中文摘要：

可控中空光束是适合于描写中央强度为零的激光束.将分数傅里叶变换用于处理可控中空光束的传输.基于广义惠更斯-菲涅耳衍射公式,导出了可控中空光束经分数傅里叶变换系统的解析传输公式.运用所得到的解析表达式,通过数值计算考查了可控中空光束在分数傅里叶变换面上的特性,分析了分数傅里叶变换面上的强度分布与各不同参数间的依赖关系.

英文摘要：

Controllable dark-hollow beams are suitable beam modes to describe the dark-hollow beams with zero central intensity.The fractional Fourier transform is applied to treat with the propagation of controllable dark-hollow beams.Based on the generalized Huygens-Fresnel diffraction formula,an analytical expression for a controllable dark-hollow beam passing through a fractional Fourier transform system has been derived.According to the derived analytical expression,the properties of a controllable dark-hollow beam in the fractional Fourier transform plane are graphically illustrated with numerical examples,and the dependence of the intensity distribution on the different parameters is also discussed in detail.