Kurtosis parameters of super Lorentzben Gauss beams 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 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.