# Computational Analysis of a 200 GHz Phased Array Using Lens-Coupled Annular-Slot Antennas
## 4 Conclusions  
Table 1 shows the lens-coupled arrays comparison between different configurations with \(\beta\) from 0\({}^{\circ}\) to \(\pm\)120\({}^{\circ}\) (for reasonably low SLL). For the same array element numbers (i.e., \(1\times 3\) array or \(1\times 5\) array), as the extension length increases, the gain improvement increases, and the beam scanning range decreases. In order to achieve a wider beam scanning range, a larger size array (e.g., \(1\times 5\) array) could be used with the same lens. However, the SLL of the \(1\times 5\) array is raised since the off-axis effect is more prominent. To solve the above issue, a shorter extension length is utilized to reduce gain improvement for low sidelobes and, hence, SLL. As a result, a \(1\times 5\) array with optimized extension length can achieve a wider beam scanning range while maintaining a reasonably low SLL. Although the reported approach is demonstrated using 200 GHz annular-slot antennas, the same approach using the lens-coupled configuration is universal and can be applied to other planar antenna topologies for phased arrays at different frequencies. The proposed lens-coupled phased array will soon be implemented with an optically controlled switch network [17] for a prototype demonstration of switchable THz beam steering.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{1\times 3}\) Arrays w/\(L\)/\(R\) = 0.1 & \(\mathbf{1\times 3}\) Arrays w/\(L\)/\(R\) = 0.2 & \(\mathbf{1\times 5}\) Arrays w/\(L\)/\(R\) = 0.0 & \(\mathbf{1\times 5}\) Arrays w/\(L\)/\(R\) = 0.05 \\ \hline Boresight gain & 16.41 dB & 19.02 dB & 13.92 dB & 15.27 dB \\ \hline Gain improvement & 9.2 dB & 11.82 dB & 6.51 dB & 7.51 dB \\ \hline Beam scanning & 44\({}^{\circ}\) & 34\({}^{\circ}\) & 62\({}^{\circ}\) & 52\({}^{\circ}\) \\ \hline SLL & \(-12\) dB to \(-9\) dB & \(-12\) dB to \(-9\) dB & \(-9\) dB to \(-7\) dB & \(-9\) dB to \(-7\) dB \\ \hline \hline \end{tabular}
\end{table}
Table 1: The lens-coupled arrays comparison between different configurations (\(\beta\) from 0\({}^{\circ}\) to \(\pm\)120\({}^{\circ}\)).  
Figure 6: The radiation pattern of the H-plane for a \(1\times 5\) array with (**a**) \(L\)/\(R\) = 0 and (**b**) \(L\)/\(R\) = 0.05 at different phase differences \(\beta\).  
This paper demonstrates the design, simulation, and analysis of a 200 GHz phased array, using lens-coupled annular-slot antennas. The simulation results show that for a \(1\times 3\) array, \(a\pm 17^{\circ}\) scanning angle, 11.82 dB gain improvement, and about \(-10\) dB SLL can be achieved using an extended hemispherical silicon lens (\(R=5000\) um, \(L=500\) um). By applying a shorter extension length (i.e., \(L=250\) um), a larger scanning angle of \(\pm 31^{\circ}\), 6.51 dB gain improvement, and a sidelobe level of about \(-8\) dB can be realized by using a \(1\times 5\) array. On the basis of the high performance reported here, we believe that the lens-coupled phased arrays have great potential and may find promising applications for future 5G and beyond wireless communications.  
Conceptualization, P.L. and L.L.; Data curation, P.L.; Formal analysis, P.L. and L.L.; Funding acquisition, L.L.; Investigation, P.L.; Methodology, P.L. and L.L.; Project administration, LL.; Software, P.L. and Y.S.; Supervision, L.L.; Writing--original draft, P.L.; Writing--review and editing, P.L., Y.S., Y.D. and L.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the National Science Foundation under Grants ECCS-1711631 and ECCS-1711052.  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors declare no conflict of interest.