Research on the temporal fresnel diffraction field of a circle aperture illuminated by a hyperbolic secant optical pulse

An equation is present to analyse the temporal diffraction intensity distribution of hyperbolic secant optical femtosecond pulse which incites a circle aperture. For convenience we calculate the temporal intensity distribution of the aperture in the horizontal central axis direction. The temporal intensity distributions are connected with the radius of the circle aperture, the Fresnel number, the width and the central wavelength of the hyperbolic optical pulse. Number calculation shows that when the Fresnel number is definite, the shorter the width of the hyperbolic optical pulse, the more different the shape of the temporal Fresnel diffraction intensity distribution from the original hyperbolic optical pulse. While the width of the hyperbolic optical pulse is definite, the smaller the Fresnel number at central frequency, the less the changes of the temporal Fresnel diffraction intensity distribution.