An orthogonal family of super Lorentz-Gauss(SLG) beam has been introduced to describe the highly divergent higher-order modes, e.g. the far-field distributions of the highly divergent higher-order mode generated by diode lasers. The fractional Fourier transform(FRFT) is applied to treat the propagation of SLG11 mode. By means of the convolution theorem of Fourier transform, an analytical expression for the field of SLG11 mode passing through an FRFT system has been derived. According to the derived analytical formula, the properties of SLG11 mode in the FRFT plane are graphically illustrated with numerical examples. The influences of the fractional order and three beam parameters on the normalized intensity of SLG11 mode in the FRFT plane are systemically analyzed. The dependence of the normalized intensity distribution of SLG11 mode in the FRFT plane on the fractional order is periodic, and the period is 2. With increasing the beam parameters, the beam spot size of SLG11 mode in the FRFT plane also increases.%引入了一簇互相正交的超洛伦兹-高斯光束以描述半导体激光器所产生的大角度高阶模远场分布.将分数傅里叶变换应用于超洛伦兹-高斯光束SLG11模的传输特性的研究中.利用傅里叶变换的卷积原理,导出了SLG11模经分数傅里叶变换系统后场分布的解析表达式.根据所得到的公式进行了数值计算,系统分析了分数傅里叶变换阶数和光束各参数对SLG11模在分数傅里叶变换面上光强分布的影响.结果显示:SLG11模在分数傅里叶变换面上的归一化强度分布随分数傅里叶变换的阶数呈周期性变化,周期为2;随着光束参数的增大,SLG11模在分数傅里叶变换面上的光斑尺寸增大.
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