Abstract Based on the second-order moments, this paper derives an analytical expression of the factor of four-petal Gaussian beam. The results show that the factor is only determined by the beam order . The corresponding numerical calculations are also given. As the beam order increases, the augment of factor is disciplinary. As the expression of factor is expressed in series form and becomes more complicated, a new concise formula of factor is also presented by using curve fitting of numerical calculations. When , 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.
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