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Numerical simulation of horizontal propagation steady-state thermal blooming effect on laser beam with different intensity distribution
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摘要:
采用数值模拟的方法，以高斯光束、平顶光束、有中心遮拦的平顶光束为例，研究了激光在均匀大气传输过程中产生的稳态热晕效应。详细分析了发射功率、传输距离、光束直径、横向风速四种参数对热晕效应的影响，得到了以上三种光束的斯特列尔比和峰值偏移量随广义热畸变参数N的变化关系。数值仿真结果表明，在其他参数一致的情况下，发射功率越大、传输距离越长，热晕效应越强；而光束直径和横向风速的增加会减小热晕效应；不同激光强度分布对热晕效应的影响不同。在同样广义热畸变参数N的条件下，高斯光束的热晕效应最严重，平顶光束次之，空心光束的热晕效应最小。
Abstract:The horizontal propagation steady-state thermal blooming effects of laser beams with different intensity distributions, such as Gaussian beam, flat-top beam, and flat-top beam with center obscuration, have been investigated by numerical simulation. The impacts of the output power, the propagation distance, the beam diameter, and the wind velocity vertical to the propagation direction on the steady-state thermal blooming have been discussed for the above mentioned three kinds of beams. Furthermore, the steady-state thermal blooming induced Strehl ratio degradation and peak intensity offset versus the generalized thermal distortion parameter N after long-path horizontal propagation of laser beams with above mentioned three types of intensity distributions have been derived. The simulation results show that, for certain other parameters, the greater output power or longer propagation distance will induce the stronger thermal blooming, and the increment of the launch diameter or the convection wind velocity vertical to the propagation direction will weaken the thermal blooming oppositely. Furthermore, for laser beams with different intensity distributions, the impacts of the thermal blooming on the propagation are so different. Under the same generalized thermal distortion parameter N, the thermal blooming effect on the Gaussian beam is the most serious, followed by the flat-top beam, and flat-top beam with center obscuration is the smallest.
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Overview: With the development of laser technology, the laser plays an increasingly important role in military and civilian fields. A series of linear and nonlinear effects can be produced when laser propagated in the atmosphere. Among them, the thermal blooming is one of the important nonlinear effects. It also limits the power and brings adverse effects to many engineering applications of laser. Thermal blooming effect is a phenomenon that the atmospheric molecular and aerosol particles of atmosphere will absorb laser energy which accordingly causes heating expansion and the decrease of the local refractive index when laser propagates in atmosphere. Eventually, the energy of this laser beam will be reduced, the spot of this laser beam will be larger and the wave-front of this laser beam will be distorted. Thus, the study of propagation rules for laser beams through the atmosphere is of great significance for the effective application of the laser. In this paper equation for paraxial beams was deduced, which is foundation of numerical algorithms to solve thermal blooming problems. Bradley-Hermann thermal distortion parameter which is important to thermal blooming was given subsequently. The horizontal propagation steady-state thermal blooming effects of laser beams with different intensity distributions, such as Gaussian beam, flat-top beam, and flat-top beam with center obscuration, have been investigated by numerical simulation. The impacts of the output power, the propagation distance, the beam diameter, and the wind velocity vertical to the propagation direction on the steady-state thermal blooming have been discussed for the above mentioned three kinds of beams. Furthermore, the steady-state thermal blooming induced Strehl ratio degradation and peak intensity offset versus the generalized thermal distortion parameter N after long-path horizontal propagation of laser beams with above mentioned three types of intensity distributions have been derived. The simulation results show that, for certain other parameters, the greater output power or longer propagation distance will induce the stronger thermal blooming, and the increment of the launch diameter or the convection wind velocity vertical to the propagation direction will weaken the thermal blooming oppositely. Furthermore, for laser beams with different intensity distributions, the impacts of the thermal blooming on the propagation are so different. Under the same generalized thermal distortion parameter N, the thermal blooming effect on the Gaussian beam is the most serious, followed by the flat-top beam, and flat-top beam with center obscuration is the smallest. This research work can provide somewhat guidance for the engineering application of lasers.
