Propagation of Hermite-Gaussian beam through paraxial optical system with hard-edge aperture

The hard-edge aperture is “moved out” in an complicated optical system, which means to transfer the system with such hard-edge aperture into an optical system with entrance and exit pupils, and the hardedge aperture is taken as an exit pupil so as to find the analytical solution of a light beam. The intensity distribution of the Hermite-Gaussian beam at the output plane can be characterized by the Collins formula and the relation between aperture and exit pupil, and the analytical expression of the beam at the output plane is obtained directly. Taking an optical system with a hard-edge aperture as an example, the intensity distributions of two low modes of Hermite-Gaussian beam were simulated and numerically calculated with the mathematical software. The analytical results show that the effect of hard-edge aperture can be replaced by the effect of exit pupil for any complicated optical system with a hardedge aperture and the calculation process is simplified.