The diffraction characteristics of a broadband light source from a circular aperture in the near field are theoretically clarified via a prompt and precise mathematical derivation. We provide a rigorous way of treating in the case of a time-dependent Gaussian-shaped pulsed beam passing through a circular aperture and give a more accurate and concrete criteria for judging the timing for the spectral red and blue shifts and the splitting of light distributions. In addition, the distortion of the space-time diffraction intensity distribution is also presented in detail. Hence, the results offer a clear understanding about the Gaussian beam quality of the output of optical resonator in the near-field diffraction.
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