Nonparaxial propagation analysis of elliptical Gaussian beams diffracted by a circular aperture

The direct integration of the diffraction integral is quite time consuming. Based on the fact that a hard-edge aperture function can be expanded into finite sum of complex Gaussian functions, a nonparaxial propagation expression for elliptical Gaussian beams diffracted by a circular aperture is derived using the well-known method of the scalar angular spectrum and the stationary phase. Simulation shows that when the f-parameter is greater and the truncation parameter is smaller, the paraxial approximation is invalid and the nonparaxial approach has to be used for apertured elliptical Gaussian beams. A circular aperture can cause the stigmatic elliptic Gaussian beam diverge in the far field but change the aspect ratio of the beam. It can also change the shape and intensity distribution of the higher-order Hermite-Gaussian beams due to the obstruction and the interference of beams.