# Computational Analysis of a 200 GHz Phased Array Using Lens-Coupled Annular-Slot Antennas
## 3 Simulation Results  
### A 1 \(\times\) 3 ASA Array Analysis  
A relatively small overall array size is preferred for a chosen silicon lens of R = 5000 um to realize a high antenna gain improvement. Therefore, as a prototype demonstration, a small 1 \(\times\) 3 array (the length of ~700 um, see Figure 3a inset.) was first analyzed by full-wave simulation using ANSYS HFSS to study the feasibility and design strategies to adopt such lens-coupled configuration for beam-steering phased arrays. Figure 3a shows the simulated array scanning beam angle (i.e., \(\theta\)) as a function of the feeding phase difference, \(\beta\), for different _L_/_R_ ratios (i.e., \(L\) changes from 0 um to 1500 um, with \(R\) fixed at 5000 um). In general, \(\theta\) increases when \(\beta\) raises from 0\({}^{\circ}\) to 180\({}^{\circ}\), and smaller extension lengths result in larger beam steering angles for the same feeding phase difference. Specifically, the \(\theta\) that can be achieved with a \(\beta\) of 180\({}^{\circ}\) changes from ~11\({}^{\circ}\) to ~20\({}^{\circ}\), ~36\({}^{\circ}\) and 41\({}^{\circ}\) when \(L\)  
Figure 2: (**a**) The configuration of the designed 200 GHz single ASA (the metal part is shown as gray) and (**b**) its radiation patterns into the dielectric half-space. decreases from 1500 um (\(L/R=0.3\)) to 1000 um (\(L/R=0.2\)), 500 um (\(L/R=0.1\)), and 0 um (\(L/R=0\)), respectively. For all cases, especially for \(L/R=0.2\) and 0.3, further increase in \(\beta\) (e.g., \(\beta>150^{\circ}\)) does not lead to a significant increase in \(\theta\). Figure 3a also shows the theoretic calculation result for a phased array without silicon lens using the array factor technique (black curve) [18], and the beam steering angle increases almost linearly with increasing \(\beta\) (maximum \(\theta=63^{\circ}\) when \(\beta=180^{\circ}\)). Compared to the lens-coupled ASA arrays studied above, ASA arrays without lenses generally show a larger achievable beam steering angle range. However, as shown later in this paper, lens-coupled array configurations could have much higher antenna gains which is much desired for mmW-THz applications. Figure 3b shows the antenna gain as a function of \(\theta\) for different configurations. For the lens-coupled ASA arrays, in general, the antenna gain increases with the increase in the extension length \(L\). At the same time, the achievable beam scanning range (when \(\beta\) changes from 0\({}^{\circ}\) to \(\pm\)180\({}^{\circ}\)) decreases. Particularly, the boresight gain (\(\theta=0^{\circ}\)) increases from 12.91 dB to 16.41 dB, 19.02 dB, and 24.01 dB, while the extension length changes from 0 um to 500 um, 1000 um, and 1500 um, respectively. For most phased-array systems, the maximum gain is typically located at boresight, but for the lens-coupled arrays with \(L/R=0\) and \(L/R=0.3\) studied here, relatively lower gains at boresight as compared to other scanning angles can be observed. This is caused by the off-axis property of the extended hemispherical lens, i.e., a higher gain at other angles can be generated by the off-axis antenna elements, which causes a lower gain at boresight [19]. For a 1 \(\times\) 3 ASA array without lens, as seen in Figure 3b, a peak gain of 7.2 dB is observed at \(\theta=0^{\circ}\), and the gain decreases when the antenna beam is steered away from the boresight (i.e., \(\theta>0^{\circ}\) or \(\theta<0^{\circ}\)). By using the lens-coupled array antenna configurations, a significant gain improvement can be achieved. Especially for the cases of \(L/R=0.1\) and 0.2, a decent gain improvement of 9.2 dB and 11.82 dB (compared to the same antenna array without the lens), respectively, have been achieved while maintaining a relatively large beam scanning range, i.e., \(\pm 36^{\circ}\) and \(\pm 20^{\circ}\), respectively, demonstrating that the proposed lens-coupled phased-arrays are promising for 5G or beyond wireless communications and other more advanced THz applications.