# An Evaluation of Orbital Angular Momentum Multiplexing Technology
## 3 Beam Focusing Effect Using Dielectric Lens for OAM Multiplexing
### Experiments of OAM Multiplexing Using Dielectric Lens  
To confirm the basic operation produced in using a dielectric lens, we performed a propagation experiment using the 28 GHz band in an anechoic chamber. Figure 4 shows the experimental setup. The measurement frequency of the network analyzer (NWA) was set from 2 to 3 GHz. Radio frequency (RF) chains up-converted 28-29 GHz inserted signals and fed them to the Tx antenna. At the receiver side, the received signals were down-converted to 2-3 GHz signals by the RF chains attached directly after the Rx antenna. We used a millimeter wave commercial lens whose directional gain and beam half-width were, respectively, 35 dBi and 3 cm (centimeters). The design requirements for dielectric lenses, including focal length, refractive index, diameter, directional gain, and beam half-width, remain open for analysis. In the propagation measurements, we measured the channel coefficient between the Tx and Rx antennas using NWA while operating the positioner to move the Tx and Rx antennas to form the Tx and Rx UCAs elements' location sequentially. In other words, we emulated Tx and Rx UCAs using a single Tx and Rx antenna by sequentially measuring the channel coefficients of two points and combined the entire measurements to obtain channel characteristics between the emulated Tx and Rx antennas. The gain for both Tx and Rx antennas element was 27 dBi. We obtained \(M\times N\) channel matrix \(H\) with measured channel coefficients consisting of all combinations between \(N\)-points (Tx side) and \(M\)-points (Rx side). Subsequently, we performed a matrix operation corresponding to OAM mode generation on the measured channel matrix and evaluated the phase and intensity distributions. The amplitude and phase characteristics of the OAM mode \(n\) were obtained by multiplying the column vector that generates OAM mode \(n\) by obtained channel matrix \(H\). Table 1 shows experimental parameters. First, to confirm that an OAM mode was generated at the Rx side, we measured the phase distribution and the intensity distribution formed by the beam passing through the lens on the Rx side. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Parameter** & **Value** \\ \hline \multirow{2}{*}{**Lens**} & Focal length: \(f\) & 0.30 m \\  & Diameter: \(D_{L}\) & 0.30 m \\ \hline \multirow{3}{*}{UCA} & Number of antenna elements & 12 \\  & Diameter: \(D_{T}\) & 0.04 m \\ \cline{1-1}  & Distance between lens and UCA: \(a\) & 0.40 m \\ \hline \multirow{2}{*}{Others} & Frequency & 28 GHz \\  & Distance between Tx and Rx: \(b\) & 3.12 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental parameters (Dielectric lens). Figure 4: Experimental environment (OAM multiplexing using dielectric lens). Figure 5 shows the measurement results and simulation results of the intensity distribution and phase distribution of OAM modes \(-\)2, \(-\)1, 0, +1, and +2. The measurements were conducted over a 60 cm \(\times\) 60 cm grid and data were acquired at 3 cm intervals. The figure results confirmed that OAM beams whose phases rotate as much as their mode order were obtained in the experiments. The results also well matched the simulation results. Further, we consider that our experimental method will make it possible to emulate OAM beam generation. Next, we conducted experiments to ascertain the beam divergence reduction effect obtained with the lens. We took into account the distance from the center of the Rx side to the location of the strongest beam intensity since it is the quantitative index for evaluating beam divergence. We defined this metric as the beam diameter. The smaller is the beam diameter, the smaller is the beam divergence at the Rx side because the beam energy is more focused close to the center of the Rx antenna. Figure 6 shows comparisons between a UCA with a 4 cm diameter, a UCA with a 16 cm diameter, and a UCA with a 4 cm diameter plus a 16 cm lens. Figure 5: Measurement results and simulation results of phase and intensity distributions.