## 3 Results
However, after using the pre-compensation of GS algorithm, it can be seen from the recovered power spectra that the density of the additional mode can be reduced to a lower level, and we can still clearly distinguish and judge the value of the transmitted target OAM mode by setting reasonable density judgment threshold at the receiver in an OAM-based communication system. Meanwhile, by comparing Figures 3 and 4 we see that the power density spectrum under turbulence channel with phase screen number of \(N=100\) and refractive index structure parameter of \(C_{n}^{2}=1\times 10^{-15}\)m\({}^{-2/3}\), as shown in Figure 3, is close to that with \(N=20\) and \(C_{n}^{2}=1\times 10^{-14}\)m\({}^{-2/3}\), demonstrated in Figure 4. This means that the turbulence intensity level is directly not only related to the refractive index structure parameter, but also to the number of the simulated random phase screens; thus, under the specific combination of these two parameters, the turbulence intensity level may be similar, so the corresponding power spectrum is relatively close. \begin{table}
\begin{tabular}{c c c c c} \hline
**OAM Mode** & **W/o or W/ GS** & **N = 20** & **N = 50** & **N = 100** \\ \hline \multirow{2}{*}{\(l=3\)} & W/o GS & 94.96\% & 88.09\% & 67.94\% \\  & W/ GS & 99.98\% & 99.88\% & 96.46\% \\  & W/o GS & 91.56\% & 82.15\% & 64.33\% \\  & W/ GS & 99.73\% & 99.42\% & 98.35\% \\ \hline \end{tabular}
\end{table} 
Table 1: The power density (PD) values of orbital angular momentum (OAM) beams without (W/o) and with (W) GS algorithm corresponding to Figure 3.  
To further explore the impact of stronger turbulence intensity levels and find the limit that the GS algorithm can correct, we increase the value of \(C_{n}^{2}\) to \(1\times 10^{-13}\)m\({}^{-2/3}\). As the intensity and phase distributions of transmitted LG beams illustrate in Figure 5, the beams with topological charges of \(l=3\) and \(l=5\) are all strongly damaged under the turbulence channels with three different phase screens number, not only without pre-compensation, but also with the pre-compensation of GS algorithm. And although the phase has recovered after using the GS algorithm for compensation, it seems to reach the range limit that the GS algorithm can correct. According to the corresponding PD spectra, we find that the PDs for both distorted and retrieval with pre-compensation are all less than 50%. Obviously, although the GS algorithm is used to compensate the light intensity and phase, when the value of \(C_{n}^{2}\) is large, the turbulence intensity will reach a strong level, and it is beyond the compensation limit range of the GS algorithm, which can also be inferred from Table 3. Therefore, according to the distribution of the power density spectrum, we are unable to accurately detect the OAM mode of the actual transmitted target LG beam. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**OAM Mode** & **W/o or W/ GS** & **N = 20** & **N = 50** & **N = 100** \\ \hline \multirow{2}{*}{\(l=3\)} & W/o GS & 70.26\% & 62.46\% & 37.69\% \\  & W/ GS & 86.24\% & 78.16\% & 69.58\% \\ \multirow{2}{*}{\(l=5\)} & W/o GS & 66.49\% & 47.57\% & 27.27\% \\  & W/ GS & 82.35\% & 73.15\% & 60.82\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The PD values of OAM beams without (W/o) and with (W) GS algorithm corresponding to Figure 4.  
Figure 4: The intensity and phase distributions of OAM beams and their PD spectra without and with the pre-compensation of GS algorithm under simulated atmospheric turbulence with \(C_{n}^{2}\) valued as \(1\times 10^{-14}\)m\({}^{-2/3}\). The parts framed in green, blue and red dashes represent simulated turbulence channel with random phase-screen number of \(N\) = 20, 50 and 100 respectively.