## 2 Double-Layer Tapered Slot Antenna Design
In Figure 4a, the reflection coefficient of the conventional TSA indicates wide impedance matching in the Ka-band, which is just attributed to the energy loss to the absorbers. The radiation efficiency is only 24%. The radiation pattern in Figure 4b shows that the conventional TSA has -1.3 dBi gain at \(\theta=\phi=0^{\circ}\), 8.3 dB lower than that of the proposed design. The main beam direction is also tilted to \(\theta=10^{\circ}\) with \(\phi=90^{\circ}\). Therefore, using a conventional TSA for array antenna design with an EM absorber layer for monostatic RCS reduction would be very challenging. Lastly, we carried out a parametric study on the EM absorber thickness \(L_{4}\) from the bottom edge along \(z\) of the tapered slot, to observe its impact on the impedance matching and radiation characteristics. The results are given in Figure 5. In Figure 5a,b, we first observe that the impedance matching and radiation pattern do not deviate much, up to \(L_{4}=5\) mm, which is the point where the EM absorber is about to meet the slotted radiator (see Figure 1c). When \(L_{4}=7\) mm, the antenna performance inevitably decreases because the EM absorbers encounter part of the radiating slot. The radiation efficiency certainly decreases as the thickness of the absorber increases, as shown in Figure 5c. Note that the radiation efficiency is 88% at 35 GHz with \(L_{4}=5\) mm, which is an acceptable value for the TSA design. The monostatic RCS values according to \(L_{4}\), calculated when the cross-polarized wave (i.e., electric field along \(x\)-axis) is incident, are plotted in Figure 5d. The cross-polarized RCS is calculated using the CST integral equation solver when the cross  
Figure 2: Simulation results for the DLTSA according to the presence of the EM absorber (FGM-125 on Figure 1b,c). (**a**) Reflection coefficients. (**b**) The \(\theta\)-sweep radiation patterns at 35 GHz (\(\phi=90^{\circ}\)). polarized wave is normally incident along \(z\)-axis. We confirm that higher RCS reduction can be achieved by placing thicker absorbers. The RCS reduction for the co-polarized wave (i.e., electric field along \(y\)-axis) should be lower because most of the field is incident into the \(y\)-aligned aperture of the DLTSA before reaching the EM absorber layers [19]. In Figure 5d, for the DLTSA with the absorber thickness of 3 mm and 5 mm showing proper radiation properties, we observe that the RCS is reduced more at higher frequencies after 10 GHz. This is because the used FGM-125 absorbs EM fields more at higher frequencies [18]. In general, the thicker the absorber thickness, the greater the RCS reduction. However, the DLTSA with the absorber thickness of 7 mm does not radiate properly, and the radiation efficiency and gain are poor. The RCS feature also shows different behavior from other design cases. Considering the antenna performance, the absorber thickness \(L_{4}\) is chosen as 5 mm, such that the upper edge of the absorber can be located right behind the slotted radiator. Figure 3: Simulation results. (**a**) Surface current distribution of a conventional TSA with the EM absorber (FGM-125) at 35 GHz. (**b**) Reflection coefficients of the conventional TSA according to the presence of the EM absorber. (**c**) The \(\theta\)-sweep radiation patterns at 35 GHz (\(\phi\) = 90\({}^{\circ}\)) for the conventional TSA. (**d**) Surface current distribution of the DLTSA with the EM absorber at 35 GHz. Figure 4: Simulation results for the conventional TSA and proposed DLTSA with the EM absorber (Figure 3a,d). (**a**) Reflection coefficients. (**b**) The \(\theta\)-sweep radiation patterns at 35 GHz (\(\phi\) = 90\({}^{\circ}\)). Figure 5: Simulation results of the DLTSA according to the thickness (\(L_{4}\)) of the EM absorber. (**a**) Reflection coefficients. (**b**) The \(\theta\)-sweep radiation pattern (\(\phi\) = 90\({}^{\circ}\)). (**c**) Radiation efficiency. (**d**) Cross-polarized monostatic RCS results.