Far-field diffraction characteristics of a Gaussian pulse incident on a sinusoidal phase grating

The far-field spectral characteristics of a time-dependent (broad-band) Gaussian pulse diffracted by a thin sinusoidal phase grating are studied both theoretically and numerically. It can be shown that the diffraction spectrum is distributed spectrally into several orders of peaks and this can be compared with its counterpart for a continuous monochromatic plane wave which distributes its power spatially into several beams. Also, diffracted spectral intensity distributions with blue -or red-shifts of the maximum are presented.