Spectral shifts and spectral switches of a pulsed Bessel–Gauss beam from a circular aperture in the far field

The far-field spectral characteristics of a broadband-pulsed Bessel–Gauss beam passing through a circular aperture are studied. Based on the expansion of a hard aperture function into a finite sum of complex Gaussian functions and starting from the Fresnel diffraction integral, the approximate analytical expression for the spectral distribution of the diffraction field is derived. The “aperture dispersion”, that is, the red and blue shifts of the spectral intensity maximum and the spectral intensity shape distortion and distribution under different conditions are studied and illustrated with numerical calculations. It is shown that the far-field, on-axis maximum spectral intensity always shifts to the right (blue shift) and the amount of the spectral shift is dependent on the source bandwidth only. However, for the cases of off-axis, when the observation angle θ approaches a critical value, a rapid spectral switch occurs.