基于柱坐标系下的空心高斯光束的分数傅里叶变换

Fractional Fourier transform of hollow Gaussian beam based on cylindrical coordinates

推导出分数傅里叶变换基于柱坐标系下的解析表达式,应用此解析表达式对空心高斯光束进行分析,得到其分数傅里叶变换的解析表达式。讨论其在分数傅里叶变换平面的光强分布与各种光束参数之间的变换关系,并进行数值计算,从而得出基于柱坐标系下的空心高斯光束的分数傅里叶变换的传输性质。所得结果为分析和计算这种光束的分数傅里叶变换提供了方便,同时对此类光束的传输控制提供了基础理论支持。

The analytic expression of the fractional Fourier transform （FRFT） based on cylindrical coordinates was derived. The transform relation between the light-intensity distribution on the fractional Fourier transform plane and the various beam parameters was discussed, and the numerical calculation was made. The transmission property of FRFT for the hollow Gaussian beam based on the on the cylindrical coordinates was obtained.