双曲余弦-高斯光束的分数傅里叶变换特性研究

基于分数傅里叶变换(FRFT)与维格纳分布函数(WDF)旋转等效的性质．推导出了双曲余弦-高斯(ChG)光束在分数傅里叶变换面上光强分布和束宽的解析公式，研究了双曲余弦-高斯光束光强和束宽随分数傅里叶变换阶数的变化规律，分析了偏心参量对双曲余弦-高斯光束分数傅里叶变换特性的影响，并对数值计算结果进行了分析和讨论。结果表明，对给定偏心参量的双曲余弦-高斯光束，可以使其经过一定阶数的分数傅里叶变换来获得平顶光束。

Fractional Fourier Transforms for Cosh-Gaussian Beams

The analytical formulae of the beam width and the intensity distribution for fractional Fourier transform (FRFT) of cosh-Gaussian (ChG) beams are derived based on the characteristic of the equality between the rotation of the Wigner distribution function (WDF) and the FRFT. By using the derived formulae, the influences of the fractional order and the decentered parameter on the transformation properties of ChG beams in the fractional Fourier plane are studied in detail. Numerical calculation examples have been presented to illustrate the propagation properties of ChG beams through FRFT optical system. It was shown that for given decentered parameter, a flatted beams can be obtained by FRFT with suitable order. The derived formulae provide a simple and convenient way to study the FRFT of ChG beams.