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The beam quality of array lasers which propagate in atmosphere will degrade in far-field. Therefore, the ultimate efficiency of combined lasers will be affected if no compensation measure is taken in some typical systems such as high energy system. Based on the model of array lasers with incoherent combination, laser propagation in atmosphere is simulated by generating a random atmospheric turbulence phase screen to modulate the phase of the laser beam. The distorted wavefront of atmospheric turbulence is divided according to the array distribution. The phase generated by tilt aberration coefficient which is solved by the method of fitting sub-wavefront data is eliminated in the phase of sub-beam, which simulates the process of correcting tilt aberration. The simulation results show that comparing with the case of tilt aberration, the power in the bucket (PIB) and the Strehl rate (SR) of combined lasers focusing in far-field are improved when the tilt aberration influenced by the same atmospheric turbulence phase screen is corrected. At the same time, coherence length ranging from 4 cm to 45 cm is used to characterize atmospheric turbulence of different intensities. At each coherent length, the PIB and SR are calculated when the distances of propagation of lasers are 2 km and 3 km, separately. The simulation results show that although PIB and SR before and after tilt aberration are corrected, they become worse with the decrease of coherence length, and PIB and SR are improved more obviously when tilt aberration is corrected in stronger turbulence. An experiment in the case of 2 km is carried out by using a prototype of incoherent combination, and the data are obtained by measuring the focused spot at the target. The measurement results confirm that the correcting of tilt aberration can improve the beam quality of array lasers with incoherent combination in far-field. In summary, the research conducted in this work can obtain tilt aberration accurately and the corresponding method of correction is easy to implement, which can provide supporting data for improving the performances high energy laser systems.
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Keywords:
- incoherent combination /
- laser propagation /
- atmospheric turbulence /
- tilt aberration correction
[1] 李怡勇, 王建华, 李智 2017 兵器装备工程学报 38 1
Li Y Y, Wang J H, Li Z 2017 Journal of Ordnance Equipment Engineering 38 1
[2] Zervas M N, Codemard C A 2014 IEEE J. Sel. Top. Quant. 20 219
Google Scholar
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Google Scholar
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Wu W M, Guo S F, Tao R M, Wu Y, Ning Y 2013 Acta. Opti. Sin. 33 1140081
[6] 王小林, 周朴, 粟荣涛, 马鹏飞, 陶汝茂, 马阎星, 许晓军, 刘泽金 2017 中国激光 44 02010011
Wang X L, Zhou P, Su R T, Ma P F, Tao R M, Ma Y X, Xu X J, Liu Z J 2017 Chin. J. Lasers 44 02010011
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Jiang M, Ma P F, Zhou P, Wang X L 2016 Acta Phys. Sin. 65 104203
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Ma Y, Yan H, Sun Y H, Peng W M, Li J M 2018 Infrared and Laser Engineering 47 01030021
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[12] 周朴, 马阎星, 王小林 2010 中国激光 37 733
Zhou P, Ma Y X, Wang X L 2010 Chin. J. Lasers 37 733
[13] 吴武明, 杨轶, 司磊, 周朴, 陈金宝 2013 强激光与粒子束 25 0003
Wu W M, Yang Y, Si L, Zhou P, Chen J B 2013 High Power Laser and Particle Beams 25 0003
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Google Scholar
Ji X L, Li X Q 2008 Acta Phys. Sin. 57 7674
Google Scholar
[15] Nelson W, Sprangle P, Davis C C 2016 Appl. Opt. 55 8338
Google Scholar
[16] Pargmann C, Hall T, Duschek F, Fischbach T 2015 SPIE Security + Defence International Society for Optics and Photonics Toulouse, France, September 21–24, 2015 p96500 L
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Geng C, Li X Y, Zhang X J, Rao C H 2011 Acta Phys. Sin. 60 114202
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Geng C, Tan Y, Mou J B, Li X Y 2013 Acta Phys. Sin. 62 024206
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图 1 高能激光系统模型
Figure 1. Model of high energy system.
图 2 近场光强分布
Figure 2. Intensity distribution in near-field.
图 3 大气湍流相位屏示意
Figure 3. Formation of atmospheric turbulence phase screen.
图 4 大气湍流畸变波前
Figure 4. Distortion wavefront of atmospheric turbulence.
图 5 二维光强分布 (a) 倾斜像差校正前; (b) 倾斜像差校正后
Figure 5. Intensity distribution of two dimensions: (a) Before correcting tilt aberration; (b) after correcting tilt aberration.
图 6 一维光强分布 (a) Y向中心剖切面; (b) X向中心剖切面
Figure 6. Intensity distribution of one dimension: (a) Central section in Y; (b) central section in X.
图 7 2 km处不同大气相干长度的激光光束质量 (a) PIB; (b) SR
Figure 7. The beam quality at 2 km corresponding to different coherence lengths: (a) PIB; (b) SR.
图 8 3 km处不同大气相干长度的激光光束质量 (a) PIB; (b) SR
Figure 8. The beam quality at 3 km corresponding to different coherence lengths: (a) PIB; (b) SR
图 9 目标端设备实物
Figure 9. Equipment at target.
图 10 光束质量分析仪测量结果 (a) 倾斜像差校正前; (b) 倾斜像差校正后
Figure 10. Measurement results of beam quality analyzer: (a) Before correcting tilt aberration; (b) after correcting tilt aberration.
表 1 子波前倾斜像差系数
Table 1. Coefficient of tilt aberration in each sub-wavefront.
子波前序数 X向倾斜系数TX Y向倾斜系数TY ① 4.24 3.31 ② –0.66 –6.20 ③ 4.92 –2.09 ④ 4.99 2.60 ⑤ 6.20 0.48 ⑥ 0.62 2.52 ⑦ –3.62 0.36 
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表 2 激光远场光束质量计算结果
Table 2. Result of the beam quality in far-field.
