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基于惠更斯-菲涅耳衍射积分公式,研究了宽带光束在菲涅耳衍射区的自由空间传输特性,得到宽带光束传输的调制深度与光束带宽Δλ及菲涅耳数F的变化关系。结果表明:一定的带宽对光束的均匀性有适当的改善;当光束的带宽Δλ<2λ0/F时,带宽越大,光束越均匀;当带宽满足条件Δλ=2λ0/F时,菲涅耳衍射完全消失;在一定的菲涅耳数范围内,宽带光束的调制深度随菲涅耳数振荡变化,振荡曲线的主极大值和次极大值分别出现在菲涅耳数为奇数和偶数处,而极小值则出现在菲涅耳数F=2k±1/3(k=1,2,3,…)处,在极小值处光束的均匀性最好。
Based on the Huygens-Fresnel diffraction integral formula, the free-space transmission characteristics of the broadband beam in the Fresnel diffraction region are studied. The relationship between the modulation depth of the broadband beam and the beam bandwidth Δλ and the Fresnel number F is obtained. The results show that: a certain bandwidth has a proper improvement on the uniformity of the beam; when the bandwidth of the beam Δλ <2λ0 / F, the larger the bandwidth, the more uniform the beam; when the bandwidth satisfies the condition Δλ = 2λ0 / F, Fresnel diffraction Disappears completely. In a certain Fresnel number range, the modulation depth of the broadband beam changes with the Fresnel number. The dominant and sub-maxima of the oscillation curve appear at odd and even Fresnel numbers , While the minimum appears at the Fresnel number F = 2k ± 1/3 (k = 1, 2, 3, ...) where the beam uniformity is best.