Analytical propagation expressions for kurtosis parameter of flat-topped beams

From the flat-topped beam model proposed recently by Li and the Collins formula, an analytical propagation expression for the kurtosis parameter (K parameter) of flat-topped beams through a paraxial ABCD system is derived. The K parameter depends on the beam order, Rayleigh length and ratio A/B of transfer matrix elements. Based on the propagation equation of intensity moments, a closed-form propagation equation of the K parameter is deduced. The two expressions are shown to be numerically equivalent. The propagation properties of the K parameter of flat-topped beams are illustrated with the caculated results.