Propagation of generalized Mathieu–Gauss beams through paraxial misaligned optical systems

Based on the generalized diffraction integral, we derive an analytical formula for generalized Mathieu–Gauss beams (gMGBs) passing through an apertured misaligned optical system. Furthermore, we use the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions to establish an approximate propagation equation of gMGBs through paraxial circularly apertured optical system. As an example, the propagation of ordinary and modified zeroth order MGBs through a misaligned thin lens is studied numerically.