中国物理B ›› 2008, Vol. 17 ›› Issue (10): 3708-3712.doi: 10.1088/1674-1056/17/10/029

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M2 factor of four-petal Gaussian beam

周国泉, 樊 艳   

  1. School of Sciences, Zhejiang Forestry University, Lin'an 311300, China
  • 收稿日期:2008-02-28 修回日期:2008-03-13 出版日期:2008-10-20 发布日期:2008-10-20
  • 基金资助:
    Project supported by the Scientific Research Fund of Zhejiang Provincial Education Department (Grant No 20060677).

M2 factor of four-petal Gaussian beam

Zhou Guo-Quan(周国泉)† and Fan Yan(樊艳)   

  1. School of Sciences, Zhejiang Forestry University, Lin'an 311300, China
  • Received:2008-02-28 Revised:2008-03-13 Online:2008-10-20 Published:2008-10-20
  • Supported by:
    Project supported by the Scientific Research Fund of Zhejiang Provincial Education Department (Grant No 20060677).

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摘要： Based on the second-order moments, this paper derives an analytical expression of the $M^{2}$ factor of four-petal Gaussian beam. The results show that the $M^{2}$ factor is only determined by the beam order $n$. The corresponding numerical calculations are also given. As the beam order increases, the augment of $M^{2}$ factor is disciplinary. As the expression of $M^{2}$ factor is expressed in series form and becomes more complicated, a new concise formula of $M^{2}$ factor is also presented by using curve fitting of numerical calculations. When $3 \le n \le 200$, the maximum error rate of fitting formula will not exceed 2.6{\%} and the average error rate is 0.28{\%}. This research is helpful to the applications of four-petal Gaussian beam.

关键词: beam propagation, four-petal Gaussian beam, second-order moment

Abstract: Based on the second-order moments, this paper derives an analytical expression of the $M^{2}$ factor of four-petal Gaussian beam. The results show that the $M^{2}$ factor is only determined by the beam order $n$. The corresponding numerical calculations are also given. As the beam order increases, the augment of $M^{2}$ factor is disciplinary. As the expression of $M^{2}$ factor is expressed in series form and becomes more complicated, a new concise formula of $M^{2}$ factor is also presented by using curve fitting of numerical calculations. When $3 \le n \le 200$, the maximum error rate of fitting formula will not exceed 2.6% and the average error rate is 0.28%. This research is helpful to the applications of four-petal Gaussian beam.

Key words: beam propagation, four-petal Gaussian beam, second-order moment

中图分类号:  (Beam characteristics: profile, intensity, and power; spatial pattern formation)

  • 42.60.Jf