## 4 Aperture Design: Parametric Analyses and Performance Evaluation
### Quadridge Radiating Elements
(**a**) Quadridge for linear polarization; (**b**) evanescent quadridge for linear polarization; (**c**) quadridge for circular polarization. S\({}_{11}\) for (\(\theta=0^{\circ}\)) is below \(-20\) dB; (**d**) evanescent quadridge for circular polarization. S\({}_{11}\) for (\(\phi=0^{\circ}/90^{\circ}\), \(\theta=30^{\circ}\)) and (\(\theta=0^{\circ}\)) is below \(-20\) dB; (**e**) quadridge for circular polarization; (**f**) evanescent quadridge for circular polarization. resonance, has been studied in [5] considering circular polarization. Here, the impact is even more apparent for linear polarization (Figure 12), where the scan blindness is shifted to higher frequencies and then out of the band, increasing the length \(l_{E}\). An optimal value of \(l_{E}\), 1 mm, has been chosen to achieve the same reflection coefficient value at the two ends of the band (around \(-5\) dB). The whole phenomenon of the scan blindness reduction is complex because it involves a multimodal interaction between the end of the ridges and the aperture. In the quadridge-to-free space discontinuity (Figure 3), the higher-order mode of the quadridge is strongly excited on the aperture because its cut-off frequency \(f_{c3}=20.4\) GHz is close to the upper limit of the frequency band. On the contrary, when the square waveguide section is added (Figure 11), both fundamental degenerate (TE\({}_{10}\), TE\({}_{01}\)) and higher-order modes (TE\({}_{11}\), TM\({}_{11}\)) are excited at the end of the ridges. However, the TE\({}_{11}\) and TM\({}_{11}\) are significantly attenuated (4.3 dB/mm at 20.2 GHz) because their cut-off frequency (31.1 GHz) is far from the operative bandwidth. In this way, the contribution of such higher-order modes to radiation is reduced with respect to the abrupt quadridge-free space interface. It should be mentioned that the TE\({}_{10}\) is also below cut-off (about 22 GHz). Nevertheless, as shown in Figure 10b, such a slightly evanescent mode (1.6 dB/mm) does not prevent radiation. However, the overall ARC is higher (at broadside and 30\({}^{\circ}\)) with respect to the quadridge element (see Figure 10a). The S\({}_{11}\) levels are quite acceptable for circular polarization (see Figure 10d) because (due to the polarizer) such a reflection coefficient basically depends on the difference between ARCs for the two linear polarizations, which is related to the difference response in the two orthogonal planes (see Equation (2)). Figure 11: Evanescent quadridge waveguide geometry. Figure 12: Scan blindness effect on the ARC depending on the evanescent length at \(\phi=0^{\circ}\) and \(\theta=60^{\circ}\). A further increment in \(I_{E}\) will result in a lower and flatter S\({}_{11}\) for circular polarization, but the S\({}_{21}\) will increase when in proximity of the lower end of the bandwidth. For this reason, \(I_{E}=1\) mm can also be considered an optimum value for circular polarization. As far as circular polarization is concerned, the evanescent quadridge provides an improvement of about 2-3 dB and overall bandwidth enlargement (Figure 10d) with respect to the nominal one (Figure 10c). The coupling S\({}_{21}\) shows values equals to \(-5\) dB at the lower end of the band due to the proximity of the cut-off frequency in both designs (Figure 10e,f). The impact of the increased ARC of the evanescent quadridge at low scanning angles is visible on S\({}_{21}\) (about \(-6\) dB) throughout the band. In conclusion, the quadridge with an evanescent section, which does not show the blindness at the expense of a higher reflection coefficient for linear polarization (and higher S\({}_{21}\) for circular), can be suitable for single-pol DRAs, where the port of the unexcited polarization is closed on a matched load (with a reduction in the overall efficiency). Figure 13 shows the scan loss at the band limits and center frequency when scanning from \(-60^{\circ}\) to \(60^{\circ}\) for both quadridge designs in both linear and circular polarization.