Models for an aperture function and corresponding analytical propagation equations of a flattened Gaussian beam through an annular apertured optical system

Abstract

Beam profiles that consist of a sum of complex-Gaussian functions and a sum of polynomial-Gaussian functions offset by some fixed amount are proposed as two types of models for a hard aperture function. By expanding an aperture function into two types of models, the approximate analytical expression of a flattened Gaussian beam through a paraxial ABCD optical system with an annular aperture is derived. As special cases, the corresponding closed forms for the unaperture or circular aperture or circular black screen cases are also obtained. The results provide a more convenient way of studying propagation and transformation than the usual method using diffraction integral formula directly. Numerical examples are given to illustrate the propagation properties of flattened Gaussian beams.