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使用惠更斯-菲涅耳衍射积分和傅里叶变换,推导了横向模式为厄米-高斯的激光束通过硬边光阑的传输表达式。利用所得公式通过数值计算详细分析了光束的频带宽度对光束横向强度分布的影响。分析发现激光束通过硬边光阑后会出现大量的强度尖峰,引起近场的强度分布不均匀。然而,当带宽增加时,强度尖峰的数量减少,幅度减小,光束的均匀性得到改善。在远场,光束的横向强度分布没有强度尖峰出现,但宽度随带宽的增加而减小。因此带宽增加会带来近场强度匀滑化和远场光束宽度变窄的效应。另外,数值结果表明带宽对模指数为1和2的厄米-高斯光束的强度分布的影响是类似的,均有近场强度匀滑化和远场光束宽度变窄的效应。
Using the Huygens-Fresnel diffraction integral and the Fourier transform, the transmission expression of the Hermitian-Gaussian laser beam passing through the hard-edged diaphragm is derived. The influence of the bandwidth of the beam on the transverse intensity distribution of the beam is analyzed in detail by numerical calculation. The analysis shows that a large number of intensity spikes appear after the laser beam passes through the hard-edge aperture, resulting in uneven intensity distribution in the near field. However, as the bandwidth increases, the number of intensity spikes decreases, the amplitude decreases, and the beam uniformity improves. In the far field, there is no intensity spike in the lateral intensity distribution of the beam, but the width decreases with increasing bandwidth. Therefore, the increase of the bandwidth brings about the effect of the near-field intensity smoothing and the narrowing of the far-field beam width. In addition, the numerical results show that the effect of bandwidth on the intensity distribution of Hermite-Gaussian beams with mode indices of 1 and 2 are similar, both with near-field intensity smoothing and narrowing of the far-field beam width.