Similar propagation property of flattened-Gaussian beams and super-Gaussian beams

The similar propagation property of flattened Gaussian beams (FGBs) and super-Gaussian beams (SGBs) is studied i n the rectangular coordinate system. It is shown that two FGB and SGB with the same M2-factor but different waist width exhibit similar intensity distributions at the position of the equal generalized Fresnel number, as they propagate through an unapertured ABCD optical system. For the apertured case and focusing by a spherically aberrated lens, similar intensity profiles at the equal propagation distance can be also obtained, if the two FGB and SGB have the same M2-factor and waist width.