## 3 Results and Discussion  
In this section, we analyze the performance of an FSO communication system utilizing non-uniformly correlated high-order Bessel-Gaussian beams carrying the OAM state under conditions of atmospheric turbulence. The parameters were set as follows, unless otherwise indicated: \(w_{0}=1\) cm, \(r_{c}=1\) cm, \(l_{0}=1\), \(\alpha=10^{3}\) m\({}^{-1}\), \(\lambda=1550\) nm, \(C_{n}^{2}=5\times 10^{-15}\)m\({}^{-2/3}\), D = 10 mm, and \(z=500\) m.  
Figure 1 shows the detection probability of the OAM mode for non-uniformly correlated high-order Bessel-Gaussian beam propagation in a turbulent atmosphere. As shown in Figure 1a, the detection probabilities of the topological charge difference \(|\,\Delta I|=1\), \(2\), and \(3\) increase when propagation increases, and the detection probability for a large topological charge difference is smaller than that for a small topological charge difference. The detection probability of the signal OAM state for the topological charge difference \(|\,\Delta I|=0\) reduces slightly when the propagation distance increases. These results show that the power of the signal OAM states spreading to the neighbor OAM states is very small when the OAM state carried by non-uniformly correlated high-order Bessel-Gaussian beams is disturbed by a turbulent atmosphere; that is, high-order Bessel-Gaussian beams with a non-uniform correlation can be used to mitigate the perturbations caused by a turbulent atmosphere. Figure 1b shows that the signal OAM state at \(|\,\Delta I|=0\) has the most power at the different propagation distances, the crosstalk of the OAM states appears in the neighboring modes for the topological charge difference \(|\,\Delta I|=1\), and the power of the other OAM states' crosstalk for the large topological charge difference is very low. Figure 2 shows the detection probability of the signal OAM state for non-uniformly correlated high-order Bessel-Gaussian beams affected by different receiving aperture diameters. As shown in Figure 2, the detection probability of the signal OAM state decreases at the different receiving aperture diameters (D = 10 mm, 20 mm, 30 mm, and 40 mm) when the propagation distance increases. At the same propagation distance, the detection  
Figure 1: Detection probability of the OAM mode for non-uniformly correlated high-order Bessel-Gaussian beams in a turbulent atmosphere with different (**a**) topological charge differences \(|\,\Delta I|\) and (**b**) propagation distances \(z\). probability of the signal OAM state limited by a small aperture is greater than it is when the receiver aperture is large. This result shows that the receiver aperture can be used to filter crosstalk from neighboring OAM states generated by a turbulent atmosphere. Therefore, choosing a suitably sized receiver aperture can effectively enhance the transmission quality of the signal OAM mode in the turbulent atmosphere channels. Figure 3 shows the detection probability of the different signal OAM states carried by the non-uniformly correlated high-order Bessel-Gaussian beams propagating in a turbulent atmosphere; the topological charges \(l_{0}\) of the signal OAM states are 1, 3, 5, and 7, respectively. As shown in Figure 3, the detection probabilities decrease when the propagation distance increases. The detection probabilities of the signal OAM state are the same at the near field; as the propagation distance further increases, the detection probabilities of the signal beam carrying the large OAM state are lower than those for the beam with the small OAM state. These results show that the non-uniformly correlated high-order Bessel-Gaussian beams carrying the large OAM states are affected easily by the turbulent atmosphere. Figure 4 shows the detection probability of the signal OAM state carried by the non-uniformly correlated high-order Bessel-Gaussian beams in a turbulent atmosphere for the different wavelengths (\(\lambda\)) studied.