Applicability of kurtosis parameter characterizing the degree of sharpness of beam intensity distribution

It is known that usually the degree of sharpness (or flatness) of beam intensity distribution is described by the kurtosis parameter (K parameter).Taking cosh-Gaussian (ChG),Bessel-modulated Gaussian (QBG),and flattened Gaussian (FG) beams as three illustrative examples,detailed numerical calculations and physical interpretations were given.It is shown that the K parameter is suited essentially to characterize the sharpness of the bell-shape beam profile,but not applicable to beams with large diffraction sidelobes,large intensity modulations,and beams with central shadow.