Temporal and time-averaged Talbot effect of grating

Talbot effect of grating with the ultra-short pulsed laser illumination is studied in time domain and space domain. The theoretical formulas of the temporal and time-averaged diffraction intensity of grating illuminated by the pulsed laser are deduced on basis of the partial coherence theory. The influence of the duration time of pulse and the chirp coefficient on the Talbot image of grating is analyzed in detail. As the duration time is long enough, the temporal and the time-averaged Talbot image can be obtained. Moreover, the influence of the pulse shape on Talbot effect of grating is also discussed. The diffraction distributions of grating illuminated by three kinds of pulses with Gaussian, super-Gaussian and sech shapes are provided. Under the same condition, the diffraction of grating illuminated by the pulsed laser with super-Gaussian shape closes much more to the grating structure.