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利用惠更斯-菲涅耳衍射积分以及叉形光栅的透射率函数,推导出了涡旋光束经叉形光栅衍射后的解析表达式。详细研究了涡旋光束通过携带拓扑电荷数l的叉形光栅后的光强分布和拓扑电荷数。结果表明,中心零级光斑和入射涡旋光束的拓扑电荷数m相同;随着衍射级数n的变化,衍射光斑的拓扑电荷数变为nl+m。当满足nl+m=0时,该n级光斑中心为平面波形的亮斑,在此光斑两侧随着衍射级数的改变,衍射光斑的空心半径逐渐增大。根据平面波光斑所在位置的级数n以及叉形光栅携带的拓扑电荷数l,由nl+m=0可确定入射涡旋光束的拓扑电荷数m。将计算结果与实验结果做了比较,发现两者基本吻合。
Using the Huygens-Fresnel diffraction integral and the transmissivity function of the fork-shaped grating, the analytical expression of the vortex beam diffracted by the fork-shaped grating is deduced. The distribution of light intensity and the number of topological charges after the vortex beam passes through the fork-shaped grating carrying the topological charges 1 are studied in detail. The results show that the number of topological charge m of the center zero-order and incident vortex beams is the same, and the number of topological charges of the diffraction spot becomes n1 + m with the change of diffraction order n. When nl + m = 0 is satisfied, the n-type spot center is a bright spot of the plane waveform, and the hollow radius of the diffracted spot gradually increases as the diffraction order changes on both sides of the spot. The topological charges m of the incident vortex beam can be determined from nl + m = 0 according to the order n of the location of the plane wave spot and the topological charge number l carried by the fork-shaped grating. Comparing the calculated results with the experimental results, we find that the two are in good agreement.