本文利用MATLAB（MATrix LABoratory），仿真模拟了径向指数（p）取任意非负整数时，两束拓扑荷数（l）相反的分数阶涡旋光束（拉盖尔-高斯光束）的干涉图样，以及径向指数取任意非负整数时，两束拓扑荷数不相等的涡旋光束（拉盖尔-高斯光束）的干涉图样。通过理论分析发现，随着拉盖尔-高斯光束的拓扑荷数和径向指数的变化，光束的干涉图样也会相应地发生变化。在等量异号分数阶拉盖尔-高斯光束干涉图案中光斑数为 \mathrm{2} \left|l\right|，光斑层数为p+1；非等量异号拉盖尔-高斯光束的干涉结果与等量异号拉盖尔-高斯光束相似；非等量同号拉盖尔-高斯光束干涉图案中，若拓扑荷数绝对值差值较小时，亮光斑数为 \left|l_{\mathrm{2}}\right| - \left|l_{\mathrm{1}}\right|；若拓扑荷数绝对值差值较大时，则会呈现一亮一暗的同心圆环。这一研究成果为涡旋光束的拓扑荷数和径向指数的测量提供了新的方法。

In this paper, we used MATLAB (MATrix LABoratory) to simulate the interference patterns of two fractional-order vortex beams (Laguerre-Gaussian beams) with opposite topological charges (l), as well as the interference patterns of two unequal vortex beams (Laguerre-Gaussian beams) with different topological charges, in which the radial indices (p) are arbitrary non-negative integers. Through theoretical analysis, we found that as the topological charges and radial indices of the beams change, the interference patterns of the Laguerre-Gaussian beams change accordingly. The number of spots in the interference pattern of the equal-heterodyne fractional-order Laguerre-Gaussian beam is \mathrm{2} \left|l\right|, and the number of spot layers is p+1; the interference result of the non-equal-heterodyne Laguerre-Gaussian beam is similar to that of the equal-heterodyne Laguerre-Gaussian beam. In the interference pattern of non-equal same-sign Laguerre-Gaussian beams, when the absolute value of the difference in topological charges is small, the number of bright spots is \left|l_{\mathrm{2}}\right| - \left|l_{\mathrm{1}}\right|. When this absolute value is large, a pattern of alternating bright and dark concentric rings appears. Our work may provide a new method for measuring the topological charges and radial indices of vortex beams.