Convergence and divergence focusing phenomena atfocal plane of ultrashort pulses

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.