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图 1 初始光束的强度立体分布((a1), (b1), (c1))和等强度分布((a2), (b2), (c2))。(a1)，(a2)高斯光束；(b1)，(b2)平顶光束；(c1)，(c2)平顶光束遮拦比40%
Figure 1. Three-dimensional plots of intensity ((a1), (b1), (c1)) and isointensity contours ((a2), (b2), (c2)) for different beam. (a1), (a2) Gaussian beam; (b1), (b2) Flat-top beam; (c1), (c2) Flat beam obscuration ratio is 40%
图 2 不同初始功率情况下激光到达靶面的强度立体分布((a1)，(b1)，(c1))和等强分布((a2)，(b2)，(c2)) (高斯光束)。(a1)，(a2)发射功率为1000 W；(b1)，(b2)发射功率为2000 W；(c1)，(c2)发射功率为3000 W
Figure 2. Three-dimensonal plots of intensity ((a1), (b1), (c1)) and isointensity contours ((a2), (b2), (c2)) for different laser power (Gaussian beam). (a1), (a2) Power is 1000 W; (b1), (b2) Power is 2000 W; (c1), (c2) Power is 3000 W
图 3 不同初始功率情况下激光到达靶面的强度立体分布((a1)，(b1)，(c1))和等强分布((a2)，(b2)，(c2)) (平顶光束)。(a1)，(a2)发射功率为1000 W；(b1)，(b2)发射功率为2000 W；(c1)，(c2)发射功率为3000 W
Figure 3. Three-dimensional plots of intensity ((a1), (b1), (c1)) and isointensity contours ((a2), (b2), (c2)) for different laser power. (flat-top beam). (a1), (a2) Power is 1000 W; (b1), (b2) Power is 2000 W; (c1), (c2) Power is 3000 W
图 4 不同初始功率情况下激光到达靶面的强度立体分布((a1)，(b1)，(c1))和等强分布((a2)，(b2)，(c2))(平顶光束遮拦比40%)。(a1)，(a2)发射功率为1000 W；(b1)，(b2)发射功率为2000 W；(c1)，(c2)发射功率为3000 W
Figure 4. Three-dimensional plots of intensity ((a1), (b1), (c1)) and isointensity contours ((a2), (b2), (c2)) for different laser power (flat-top beam obscuration ratio is 40%). (a1), (a2) Power is 1000 W; (b1), (b2) Power is 2000 W; (c1), (c2) Power is 3000 W
图 5 传输距离不同时激光达到靶面的强度立体分布((a1)，(b1)，(c1))和等强分布((a2)，(b2)，(c2))(高斯光束)。(a1)，(a2)传输距离为2000 m；(b1)，(b2)传输距离为3000 m；(c1)，(c2)传输距离为4000 m
Figure 5. Three-dimensional plots of intensity ((a1), (b1), (c1)) and isointensity contours ((a2), (b2), (c2)) for different distance (Gaussian beam). (a1), (a2) 2000 m; (b1), (b2) 3000 m; (c1), (c2) 4000 m
图 6 传输距离不同时激光达到靶面的强度立体分布((a1)，(b1)，(c1))和等强分布((a2)，(b2)，(c2))(平顶光束)。(a1)，(a2)传输距离为2000 m；(b1)，(b2)传输距离为3000 m；(c1)，(c2)传输距离为4000 m
Figure 6. Three-dimensional plots of intensity ((a1), (b1), (c1)) and isointensity contours ((a2), (b2), (c2)) for different distance (flat-top beam). (a1), (a2) 2000 m; (b1), (b2) 3000 m; (c1), (c2) 4000 m
图 7 传输距离不同时激光达到靶面的强度立体分布((a1)，(b1)，(c1))和等强分布((a2)，(b2)，(c2))(平顶光束遮拦比40%)。(a1)，(a2)传输距离为2000 m；(b1)，(b2)传输距离为3000 m；(c1)，(c2)传输距离为4000 m
Figure 7. Three-dimensional plots of intensity ((a1), (b1), (c1)) and isointensity contours ((a2), (b2), (c2)) for different distance (flat-top beam obscuration ratio is 40%). (a1), (a2) 2000 m; (b1), (b2) 3000 m; (c1), (c2) 4000 m
