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.
Received: 28 February 2008
Revised: 13 March 2008
Accepted manuscript online:
PACS:
42.60.Jf
(Beam characteristics: profile, intensity, and power; spatial pattern formation)
Fund: Project supported by
the Scientific Research Fund of Zhejiang Provincial Education
Department (Grant No 20060677).
Cite this article:
Zhou Guo-Quan(周国泉) and Fan Yan(樊艳) M2 factor of four-petal Gaussian beam 2008 Chin. Phys. B 17 3708
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