激光辐射波前像差矫正模型的对称性和不变解

量子电子学报

激光辐射波前像差矫正模型的对称性和不变解

郑明亮*，冯鲜，邓斌，谭飞

无锡太湖学院机电学院，江苏，无锡 214064

出版日期:2019-05-28 发布日期:2019-05-14
作者简介:郑明亮（1988-），男，安徽马鞍山，博士，讲师，主要从事光电机械和力学方面的研究。E-mail：zhmlwxcstu@163.com
基金资助:
Supported by the National Natural Science Foundation of China (国家自然科学基金面上项目“11472247”), the Natural Science Foundation of Jiangsu higher education institutions(江苏省高等学校自然科学基“18KJB460027”)

Symmetries and invariant solution of the correction model for the wavefront aberration of laser radiation

Zheng Mingliang*, Feng Xian, Deng Bin, Tan Fei

School of mechanical and electrical of Taihu University of Wuxi , Wuxi 310018, China

Published:2019-05-28 Online:2019-05-14

摘要/Abstract

摘要： 相位共轭技术能够矫正激光系统光学辐射的波前畸变，本文基于亥姆霍兹方程，建立了激光辐射波前像差矫正模型的常规相位共轭反射方程组。应用李群分析方法，推导出系统偏微分方程组的多组允许无穷小对称性以及群不变解，更重要的是给出了它们详细的解析表达式和性质讨论。本文的内容为考虑边界和初始条件的自适应激光传播精确解析解提供了有效途径，可揭示激光波前像差矫正的内在原理，也为非线性光波动方程数值算法提供了验证。

关键词: 激光, 波前矫正, 相位共轭, Lie对称性, 不变解

Abstract: The phase conjugation technology can correct wavefront aberration of optical radiation in laser system. Based on Helmholtz equation, a conventional phase conjugate reflection equation set about the correction model for wavefront aberration of laser radiation are established. By using the Lie Group analytic procedure, it deduces the multiple groups of allowed infinitesimal Lie symmetries and invariant solution of the partial differential equations, and more importantly, it also points out their detailed analytical expressions and properties. The content and method can provide an effective way for the exact analytical solution of the adaptive laser propagation considering the boundary and initial conditions, and it reveals the inherent principle of the laser wavefront correction, and it also provides a verification for the numerical algorithm of the nonlinear optical wave equations.

Key words: Laser, Wavefront correction, Phase conjugation, Lie symmetries, Invariant solution

郑明亮*，冯鲜，邓斌，谭飞. 激光辐射波前像差矫正模型的对称性和不变解[J]. 量子电子学报.

Zheng Mingliang*, Feng Xian, Deng Bin, Tan Fei. Symmetries and invariant solution of the correction model for the wavefront aberration of laser radiation[J]. Chinese Journal of Quantum Electronics.

参考文献

1] Spaeth M I, Manes K R, Widmayer C C, etal. The national ignition facility wavelront requirements and optical architecture[C].SPIE,2004,5341:25-42. [2] Shang Qinhu. Optical phase coniugation and four-wave mixing[J](光学相位共轭与四波混频).Optics and Photoelectric Technology（光学与光电技术）,2003,1(3):9-11(in Chinese). [3] Du X W. Four factors describing of the beam quality of high-power lasers[C].SPIE,2005,5777:650- 653. [4] Zhang H R, Yao J Q. High power diode single-end-pumped nd:yvO4 laser[J].Optics Laser Technology,2003,35(6): 445-449. [5] Wang Xiaolin, Liu Zejing, Zhao Yijun, etal. Investigation on influence of laser intensity fluctuation on beam cleanup system based on stochastic parallel gradient descent algorithm[J](SPGD算法光束净化中光强起伏对校正效果的影响研究）.Acta Optica Sinica(光学学报),2009,29(1):97-101(in Chinese). [6] Wang Sanghong, Yu Qifeng. Experimental research of laser beam cleanup for dynamic aberrations based on stochastic parallel-gradient-descent method[J](基于随机并行梯度下降方法的动态光束净化实验研究).Acta Optica Sinica(光学学报),2009,29(1):97-101(in Chinese). [7] Ma Haotong. Research on the Optimal beam shaping based on adaptive optics[D](基于优化式自适应光学的光束全场整形研究,硕士). Hunan: National University of Defense Technology,2011:38-50(in Chinese). [8] Guo Ailin,ZHu Haidong,Yang Zeping,etal. Deformable mirror control algorithm based on the phase correction at the actuator position[J](基于驱动器位置相位校正的变形镜控制算法).Acta Optica Sinica(光学学报),2013,33(3):0311001(in Chinese).. [9] Guo Ailin,Zhu Haidong,Yang Zeping,etal. Wavefront propagation modeling and verification of the SG-II updated laser facility[J](神光II升级装置波前传输计算模型与验证).Acta Optica Sinica(光学学报),2013,33(2):0214001(in Chinese). [10] Hoffnagle J A. Design and performance of a refractive optical system that converts a gaussian to a flattop beam[J].Applied Optics,2000,39(30):5488-5499. [11] Zacharias R A, Beer N R, Bliss E S, etal. Alignment and wavefront control systems of the national ignition facility[J].Optical Engineering,2004,43(12):2873-2884. [12] Kanev F, Makenova N, Lukin V. Phase and amplitude-phase control of a laser beam propagating in the atmosphere[J].Quantum Electronics,2004,34(9):825-832. [13] Ibragimov N H. Differential Equations and Problems of Mathematical Physics[M](微分方程和数学物理问题).Lu Yi,Transl.Beijing:Higher Education Press,2013,101-123(in Chinese). [14] Li Kaihui,Liu Hanze. Lie symmetry analysis and exact solutions for nonlinear LC circuit equation[J](非线性LC电路方程的李群分析和精确解).Chinese Journal of Quantum Electronics(量子电子学报), 2016,33(3):280-287. [15] Cong Shuang,Dong Ning. Comparative study on controllability relationship of quantum mechanical systems and bilinear systems[J](量子力学系统与双线性系统可控性关系的对比研究).Chinese Journal of Quantum Electronics(量子电子学报), 2006,23(1):84-93. [16] Jiang Zhipeng. The study of beam shaping and phase correction[D](光束整形和相位校正相关问题研究，硕士). Hunan: National University of Defense Technology,2011:15-32(in Chinese). [17] Bluman G W, Anco S C. Symmetry and Integral Method of Differential Equations[M](微分方程的对称性和积分方法).Yan Zhengya,Transl.Beijing: Science Press,2009:54-67(in Chinese).

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