Validity of the Fresnel approximation for hard-edged diffracted beams

The diffraction of Gaussian beams at an square aperture is studied based on the Kirchhoff and Fresnel diffraction integrals.Detailed numerical results are presented and compared.It is shown that for a given waist width w0(w0≥λ,λ is wavelength),the valid range of the Fresnel diffraction integral depends on the truncation parameter.Otherwise,if the waist width w0 is comparable to or evenless than the wavelength λ,the Kirchhoff diffraction integral should be used.