量子电子学报

• 激光技术与器件 • 上一篇    下一篇

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   

  1. 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   

  1. School of mechanical and electrical of Taihu University of Wuxi , Wuxi 310018, China
  • Published:2019-05-28 Online:2019-05-14

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