Propagation of the kurtosis parameter of a Lorentz-Gauss beam through a paraxial and real ABCD optical system

Based on the propagation equation of higher-order intensity moments, analytical propagation expressions for the kurtosis parameters of a Lorentz-Gauss beam through a paraxial and real ABCD optical system have been derived. The kurtosis parameters of a Lorentz-Gauss beam through a paraxial and real ABCD optical system depend on two parameters. One parameter is related to the ratio of the beam width of the Lorentz part to the waist of the Gaussian part. The other parameter is the ratio of the transfer matrix element B to the product of the transfer matrix element A and the diffraction-free range of the Lorentz part. As special cases of the general formula, the kurtosis parameters of the Gaussian and the Lorentz beams are also presented and are consistent with the well-known results. The properties of the kurtosis parameters of a Lorentz-Gauss beam are illustrated with numerical examples. This research is beneficial to the practical applications of Lorentz-Gauss beams.