Study of the correspondence between flat-topped multi-Gaussian beams and super-Gaussian beams

Abstract

Based on the Wigner distribution function and irradiance moments method, the characteristic parameters of flat-topped multi-Gaussian beams (FMGBs), such as the M2 factor and beam width, are derived analytically. Then, from a comparison of the propagation of FMGBs and super-Gaussian beams (SGBs), it is found that two FMGBs and SGBs with the same M2 factor exhibit a similar transverse irradiance distribution at a position of the equal generalized Fresnel number despite the fact that the beam width and propagation distance may be different.