1维线阵离轴高斯光束的分数傅里叶变换

Fractional Fourier transform for incoherent one-dimensional off-axis Gaussian beams

为研究非相干的1维线阵离轴高斯光束通过分数傅里叶变换(FRFT)系统的传输特性,利用Collins积分公式,导出了其在FRFT面上的光强分布解析式,并利用此解析式作数值计算和分析。研究表明:非相干的1维线阵离轴高斯光束在FRFT面上的光强分布由FRFT的阶数和子光束数目共同决定,其归一化的光强分布随FRFT的阶数周期性变化,周期为2;子光束数目的大小及其奇偶性对归一化光强分布的影响取决于FRFT的阶数;轴上归一化光强分布也随FRFT的阶数周期性变化,变化周期也为2。

Based on the Collins formula, the transformation properties of incoherent one dimensional off-axis Gaussian beams passing through the fractional Fourier transform（FRFT） system were studied. The analytical expressions for the intensity distribution of this beam were derived. By using the derived expressions, some numerical calculation examples were presented to illustrate the intensity properties on the FRFT plane. It is shown that the intensity distribution on the FRFT plane depend on FRFT order and sub-beams number. The variation of intensity distribution with FRFT order is periodic, and the period is 2. When the FRFT order is even, the number of sub-beam has a great effect on the normalized intensity distribution and the effect decreases with the order in crease; when the FRFT order increases to the adjacent odd number, the number of sub-beams almost has no effect on the intensity distribution, but has a great influence on the peak intensity. At last, the on-axis intensity distribution changes with FRFT order as well, with a period of 2.