Using the Richards–Wolf diffraction integral theory and the tightly focused ultrashort pulse vector model, the focusing phenomena at the focal plane of subcycle and few-cycle radially polarized ultrashort pulses are studied. The dynamic focusing is revealed at the focal plane. First, the subcycle or few-cycle ultrashort pulses shrink towards the focus. Then the ultrashort pulses diverge from the focus. So, the convergence and divergence moving halo at the focal plane can be observed. When approaching the focus, the amplitude of the pulse becomes larger. The phenomena can be understood from the Huygens–Fresnel principle and are important for applications of the focused ultrashort pulses.

中文翻译：

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超短脉冲焦平面处的会聚和发散聚焦现象。

利用理查兹-沃尔夫衍射积分理论和紧聚焦超短脉冲矢量模型，研究了亚周期和几周期径向极化超短脉冲在焦平面上的聚焦现象。动态聚焦显示在焦平面上。首先，子周期或几个周期的超短脉冲朝着焦点方向收缩。然后，超短脉冲从焦点发散。因此，可以观察到焦平面上的会聚和发散移动光环。当接近焦点时，脉冲的幅度变大。从惠更斯-菲涅耳原理可以理解该现象，这对于聚焦超短脉冲的应用很重要。