Shortening of a laser pulse with a self-modulated phase at the focus of a lens

We found that, at the focus of a chromatic lens, a laser pulse with a self-modulated phase can be shortened due to the radial dependence of the group delay imposed by the lens. Normally, this group delay stretches a short pulse into a long pulse by spreading the arrival time of the pulse at the focus. However, for a pulse with a self-modulated phase, it causes the fields with different phases to overlap, thus resulting in destructive interference that shortens the pulse.