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利用Wigner分布函数(WDF)方法，对光束的分数傅里叶变换特性进行了研究.以厄米高斯(HG)光束为例，导出了HG光束在分数傅里叶变换面上光强分布的解析公式和HG光束在分数傅里叶变换面上束宽的解析计算公式.通过数值计算研究了HG光束光强随分数傅里叶变换阶数变化的规律.研究表明：选取适当的分数傅里叶变换阶数p，在x，y方向可以得到相等束宽的对称光强分布.
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关键词:
- Wigner分布函数 /
- 厄米高斯(HG)光束 /
- 分数傅里叶变换
By using the Wigner distribution function(WDF)method,the fractional Fourier transform (FRFT) of beams is studied.HermiteGaussian (HG) beams are taken as an example; closedform expressions for the intensity distribution and beam widths of HG beams at the FRFT's plane are derived and changes in the intensity dist ribution of HG beams with the order of the FRFT are illustrated with numerical examples.It is shown that a symmetrical intensity distribution with equal beam width in the x and y directions can be achieved by a suitable choice of the transform order p.
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