The correspondence between flattened Gaussian beams and flat-topped multi-Gaussian beams

The comparison of the two mathematical-physical models describing flat-topped beams,i.e.,the flattened Gaussian beam (FGB) and flat-topped multi-Gaussian beam (FMGB) is made.Numerical results and physical analysis are given.It is found that both FMGB and FGB having the same M2 factor exhibit a similar transversal intensity distribution at a position of the equal generalized Fresnel number,whenever their waist width is equal or not.This conclusion is useful for practical applications.