简介：Basedonthesecond-ordermoments,thispaperderivesananalyticalexpressionoftheM2factoroffour-petalGaussianbeam.TheresultsshowthattheM2factorisonlydeterminedbythebeamordern.Thecorrespondingnumericalcalculationsarealsogiven.Asthebeamorderincreases,theaugmentofM2factorisdisciplinary.AstheexpressionofM2factorisexpressedinseriesformandbecomesmorecomplicated,anewconciseformulaofM2factorisalsopresentedbyusingcurvefittingofnumericalcalculations.When3≤n≤200,themaximumerrorrateoffittingformulawillnotexceed2.6%andtheaverageerrorrateis0.28%.Thisresearchishelpfultotheapplicationsoffour-petalGaussianbeam.
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