光束分数傅里叶变换的Wigner分布函数分析方法

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(H G)光束为例，导出了H G光束在分数傅里叶变换面上光强分布的解析公式和H G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H G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. 关键词： Wigner分布函数 厄米 高斯(H G)光束 分数傅里叶变换

Fractional Fourier transform of beams in the use of the Wigner distribution function method

By using the Wigner distribution function(WDF)method,the fractional Fourier transform (FRFT) of beams is studied.Hermite Gaussian (H G) beams are taken as an example; closed form expressions for the intensity distribution and beam widths of H G beams at the FRFT's plane are derived and changes in the intensity dist ribution of H G 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.