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’s 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.