Behavior of phase singularities for laser beam propagating through uplink and downlink atmospheric turbulence paths
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摘要: 利用激光大气传输四维程序数值模拟了激光在湍流大气中上行和下行传输时产生的相位奇点的变化过程。由模拟结果可知，当光束自地面向空中垂直上行传输时，相位奇点数密度随传输高度的变化有一个从无到有、从快速增加到缓慢增加、达到峰值后又减小的过程；湍流越强，畸变光场中产生的相位奇点数密度越大，达到的峰值越高，且达到峰值后减小的幅度也越大，但达到峰值时对应的传输高度越低；当激光自空中某一位置垂直下行传输时，相位奇点数密度随传输距离的增加有一个从无到有、从缓慢增加到快速增加且在接近地平面处急剧增加的过程。另外，通过对模拟结果的曲线拟合发现，激光在湍流大气中上行传输时产生的相位奇点数密度与传输高度的关系符合黑体辐射公式；当激光在湍流大气中下行传输时，相位奇点数密度随传输距离的增加呈指数增加。Abstract: Behavior of phase singularities in the distorted optical field is studied by numerical modeling using four-dimension code when a laser beam propagates through uplink and downlink atmospheric turbulence paths. The results reveal that, when the laser beam propagates along an uplink turbulent atmosphere path, the density of phase singularities (DPS) starts at zero and then grows rapidly with the increasing of the propagating height. When the beam propagates to a certain height, the DPS reaches its maximum and then begins to decrease. Such a height changes with the turbulence strength. The stronger the turbulence strength, the bigger the generated DPS, and the lager the maximum DPS with correspondingly lower height. When the laser beam propagates along a downlink turbulent atmosphere path, the stronger turbulence strength is taken, the phase singularities emerge at a higher altitude and the DPS in distorted optical field is bigger near the ground. The functional form of the DPS has a shape of monotone increase with the decrease of the propagation height and the DPS reaches its maximum near the ground. In addition, formulas describing the relationship between the DPS and propagation height/distance are found out. When the laser beam propagates through turbulent atmosphere along an uplink path, the formula is very similar to the formula used for describing the Blackbody radiation in physics. When the laser beam propagates along a downlink atmospheric turbulence path, the DPS seems to be growing exponentially with the propagating distance.
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Key words:
- atmospheric optics /
- laser propagation /
- phase singularity /
- atmosphere turbulence
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图 1 湍流强度按H-V模型的垂直分布廓线
Figure 1. Vertical profile of turbulence strength with H-V model
图 3 上行传输时，不同湍流强度下相位奇点数密度随传输高度的变化
Figure 3. Density of phase singularities vs propagation height with different turbulence strength along an uplink path
图 4 下行传输时，不同湍流强度下的相位奇点数密度随传输距离的变化
Figure 4. Density of phase singularities versus propagation height with different turbulence strength along a downlink path
表 1 上行传输时，不同湍流强度下的拟合参量值
Table 1. Values of fitting parameters for different turbulence strength along an uplink path
Cn2(0)/m-2/3 A B n 4.18×10-15 7.263 89×106 51.836 23 2.963 80 2.09×10-14 1.179 76×105 14.975 62 2.015 38 4.18×10-14 4.055 25×104 8.632 92 1.735 97 
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表 2 下行传输时，不同湍流强度下的拟合参量值
Table 2. Values of fitting parameters for different turbulence strength along a downlink path
Cn2(0)/m-2/3 y0 A B 4.18×10-15 -0.047 72 7.741 74×10-7 1.208 82 2.09×10-14 -0.283 51 0.001 60 1.815 64 4.18×10-14 -0.889 90 0.069 23 2.473 72
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