分数傅里叶变换面上厄米-拉盖尔-高斯光束的变换特性

Transformation Properties of Hermite-Laguerre-Gaussian Beam in Fractional Fourier Transform Plane

为了研究厄米-托盖尔-高斯(HLG)光束在分数傅里叶变换(FRFT)面上的变换特性,利用柯林斯(Collins)公式,导出了其通过分数傅里叶变换系统后,在分数傅里叶变换面上的光强分布解析式。并利用此解析式作数值计算,研究了其在分数傅里叶变换面上的光强分布特性。研究表明,厄米-拉盖尔-高斯光束在分数傅里叶变换面上的光强分布受参量α,模指数m,n和分数傅里叶变换阶数p的影响。光强分布随p和α周期性变化,周期分别为2,2n。此外,厄米拉盖尔-高斯光束通过分数傅里叶变换系统后,光束形状保持不变。

In order to study the transformation properties of a Hermite-Laguerre-Gaussian （HLG） beam though a fractional Fourier transform （FRFT） system in detail, the analytical expressions for the intensity distribution of HLG beam on the FRFT plane are derived from Collins formula . By using the derived expressions, numerical calculation examples have been presented to illustrate its propagation properties. It is shown that apart from the mode indices m,n , the intensity distribution on the FRFT plane depends on the fractional order p and parameter a , the variation with fractional order p and a is periodic, with the periods of 2 and 2π respectively . Furthermore, the beam shape of HLG beam maintains invariable in FRFT plane.