# Dielectric Slabs-Based Lens for Millimeter-Wave Beamforming
## 4 Conclusions  
A dielectric slab-based lens has been proposed for millimeter-wave beamforming systems based on graded steps of the effective refractive index of the semi-spherical dielectric lens. The proposed lens has a simple and scalable design. The horn antenna is used with the proposed lens to test the performance of the designed lens using a numerical full-wave simulator. For a centered horn antenna with a 50.5 mm focal point, the horn-lens system demonstrates a gain of 30 dBi, HPBW of 10\({}^{\circ}\), and sidelobe level less than \(-\)21.2 dB mm. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Antenna \#** & **Gain (dBi)** & **Sidelobe Level (dB)** & **HPBW (Degree)** & \(\mathbf{\theta}\) & \(\mathbf{\phi}\) \\  & & & & **(Degree)** & **(Degree)** \\ \hline ANT1, ANT2 & 27.2 & \(-\)20.1 & 6.2 & \(-\)27 & 40, \(-\)40 \\ \hline ANT3, ANT4 & 27.9 & \(-\)20.43 & 6.6 & \(-\)21 & 15, \(-\)15 \\ \hline ANT5, ANT6 & 26.6 & \(-\)21.6 & 7.8 & \(-\)7 & 40, \(-\)40 \\ \hline ANT7, ANT8 & 26.6 & \(-\)21.6 & 7.8 & 7 & 40, \(-\)40 \\ \hline ANT9, ANT10 & 27.9 & \(-\)20.43 & 6.6 & 21 & 15, \(-\)15 \\ \hline ANT11, ANT12 & 27.2 & \(-\)20.1 & 6.2 & 27 & 40, \(-\)40 \\ \hline ANT13, ANT14 & 27.3 & \(-\)21.6 & 5.9 & \(-\)19 & 70, \(-\)70 \\ \hline ANT15, ANT16 & 27.3 & \(-\)21.6 & 5.9 & 19 & 70, \(-\)70 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The performance of the millimeter-wave beamforming of 16 switchable antennas. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Reference** & **Gain (dBi)** & **Sidelobe Level (dB)** & **HPBW** & **Frequency** & **Designed Lens** & **Tested Antennas** \\ \hline
**Proposed** & 30 & \(-\)19.8 & 6 & 28 GHz & Dielectric slabs & Circular horn \\
**work** & 25 to 27 & \(-\)20 to \(-\)21.6 & 5.9 to 7.8 & 28 GHz & Dielectric slabs & Rectangular horn \\
[7] & 29.4 & \(-\)22 & 6 & 28 GHz & Spherical dielectric flat lens & Rectangular horn \\  & & & & & & \\  & & & & & & \\
[25] & 15.4 to 18.9 & \(-\)18 & 12 to 20 & 60, 77 GHz & \
\begin{tabular}{c} with holes on \\ concentric rings of \\ different \\ permittivity \\ Metamaterials \\ lenses \\ \end{tabular} &
\begin{tabular}{c} Conical horn \\ antenna \\ with holes on \\ \end{tabular} \\
[26] & 21.25 & \(-\)23 & 9.6 & 9.4 GHz &
\begin{tabular}{c} Metamaterials \\ lenses \\ with a set of \\ concentric rings of \\ different \\ permittivity \\ Dielectric flat lens \\ with holes on \\ \end{tabular} \\
[27] & 16.9 to 21.2 & \(-\)3.5 to \(-\)20 & 10.5 to 22.3 & 60 GHz &
\begin{tabular}{c} with a set of \\ concentric rings of \\ different \\ permittivity \\ Dielectric flat lens \\ with holes on \\ \end{tabular} \\
[28] & 14 to 18.4 & \(-\)10 to \(-\)15 & 10 to 20 & 60 GHz &
\begin{tabular}{c} concentric rings of \\ different \\ permittivity \\ Metasurfaces \\ layered lens \\ \end{tabular} & Array antenna \\
[29] & 16.4 & 15 & 30.2 & 10 GHZ &
\begin{tabular}{c} Metasurfaces \\ layered lens \\ \end{tabular} & Patch antenna \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the proposed lens with other works. The designed lens represents a perfect approximation of a semi-spherical lens, in which they have the same performance. The designed lens realizes a spatial beam scanning of \(\theta\approx\pm 30^{\circ}\), \(\phi=\pm 70^{\circ}\) with a maximum gain range of 26.6-27.9 dB by switching on one of the sixteen ports of horn antennas in each time. The proposed lens can represent an alternative solution to the existing spherical dielectric lens configurations at millimeter-wave frequencies. Conceptualization, Y.T.A. and A.H.A. ; software, Y.T.A. ; methodology, Y.T.A. and A.H.A. ; formal analysis, Y.T.A. and A.H.A. ; validation, Y.T.A. and A.H.A. ; investigation, Y.T.A. and M.T.A. resources, M.T.A. ; data curation, Y.T.A. ; writing--original draft preparation, Y.T.A. ; writing--review and editing, Y.T.A. and A.H.A. ; visualization, Y.T.A. and A.H.A. ; supervision, A.H.A. and M.T.A. All authors have read and agreed to the published version of the manuscript.