评价指标
类型子波前倾斜像差
校正前子波前倾斜像差
校正后PIB 0.30 0.64 SR 0.21 0.63
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表 3 实验条件
Table 3. Experimental condition.
参数类型 指标值 温度/℃ 28 湿度/% 62 风速/$\rm m\cdot s^{-1} $ < 4 大气能见度/km > 23 大气相干长度/cm 19
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表 4 光斑参数计算结果
Table 4. Calculation results of spot parameters.
光斑参数 子波前倾斜像差
校正前子波前倾斜像差
校正后相对峰值强度Im/cnt 2944 4053 环围直径D(4σ)/mm 108 89
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[1] 李怡勇, 王建华, 李智 2017 兵器装备工程学报 38 1
Li Y Y, Wang J H, Li Z 2017 Journal of Ordnance Equipment Engineering 38 1
[2] Zervas M N, Codemard C A 2014 IEEE J. Sel. Top. Quant. 20 219
Google Scholar
[3] Sprangle P, Ting A, Penano J, Fischer R 2009 IEEE J. Quant 45 138
Google Scholar
[4] Tao R M, Si L, Ma Y X, Zou Y C 2011 Chin. Phys. Lett. 28 074219
Google Scholar
[5] 吴武明, 郭少锋, 陶汝茂, 吴毅, 宁禹 2013 光学学报 33 1140081
Wu W M, Guo S F, Tao R M, Wu Y, Ning Y 2013 Acta. Opti. Sin. 33 1140081
[6] 王小林, 周朴, 粟荣涛, 马鹏飞, 陶汝茂, 马阎星, 许晓军, 刘泽金 2017 中国激光 44 02010011
Wang X L, Zhou P, Su R T, Ma P F, Tao R M, Ma Y X, Xu X J, Liu Z J 2017 Chin. J. Lasers 44 02010011
[7] 肖瑞, 侯静, 姜宗福, 刘明 2006 55 6464
Google Scholar
Xiao R, Hou J, Jiang Z F, Liu M 2006 Acta Phys. Sin. 55 6464
Google Scholar
[8] Thielen P A, Ho J G, Burchman D A, Goodno G 2012 Opt. Express 37 3714
[9] 姜曼, 马鹏飞, 周朴, 王小林 2016 65 104203
Jiang M, Ma P F, Zhou P, Wang X L 2016 Acta Phys. Sin. 65 104203
[10] 马毅, 颜宏, 孙殷宏, 彭万敏, 李建民 2018 红外与激光工程 47 01030021
Ma Y, Yan H, Sun Y H, Peng W M, Li J M 2018 Infrared and Laser Engineering 47 01030021
[11] Andrusyak O, Smirnov V, Venus G, Rotar V 2009 IEEE J. Sel. Top. Quant. 15 344
Google Scholar
[12] 周朴, 马阎星, 王小林 2010 中国激光 37 733
Zhou P, Ma Y X, Wang X L 2010 Chin. J. Lasers 37 733
[13] 吴武明, 杨轶, 司磊, 周朴, 陈金宝 2013 强激光与粒子束 25 0003
Wu W M, Yang Y, Si L, Zhou P, Chen J B 2013 High Power Laser and Particle Beams 25 0003
[14] 季小玲, 李晓庆 2008 57 7674
Google Scholar
Ji X L, Li X Q 2008 Acta Phys. Sin. 57 7674
Google Scholar
[15] Nelson W, Sprangle P, Davis C C 2016 Appl. Opt. 55 8338
Google Scholar
[16] Pargmann C, Hall T, Duschek F, Fischbach T 2015 SPIE Security + Defence International Society for Optics and Photonics Toulouse, France, September 21–24, 2015 p96500 L
[17] Zheng Y, Yang Y, Wang J, Hu M 2016 Opt. Express 24 12063
Google Scholar
[18] 耿超, 李新阳, 张小军, 饶长辉 2011 60 114202
Geng C, Li X Y, Zhang X J, Rao C H 2011 Acta Phys. Sin. 60 114202
[19] 耿超, 谭毅, 牟进博, 李新阳 2013 62 024206
Geng C, Tan Y, Mou J B, Li X Y 2013 Acta Phys. Sin. 62 024206
[20] Wang X, Wang X L, Zhou P, Su S T 2012 IEEE Photonic Tech. L. 24 1781
Google Scholar
[21] Weyrauch T, Vorontsov M A, Carhart G W, Beresnev L A, Rostov A P, Polnau E E Liu J J 2011 Opt. Lett. 36 4455
Google Scholar
[22] Beresnev L A, Weyrauch T, Vorontsov M A, Liu L, Carhart G W 2008 Proceedings of SPIE—The International Society for Optical Engineering San Diego, California, United States, Augest 10–14, 2008 p709008
[23] Geng C, Zhao B Y, Zhang E T, Luo W 2013 IEEE Photonic Tech. L. 25 1286
Google Scholar
[24] Geng C, Li F, Wang X L, Su R T 2015 Chin. J. Lasers 42 1005001
Google Scholar
[25] Song J K, Yang G Q, Li Y Y, Wang T F 2018 Optik 168 01
Google Scholar
[26] Yang G Q, Liu L S, Jiang Z H, Wang T F, Guo J 2016 J. Mod. Optic 64 251
[27] Voelz D G 2011 Computational Fourier optics: A MATLAB Tutorial (Washington: SPIE)
[28] Hage S G E, Berny F 1973 Opt. Soc. Am. 63 205
Google Scholar
[29] Roddier N A 1990 Opt. Eng. 29 1174
Google Scholar
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