Time-dependence of Talbot effect under ultrashort laser illumination

An equation is given to study the time dependence of the Fresnel diffraction field of a grating illuminated by an ultrashort pulsed-laser beam. Through numerical calculation, we find the temporal Talbot effect is both time-dependent and distance-dependent. For the width of the input pulse Delta tau within a few decade femtoseconds, the shorter Talbot distance, and /or the longer length of the input pulse, the more similar the outline of the temporal intensity distribution to that of the input pulse. While for Delta tau within a few thousand femtoseconds, the outline of the temporal intensity distribution is almost the same as that of the input pulse except for a time-delay.