Propagation of flat-topped multi-Gaussian laser beams

The multi-Gaussian beam shape is proposed as a model for aperture functions and laser beam profiles that have a nearly flat top but whose sides decrease continuously. Beams and apertures of this type represent a simple, elegant, and intuitive alternative to super-Gaussian beams, which are important in a number of applications such as laser resonator design. Analytical formulas are developed for the propagation of these beams through free space and optical systems representable by ABCD matrices.