图 8 光束直径不同时激光达到靶面的强度立体分布((a1)，(b1)，(c1))和等强分布((a2)，(b2)，(c2))(高斯光束)。(a1)，(a2)光束直径为0.1 m；(b1)，(b2)光束直径为0.2 m；(c1)，(c2)光束直径为0.6 m
Figure 8. Three-dimensional plots of intensity ((a1), (b1), (c1)) and isointensity contours ((a2), (b2), (c2)) for different beam diameter (Gaussian beam). (a1), (a2) Beam diameter is 0.1 m; (b1), (b2) Beam diameter is 0.2 m; (c1), (c2) Beam diameter is 0.6 m
图 9 光束直径不同时激光达到靶面的强度立体分布((a1)，(b1)，(c1))和等强分布((a2)，(b2)，(c2))(平顶光束)。(a1)，(a2)光束直径为0.1 m；(b1)，(b2)光束直径为0.2 m；(c1)，(c2)光束直径为0.6 m
Figure 9. Three-dimensional plots of intensity ((a1), (b1), (c1)) and isointensity contours ((a2), (b2), (c2)) for different beam diameter (flat-top beam). (a1), (a2) Beam diameter is 0.1 m; (b1), (b2) Beam diameter is 0.2 m; (c1), (c2) Beam diameter is 0.6 m
图 10 光束直径不同时激光达到靶面的强度立体分布((a1)，(b1)，(c1))和等强分布((a2)，(b2)，(c2)) (平顶光束遮拦比40%)。(a1)，(a2)光束直径为0.1 m；(b1)，(b2)光束直径为0.2 m；(c1)，(c2)光束直径为0.6 m
Figure 10. Three-dimensional plots of intensity ((a1), (b1), (c1)) and isointensity contours((a2), (b2), (c2)) for different beam diameter (flat-top beam obscuration ratio is 40%). (a1), (a2) Beam diameter is 0.1 m; (b1), (b2) Beam diameter is 0.2 m; (c1), (c2) Beam diameter is 0.6 m
图 11 横向风风速不同时激光到达靶面时的强度立体分布((a1)，(b1)，(c1))和等强分布((a2)，(b2)，(c2))(高斯光束)。(a1)，(a2)风速为2 m/s；(b1)，(b2)风速为4 m/s；(c1)，(c2)风速为6 m/s
Figure 11. Three-dimensional plots of intensity ((a1), (b1), (c1)) and isointensity contours((a2), (b2), (c2)) for different wind velocity (Gaussian beam). (a1), (a2) Wind velocity is 2 m/s; (b1), (b2) Wind velocity is 4 m/s; (c1), (c2) Wind velocity is 6 m/s
图 12 横向风风速不同时激光到达靶面时的强度立体分布((a1)，(b1)，(c1))和等强度分布((a2)，(b2)，(c2)) (平顶光束)。(a1)，(a2)风速为2 m/s；(b1)，(b2)风速为4 m/s；(c1)，(c2)风速为6 m/s
Figure 12. Three-dimensional plots of intensity ((a1), (b1), (c1)) and isointensity contours ((a2), (b2), (c2)) for different wind velocity (flat-top beam). (a1), (a2) Wind velocity is 2 m/s; (b1), (b2) Wind velocity is 4 m/s; (c1), (c2) Wind velocity is 6 m/s
图 13 横向风风速不同时激光到达靶面时的强度立体分布((a1)，(b1)，(c1))和等强分布((a2)，(b2)，(c2)) (平顶光束遮拦比40%)。(a1)，(a2)风速为2 m/s；(b1)，(b2)风速为4 m/s；(c1)，(c2)风速为6 m/s
Figure 13. Three-dimensional plots of intensity ((a1), (b1), (c1)) and isointensity contours((a2), (b2), (c2)) for different wind velocity (flat-top beam obscuration ratio is 40%). (a1), (a2) Wind velocity is 2 m/s; (b1), (b2) Wind velocity is 4 m/s; (c1), (c2) Wind velocity is 6 m/s
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