## 3 Results
The concrete PD values of OAM beams without (W/o) and with (W) GS algorithm corresponding to Figure 3 have been concluded and demonstrated in Table 1. Obviously, the results demonstrate that for weak turbulence strength levels, i.e., \(C_{n}^{2}=1\times 10^{-15}\)m\({}^{-2/3}\) (with three different phase screen numbers), the retrieval of the pre-compensation based on the GS algorithm is effective for enhancing the OAM's detecting resolution. Furthermore, the results also indicate the increasing phase screens directly affect the turbulence strength level at a fixed transmission distance. At the same time, the recovery results of the OAM beam with \(l=5\) are slightly worse than those with \(l=3\), which can be attributed to the relatively large radius of the OAM beam with higher topological charge. In general, the higher topological charge, the larger  
Figure 3: The intensity and phase distributions of orbital angular momentum (OAM) beams and their power density (PD) spectra without and with the pre-compensation of GS algorithm under simulated atmospheric turbulence with refractive index structure parameter \(C_{n}^{2}\) valued as \(1\times 10^{-15}\)m\({}^{-2/3}\). The parts circled in green, blue and red dashes’ frames represent simulated turbulence channel with random phase screens number of \(N=20\), 50 and 100 respectively. (a1, c1, e1) and (b1, d1, f1) are intensity profiles without pre-compensation for topological charge \(l=3\) and \(l=5\) respectively, (a3, c3, e3) and (b3, d3, f3) are their corresponding phase distributions, (a5, c5, e5) and (b5, d5, f5) are their corresponding PD spectra. (a2, c2, e2) and (b2, d2, f2) are intensity profiles with the pre-compensation of GS algorithm, (a4, c4, e4) and (b4, d4, f4) are their corresponding phase distributions, (a6, c6, e6) and (b6, d6, f6) are their corresponding PD spectra. beam's contacting area with turbulence flow; therefore, the introduced crosstalk is relatively larger, and the corresponding effect of the compensation with the GS algorithm is slightly worse. Then, as shown in Figure 4, we also investigated the influence of the increasing the turbulence level with \(C_{n}^{2}\) as \(1\times 10^{-14}\)m\({}^{-2/3}\). The concrete retrieving performances based on the GS algorithm have also been investigated. We can see that with increasing \(C_{n}^{2}\), the transmitted intensity and phase of the OAM beams will be more divergent. Notably, when the random phase-screens number reach 100 (as shown in the third column), it is very difficult to judge the concrete topological charge according to the phase distributions alone. The corresponding obtained PD spectrum for both \(l=3\) and \(l=5\) with and without pre-compensation under turbulence channel with \(C_{n}^{2}=1\times 10^{-14}\)m\({}^{-2/3}\) are illustrated in Figure 4. Here, the PDs of distorted LG beam are respectively 70.26%, 62.46%, and 37.69% corresponding to phase screen number \(N=20\), 50 and 100 for \(l=3\), and 66.49%, 47.57% and 27.27% for \(l=5\). The retrieval OAM power density after the compensation of GS algorithm corresponding to \(N=20\), 50 and 100 is respectively 86.24%,78.16% and 69.58% for \(l=3\), and 82.35%, 73.15% and 60.82% for \(l=5\). We also concluded and demonstrated the concrete PD values of OAM beams without (W/o) and with (W) GS algorithm corresponding to Figure 4, as shown in Table 2. According to these measured power spectrum distribution and concrete PD values, we find that when the refractive index structure parameter \(C_{n}^{2}\) is fixed as \(1\times 10^{-14}\)m\({}^{-2/3}\), with the increase of the phase screen number, the introduced crosstalk is more obvious, especially for the case of high topological charge in which the power density of the additional measured OAM mode has exceeded more than half of the power density of the target OAM mode due to crosstalk.