Scintillation index analysis of radial Gaussian vortex beam array propagation in the atmosphere
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摘要:
涡旋光束阵列在自由空间光通信领域有很大的应用价值。本文采用多相位屏模拟大气湍流，研究了径向高斯涡旋光束阵列在大气湍流环境中传输的光场演化过程和轴上闪烁特性，分析了不同初始光束参数对径向高斯涡旋光束阵列的轴上闪烁指数的影响，并将其与单束高斯涡旋光束的轴上闪烁指数进行对比。研究结果表明：在弱湍流区域，rytov指数小于0.5时，单束高斯涡旋光束的轴上闪烁指数一直保持在小于1的数值区域，远小于径向高斯涡旋光束的轴上闪烁指数；而在中等强度湍流区域，径向高斯涡旋光束阵列的轴上闪烁指数小于单束高斯涡旋光束的轴上闪烁指数。此外，还发现径向高斯涡旋光束阵列的轴上闪烁指数会随着轨道角动量值的减小和径向阵列半径的增大而减小。研究结果对于大气湍流环境下的涡旋光通信具有一定的理论意义和应用价值。
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关键词:
- 径向高斯涡旋光束阵列 /
- 轴上闪烁指数 /
- 相位屏仿真
Abstract:Beam arrays have great application value in free-space optical communication. In this paper, the light intensity evolution and the on-axis scintillation index of radial Gaussian vortex beam arrays propagating through atmospheric turbulence are analyzed using multi-phase screen simulation. The effect of initial beam parameters on the on-axis scintillation index of radial Gaussian vortex beam arrays is studied, and the on-axis scintillation index of radial Gaussian vortex beam arrays Ais a single compared with that of Gaussian vortex beam. The results indicate that in the weak fluctuation regime and when the rytov index is less than 0.5, the on-axis scintillation index of Gaussian vortex beams remains within a numerical range of less than 1, while the on-axis scintillation index of radial Gaussian vortex beam arrays is around 1. In the medium fluctuation regime, the on-axis scintillation index of the radial Gaussian vortex beam arrays is smaller than that of a single Gaussian vortex beam. The on-axis scintillation index of radial Gaussian vortex beam arrays decreases with the decrease of orbital angular momentum and the increase of radial array radius. The research results hold theoretical significance and application value for vortex optical communication in turbulent atmospheric environments.
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图 1
$Z = 0$ 处径向高斯涡旋光束阵列分布示意图Figure 1. Schematic diagram of radial Gaussian vortex beam array distribution at
$Z = 0$ 
图 3 RGVBA在真空中不同传输距离处的(a)~(d)光强和(e)~(h)相位分布图。
Figure 3. (a)~(d) Light intensity and (e)~(h) phase distribution of RGVBA at various propagation distances in free space.
图 4 不同折射率结构常数
$C_n^2$ 下RGVBA的光强分布($l = 2$ ，$Num = 9$ ，Z=2000 m)。(a)$C_n^2 = 0$ ；(b)$ C_n^2 = $ $ 5 \times {10^{ - 15}}{m^{{{ - 2} / 3}}} $ ；(c)$ C_n^2 = 5 \times {10^{ - 14}}{m^{{{ - 2} \mathord{\left/ {\vphantom {{ - 2} 3}} \right. } 3}}} $ ；(d)$ C_n^2 = 1 \times $ $ {10^{ - 13}}{m^{{{ - 2} / 3}}} $ Figure 4. The intensity distribution of RGVBA under different refractive index structure constants
$C_n^2$ ($l = 2$ ,$Num = $ $ 9$ , Z=2000 m). (a)$C_n^2 = 0$ ; (b)$ C_n^2 =5 \times {10^{ - 15}}{m^{{{ - 2} / 3}}} $ ; (c)$ C_n^2 = 5 \times {10^{ - 14}}{m^{{{ - 2} \mathord{\left/ {\vphantom {{ - 2} 3}} \right. } 3}}} $ ; (d)$ C_n^2 = 1 \times {10^{ - 13}}{m^{{{ - 2} /3}}} $ 
图 5 不同传输距离下(a) RGVBA及(b) GVB的轴上闪烁指数变化曲线
Figure 5. Variation of the on-axis scintillation index values of (a) RGVBA and (b) GVB at different propagation distances
图 6 中等湍流下GVB和RGVBA的轴上闪烁指数随着rytov指数增加的变化曲线
Figure 6. On-axis scintillation index values of GVB and RGVBA varying with rytov index in the medium fluctuation region
图 7 相同湍流条件下不同初始光束参数的RGVBA轴上闪烁指数值随子光束数目(Num)的变化情况。 (a)不同OAM值；(b)不同径向阵列半径
${r_0}$ Figure 7. Under the same turbulence conditions, the variation of on-axis scintillation index values of RGVBA with different initial beam parameters as a function of the number of beamlets (Num). (a) With different OAM values; (b) With different radial array radii
${r_0}$ 表 1 相位屏仿真参数
Table 1. Phase screen simulation parameters
采样网格$N$ 采样间隔$\Delta x$/mm 相位屏间隔$\Delta Z$/m 湍流内尺度${l_0}$/m 湍流外尺度${L_0}$/m 1024 1.7 200 0.01 10 波长$\lambda $/nm OAM值$l$ 子光束半径${w_0}$/mm 阵列半径${r_0}$/cm 子光束数目$Num$ 1550 1~3 3 1.8 6 
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表 2 不同折射率结构常数和传输距离对应的rytov指数
Table 2. The rytov index corresponding to each refractive index structure constant and transmission distance
折射率结构常数$C_n^2$ 传输距离范围$Z$ rytov指数$\sigma _R^2$ $1 \times {10^{ - 15}}{m^{{{ - 2} \mathord{\left/ {\vphantom {{ - 2} 3}} \right. } 3}}}$ 200~ 2400 m0.0010 ~0.0991 $5 \times {10^{ - 15}}{m^{{{ - 2} \mathord{\left/ {\vphantom {{ - 2} 3}} \right. } 3}}}$ 200~ 2400 m0.0052 ~0.4953 $1 \times {10^{ - 14}}{m^{{{ - 2} \mathord{\left/ {\vphantom {{ - 2} 3}} \right. } 3}}}$ 200~ 2400 m0.0104 ~0.9905
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