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高斯镜平凸非稳腔本征模场的有限元数值计算

范泛, 杨克成, 张波, 许德胜

范泛, 杨克成, 张波, 许德胜. 高斯镜平凸非稳腔本征模场的有限元数值计算[J]. 激光技术, 2007, 31(2): 192-195.
引用本文: 范泛, 杨克成, 张波, 许德胜. 高斯镜平凸非稳腔本征模场的有限元数值计算[J]. 激光技术, 2007, 31(2): 192-195.
FAN Fan, YANG Ke-cheng, ZHANG Bo, XU De-sheng. Numerical calculation of mode-fields of the spherical plano-convex unstable resonator with Gaussian reflectivity mirror by means of the finite element method[J]. LASER TECHNOLOGY, 2007, 31(2): 192-195.
Citation: FAN Fan, YANG Ke-cheng, ZHANG Bo, XU De-sheng. Numerical calculation of mode-fields of the spherical plano-convex unstable resonator with Gaussian reflectivity mirror by means of the finite element method[J]. LASER TECHNOLOGY, 2007, 31(2): 192-195.

高斯镜平凸非稳腔本征模场的有限元数值计算

详细信息
    作者简介:

    范泛(1980- ),男,硕士研究生,现主要从事新型激光谐振腔理论的研究.

    通讯作者:

    杨克成,E-mail:kcyang@hust.edu.cn

  • 中图分类号: O435

Numerical calculation of mode-fields of the spherical plano-convex unstable resonator with Gaussian reflectivity mirror by means of the finite element method

  • 摘要: 为了研究激光在高斯镜平凸非稳腔中的模式和相位特征,在SIEGMAN分析多元件非稳腔的理论基础上,采用有限元数值方法计算耦合输出镜镜面反射率为高斯分布的圆镜平凸非稳腔本征模场分布。将光场在腔内一次往返的ABCD系数代入惠更斯-基尔霍夫衍射积分方程,可以写出光场往返一次的衍射积分方程。将镜面分割成若干个等宽圆环,把衍射积分方程转化成矩阵相乘形式,经过数值计算,得到理想空腔和非共轴空腔优先起振的光场本征模式分布结果与相位特性。计算结果表明,当合适选择输出镜半径与高斯反射率分布,可以得到光斑半径为0.3cm的基模高斯光束输出,此计算结果与实验结果相符。同时也讨论了耦合输出镜对光束质量的影响。
    Abstract: In order to study the mode and the phase characteristic of laser in an unstable resonator with Gaussian reflectivity mirrors,a finite element method is presented to numerically calculate mode-fields of the spherical plano-convex unstable resonator with Gaussian reflectivity mirrors,which is based on the canonical formulation of SIEGMAN's theory for analyzing multi-element unstable resonators.The round-trip cylindrical Huygen's integral is expressed for the resonator in terms of spherical resonator analysis and ABCDM matrix.The Huygen's integral is transformed to a finite sum format by dividing the output mirror into several width-equal circles.The eigenmode and phase result of self-reproduce field of perfect empty resonator and misalignment empty resonator are obtained via numerical calculation.The calculation result indicates that when the radius and Gaussian reflectivity of output mirror are appropriately selected,the fundamental mode distribution of Gaussian beam which has a spot radius of 0.3cm can be obtained.The calculation result accords with the experiment result.Simultaneously the influence of the output mirror on the beam quality is also discussed.
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出版历程
  • 收稿日期:  2006-01-24
  • 修回日期:  2006-03-23
  • 发布日期:  2007-04-24

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