# Effects of Atmospheric Turbulence on OAM-POL-FDM Hybrid Multiplexing Communication System
## 3 Discussion on Transmission Performance under the Turbulence
In other words, the greater the influence on the phase when there is a larger topological charge, the more prone the phase of the central portion will be affected. Therefore, at the same turbulence intensity and transmission distance, when the topological charge is larger, the influence of turbulence on the central portion of the beam will be more severe. Figure 4: Distributions of intensity and phase of a vortex beam with a topological charge of \(l=+8\) at different transmission distances under a turbulence intensity of \({\rm C_{n}}^{2}=10^{-15}\) m\({}^{-2/3}\). The intensity distribution becomes more dispersed and the phase distortion becomes more apparent as the transmission distance increases. Figure 5: Optical intensity and phase distribution of the vortex beam after transmission through different turbulence intensities. Here, the topological charge of the vortex beam is \(l=+8\) and the transmission distance is 3 km. Turbulence intensity varies from weak turbulence (\({\rm C_{n}}^{2}=10^{-16}\) m\({}^{-2/3}\)) to strong turbulence (\({\rm C_{n}}^{2}=10^{-13}\) m\({}^{-2/3}\)). During the transmission, when the vortex beam is influenced by turbulence, the original topological charge will become a new topological charge due to the phase distortion, and energy leak will cause channel crosstalk between the vortex beams [30]. We compared the crosstalk of the OAM mode after the signal passed through the turbulent channel under different turbulence intensities and the results are shown in Figure 7. When the vortex beam passes through the turbulence channel, the OAM will leak from \(l=\) n to n \(\pm\) 1, n \(\pm\) 2,... Crosstalk will cause a power loss of the original OAM mode after long-distance transmission, while the noise of the neighbor OAM mode will increase [31]. Figure 7c,d reveal the crosstalk of the signal under turbulence. When the OAM beam passes through weak (\({\text{C}_{\text{n}}}^{2}=10^{-16}\) m\({}^{-2/3}\)) and strong (\({\text{C}_{\text{n}}}^{2}=10^{-14}\) m\({}^{-2/3}\)) turbulence, 7.2% and 46.8% of the energy is leaked into the neighbor OAM mode, respectively. When the turbulence intensity increases, the crosstalk becomes increasingly obvious and the energy distribution becomes more dispersed. When two OAMs are multiplexed information transmission, mutual interference will occur between these two OAM modes [30; 32; 33]. Figure 7f-h depict the circumstance when two OAMs are transmitted simultaneously. In the case of weak turbulence (\({\text{C}_{\text{n}}}^{2}=10^{-16}\) m\({}^{-2/3}\)), approximately 7% of the energy leaks to other neighboring OAM modes. While in the case of strong turbulences  
Figure 6: The distribution of intensity and phase of the vortex beam with different topological charges. Turbulence intensity is \({\text{C}_{\text{n}}}^{2}=5\times 10^{-15}\) m\({}^{-2/3}\) and transmission distance is 2 km. Figure 7: Contrast of signal crosstalk and comparisons of bit error rate (BER) under different turbulence intensities. **(a,b)** Single OAM mode distribution of a channel at the transmitter and that without turbulence. **(c,d)** Comparison of mode crosstalk in the case of strong turbulence (\({\text{C}_{\text{n}}}^{2}=10^{-14}\) m\({}^{-2/3}\)) and weak turbulence (\({\text{C}_{\text{n}}}^{2}=10^{-16}\) m\({}^{-2/3}\)). **(e,f)** Two-OAM modes distribution at the transmitter and that without turbulence. **(g,h)** Superposition of different OAM modes under strong turbulence and weak turbulence. **(i)** Comparison of BER of received signals. BER: bit error rate. (\({\rm{C_{n}}^{2}=10^{-14}~{}m^{-2/3}}\)), 49.6% and 46.7% of the energy from these two OAM modes leaks to the neighbor OAM modes, respectively. As is demonstrated in Figure 7h, since the energy distribution of the signal under strong turbulence is relatively scattered, the energy leaked from OAM mode A is superimposed with the energy of the adjacent OAM mode B, which affects the information of OAM mode B [34]. That is to say, when the turbulence increases, the mode crosstalk becomes worse, so the SNR of the signal decreases.