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 propagation representations of pulses with Hermite-Gaussian transverse modes passing through a hard-edged aperture are derived. Influences of the bandwidth on the transverse intensity distributions are analyzed in detail from numerical calculations. It is found that lots of intensity spikes emerge and the near field intensities are non-uniformity when the pulses pass through the aperture. However, when the bandwidth increases, the number and the amplitude of the spikes are reduced and thus the beam uniformity is improved, the intensity spike does not appear in the far field, and also the beam width decreases in the far field. Therefore, the smoothing and narrowing effects can be brought forth by increasing the bandwidth. In addition, it is found from the numerical results that the effects are similar in the pulses with Hermite-Gaussian transverse modes of mode indices 1 and 2.