Based on the Fresnel diffraction integral and by introducing a hard-aperture function into a finite sum of complex Gaussian functions, the approximate analytical expression for the near-field spectral intensity distribution of a space–time-dependent Gaussian pulsed beam passing through an annular aperture is derived, which permits us to study the on- and off-axis spectral anomalies that are near phase singularities of the diffracted Gaussian pulsed beam in the near-field. The expressions for a circular black screen and a circular aperture are given as special cases of the general results. The relative spectral shift of a space–time-dependent Gaussian pulsed beam versus the different values of the truncation parameters and the position parameters of observation points are also studied and illustrated with numerical calculations. It is shown that the spectral switch appears near phase singularities in the near-field, and the near-field spectral behavior depends on the truncation parameters, the pulse duration τ, and the position parameter. The results of this work have potential applications in free-space information encoding and transmission.
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