the upper stopband, this work analyzes the corresponding surface current distributions, radiation patterns, and parametric variations. Figure 3 presents the simulated surface current distributions of the proposed antenna at its two upper stopband radiation null frequencies (6.20 GHz and 7.25 GHz, when t = 0). At 6.20 GHz, the surface currents are predominantly concentrated on the grid slots and exhibit significant out-of-phase components. Since the grid slots are essentially defect structures on the ground plane, their geometric dimensions determine the resonant frequency. When the incident wave frequency approaches the slot's resonant frequency, the excited counter-circulating currents around the resonant slots interact with the original ground plane currents to generate oppositely directed radiation components. This results in destructive interference in the far-field, causing a sharp radiation power reduction at this frequency. Conversely, at 7.25 GHz, the currents are mainly localized on the open-circuited stubs of the feed line, where the open-circuit stub, functioning as a terminal-open \(\lambda/4\) transmission line, exhibits an equivalent short-circuit condition at its resonant frequency. This results in high impedance characteristics that effectively suppress radiation at this specific frequency. The normalized radiation patterns at the three radiation null frequencies (including the lower stopband null) are displayed in Figure 4. It is evident from the figure that both the right-hand circularly polarized (RHCP) and left-hand circularly polarized (LHCP) components fall below \(-20\) dBic at these frequencies, demonstrating effective radiation suppression. Figure 4: Simulated radiation nulls radiation patterns at (**a**) 2.55 GHz, (**b**) 6.20 GHz, and (**c**) 7.25 GHz. Figure 3: Current distribution of the proposed antenna at two upper-band radiation nulls. (**a**) 6.20 GHz. (**b**) 7.25 GHz. Parametric studies showing the frequency shifts of the radiation nulls with key geometrical variations are provided in Figure 5. As illustrated in Figure 5a, when the planar dimension of the ME dipoles (\(L\)) decreases from 10 mm to 8 mm, the lower stopband radiation null shifts from approximately 2.55 GHz to 2.75 GHz, while the two upper stopband nulls remain unaffected. Figure 5b indicates that reducing the width of the grid slots (\(w_{8}\)) causes the radiation null at 6.2 GHz to shift towards higher frequencies. In Figure 5c, when w6 increases from 3 mm to 5 mm, the radiation null at 7.25 GHz shifts to 7.60 GHz, with the other two radiation nulls unchanged. Collectively, the evidence presented in Figures 3-5 demonstrates that the three radiation nulls are introduced by the ME dipoles, the grid slots, and the open-circuited stubs, respectively. Figures 6 and 7 elucidate the generation mechanism of the two circularly polarized operating frequencies in the proposed antenna. Figure 6a,b present the surface current distributions at 3.65 GHz and 4.45 GHz, respectively, captured at t = 0 and t = T/4. The current distributions reveal that at 3.65 GHz, the currents are predominantly concentrated on the crossed ME dipoles and exhibit distinct LHCP characteristics, while at 4.45 GHz, the currents are mainly localized at the coupling region between the inverted-L-shaped shorted metallic plates and the ME dipoles while maintaining the same LHCP properties. Figure 7 demonstrates the parametric effects on the axial ratio frequencies. As the length of the ME dipoles (\(w\)) increases, the AR frequency at 3.65 GHz shifts toward the lower band. When the length of the parasitic element (\(w_{1}\)) increases, the 4.45 GHz circularly polarized resonating frequency shifts toward the lower band.