Propagation properties of the pulsed hollow Gaussian beam through a circular aperture

Based on the angular spectrum representation of the Maxwell equations and the method of stationary phase, this paper presents the far-field analytical expression of a pulsed hollow Gaussian beam with constant waist width diffracted by the circular aperture, and the result can be simplified for the case of the paraxial propagation of pulsed Gaussian beam in the free space. Based on the analytical result, the influences of truncation parameter on the transverse intensity distribution of the pulsed beam are analyzed. Comparisons of normalized temporal intensity between the pulsed Gaussian beam and the fourth order pulsed hollow Gaussian beam are presented. We find that the spatial mode can induce the temporal shape changing.