# Effects of Atmospheric Turbulence on OAM-POL-FDM Hybrid Multiplexing Communication System
## 3 Discussion on Transmission Performance under the Turbulence  
Different topological charges in OAM multiplexing determine the channel of communication, and the change of topological charge will influence the transmission of signals in the corresponding channel. We studied the influence of different transmission distances, turbulence intensities, and topological charges on the phase. The simulation was carried out under FSO atmospheric turbulence [27], and the results are shown in Figure 3a. At the same turbulence intensity, the size of the light spot increases with the increase in transmission distance. Due to the inhomogeneity of atmospheric mediators, increasing the turbulence intensity will increase the spot size. When the beam passes through a non-uniform atmosphere, it may come up with random refraction that will cause the beam spot size to become larger and the power is reduced after the beam is transmitted for a span of distance. This phenomenon can be optimized by increasing the optical power of transmission or adding optic devices with the function of converging beams at the receiving end. In addition, because of the existence of random refraction, the beam has a certain deviation angle after passing through the turbulent channel. As shown in Figure 3b, when the turbulence intensity is fixed, the deviation angle gradually increases as the transmission distance increases, and the intensification of turbulence also causes the increase in deviation angle under the same distance. When a vortex beam with a topological charge of \(l=+8\) is transmitted under turbulence with an intensity of \(\text{C}_{\text{n}}{}^{2}=10^{-15}\) m\({}^{-2/3}\) (moderate turbulence), its intensity is affected differently with the change in transmission distance. The phase is distorted as the transmission distance increases, as shown in Figure 4. It can be discovered that as the transmission distance increases, the optical field becomes increasingly scattered and the spot size also becomes larger [28]. The phase of the vortex beam is changed from the original regular phase distribution to a distorted spiral phase distribution. To completely receive the energy of the beam at the receiving end, receivers with a larger size or converging lens are required. When the size of the receiver aperture is kept constant, the rise of the transmission distance leads to a decrease in both the energy that enters the receiver and signal-to-noise ratio (SNR). Figure 3: (**a**) Spot size distribution of the vortex beam of \(l=+4\) under different transmission distances. (**b**) Comparison of different deviation angles of beam under different transmission distances. Figure 5 shows the intensity and phase distribution of a vortex beam of \(l=+8\) at different turbulence intensities. The phase of the vortex beam is distorted as it passes through the atmospheric turbulence and the phase distortion will become more severe as the turbulence intensity increases [29]. When the turbulence intensity is higher than \({\rm C_{n}}^{2}=10^{-14}\) m\({}^{-2/3}\), the phase is almost indistinguishable. Therefore, when the transmission distance is 3 km, the turbulence intensity should be less than \({\rm C_{n}}^{2}=5\times 10^{-15}\) m\({}^{-2/3}\) to ensure that the phase can be distinguished and the receiver can separate the signals according to the phase. With constant transmission distance and turbulence intensity, when the topological charge is changed, the distributions of intensity and phase in the link are demonstrated in Figure 6. After long-distance transmission, the beam center is more susceptible when the topological charge increases. Phase distortion is more severe in central areas than in edge areas. The center of the vortex beam is the phase singularity, and the amplitude at the center is almost zero, so turbulence has a relatively larger impact on the phase of the position where the amplitude is small.