On-axis diffraction of an ultrashort light pulse by circularly symmetric hard apertures

The analytical solution of the Rayleigh-Sommerfeld on-axis diffraction integral for an ultrashort light pulse diffracted by circularly symmetric hard apertures is derived. The particular case of a circular aperture is treated in detail. The time changes of the instantaneous intensity along the axial direction are predicted. An analysis of the standard deviation width shows a pulse broadening about the axial positions where the instantaneous intensity reaches a zero value. We show that the temporal shape of the instantaneous intensity depends on the number of oscillation cycles at the central frequency of the real electric field.