利用Wigner分布函数的方法,研究了余弦-高斯光束的分数傅里叶变换特性.导出了余弦-高斯光束在分数傅里叶变换面上光强分布和束宽的解析计算公式,并对此进行了数值模拟计算.研究表明:分数傅里叶变换阶数对余弦-高斯光束的光强分布有明显影响,余弦-高斯光束的轴上光强随分数傅里叶变换阶数呈周期性变化,束宽随分数傅里叶变换阶数也呈周期性变化,周期为2;对给定调制参数的余弦-高斯光束,通过适当选取分数傅里叶变化阶数可以获得平顶的光强分布.

By using the Wigner distribution function(WDF) method,the transformation properties of a Cosine-Gaussian beam in the fractional Fourier transform plane are studied.Closed-form expressions for the intensity distribution and beam widths of Cosine-Gaussian beams in the FRFT's plane are derived and changes in the intensity distribution of Cosine-Gaussian beams with the order of the FRFT are illustrated with numerical examples.It is shown that the intensity in the FRFT plane depends on the fractional order,the variation of the on-axis intensity and beam width with fractional order are periodic,and the period is 2.A flat-topped beam can be achieved by a suitable choice of the transform order for the Cosine-Gaussian beams with the modulation parameter.