# Tilted Beam Fabry-Perot Antenna with Enhanced Gain and Broadband Low Backscattering
## 2 Proposed Antenna System and Its Operation
### Unit Cell Configuration
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Parameter** & \(g\) & \(m\) & \(l\) & \(w\) & \(r\) & \(p\) & \(h\) & \(v\) & \(R\) \\ \hline
**Value** & 3.2 & 16 & 8 & 0.9 & 0.5 & 14.7 & 20 & variable & 100 \(\Omega\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Finalized structural dimensions (unit, mm). For varying patch size, the frequency response of reflection magnitude (S\({}_{11}\)) for a wave incident towards the negative \(z\)-axis is shown in Figure 4a. It can be seen that the magnitude of reflection is below \(-10\) dB over a wide band, i.e., from about 7 GHz to 16 GHz. Around 6.6 GHz and slightly below, the reflection magnitude stays about \(-4\) dB. This means that most of the incident wave is not being reflected backwards towards the positive \(z\)-axis. Before explaining how absorption of the incident wave takes place, it is necessary to also analyze transmission response (S\({}_{21}\)) of the wave when it is incident towards the negative \(z\)-axis. This response is shown in Figure 4b for various values of patch size, and it can be seen that from 7 GHz to 14.5 GHz, the magnitude of transmission is well below \(-10\) dB. Around 6.6 GHz, it is about \(-8\) dB (for \(v=10\) mm) and below. Therefore, from the above discussion, it is clear that reflection, as well as transmission, has been minimized over a wide range of frequencies, and this implies that most of the incident wave should  
Figure 2: (a) Unit cell structure; (b) Unit cell boundary conditions (dimensions are shown in Table 1). be absorbed on the top resistive surface. Mathematically, the absorption can be calculated using Equation (2) as [26]:  
\[A(\omega)=1-\Gamma(\omega)-T(\omega) \tag{2}\]  
where \(A\) is absorption, \(\Gamma\) is reflection, \(T\) is transmission, and \(\omega\) is frequency. From Equation (2), when reflection and transmission is \(-10\) dB and below, the absorption of incident wave is 80% or more. From Figure 4, it can be witnessed that from 7 GHz to 14.5 GHz, both reflection and transmission are below \(-10\) dB; thus, good out-of-band RCS reduction has been achieved. Around operating frequency, some degree of absorption degradation can be seen; nevertheless, in-band RCS reduction along with antenna gain enhancement can still be obtained [13; 27]. The transmission response shown in Figure 4b corresponds to the incident wave from Port 1 to Port 2 (S\({}_{21}\)) of the unit cell. Its S\({}_{12}\) response (from Port 2 to Port 1) is exactly alike, as the unit cell (and thus the superstrate) is a passive structure. To avoid repetition, the plot has not been shown here. However, it is important to highlight that the transmission at operating frequency is about \(-8\) dB and below (S\({}_{21}\) = S\({}_{12}\)), which implies the radiation efficiency of the F-P antenna is expected to be somewhat compromised. The presented plots in Figure 3; Figure 4 are for TE wave polarization. Because the unit cell design is symmetric, TM wave polarization would give exactly the same response, and therefore has been omitted for brevity. Figure 3: Reflection response of the positive \(z\)-axis incident wave. (**a**) Reflection phase; (**b**) Reflection magnitude (linear); (**c**) Reflection phase versus gradient patch size (shown at 6.6 GHz). It is noteworthy that the top absorptive surface (absorptive FSS) alone would only act as a bandpass/bandstop filter, and its interaction with the incident wave is based on the resonance determined by its dimensions. However, the key to achieve incident wave absorption is the integration of the top surface with the composite PRS, which (as an integrated unit) would aid in achieving the suppression of radar backscattering. Before proceeding to the next section, it is important to discuss how the absorptive FSS and PRS behave individually to the application of the incident wave. For the absorptive FSS alone, the frequency responses of reflection (S\({}_{11}\)) and transmission (S\({}_{21}\)) magnitude are shown in Figure 5a. The inset shows the simulated model.