Propagation and Wigner distribution of the Airy–Gauss beam through an apertured paraxial optical system

Abstract

By applying the Collins–Fresnel diffraction integral formula and expanding the hard-edge aperture function into the approximate finite sum of complex Gaussian functions, we can obtain the approximate closed-form analytical expressions of the Airy–Gauss beam passing through a hard-edge aperture. The numerical results show the feasibility of the approximate process. We investigate the irradiance distribution and the Wigner distribution of the Airy–Gauss beam for different aperture calibers. It is shown that the diffraction effect reduces when the width of the aperture increases. Moreover, some properties of the Airy–Gauss beam are lost when the width of the aperture decreases. Besides, we find that when the distribution factor increases, the Airy–Gauss beam would reduce to the Gauss beam.