Kurtosis parameters of super Lorentz—Gauss beams through a paraxial and real ABCD optical system

Abstract

Based on the propagation equation of higher-order intensity moments, analytical propagation expressions for the kurtosis parameters of a super Lorentz—Gauss (SLG) SLG01 beam through a paraxial and real ABCD optical system are derived. By replacing the parameters in the expressions of the kurtosis parameters of the SLG01 beam, the kurtosis parameters of the SLG10 and SLG11 beams through a paraxial and real ABCD optical system can be easily obtained. The kurtosis parameters of an SLG01 beam through a paraxial and real ABCD optical system depend on two ratios. One 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 super-Lorentzian part. The other is the ratio of the width parameter of the super-Lorentzian part to the waist of the Gaussian part. As a numerical example, the properties of the kurtosis parameters of an SLG01 beam propagating in free space are illustrated. The influences of different parameters on the kurtosis parameters of an SLG01 beam are analysed in detail.