Propagation of Airy beam passing through the misaligned optical system with hard aperture

By expanding the hard aperture function into a finite sum of complex Gaussian functions, an approximate analytical expression for the two-dimensional Airy beam passing through an apertured and misaligned paraxial ABCD optical system has been derived. Based on the derived formula, the propagation properties of Airy beam through the misaligned optical system with hard aperture are illustrated numerically. From the numerical results we find that the center of the output beam is deviated from the optical axis and the position of the output beam is affected by the misaligned parameters, and can be controlled by adjusting them. Our results provide an effective and fast way for studying the paraxial propagation of Airy beam through apertured and misaligned paraxial ABCD optical systems.