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) SLG 01 beam through a paraxial and real ABCD optical system are derived. By replacing the parameters in the expressions of the kurtosis parameters of the SLG 01 beam, the kurtosis parameters of the SLG 10 and SLG 11 beams through a paraxial and real ABCD optical system can be easily obtained. The kurtosis parameters of an SLG 01 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 SLG 01 beam propagating in free space are illustrated. The influences of different parameters on the kurtosis parameters of an SLG 01 beam are analysed in detail.

Orbital angular momentum density and spiral spectra of Lorentz–Gauss vortex beams passing through a single slit

“…[5,6] The Lorentz-Gauss beam is the lowest-order mode of a super-Lorentz-Gauss beam family. [7,8] The properties of Lorentz-Gauss beams, including the beam propagation factor, [9] the focal shift, [10] the Wigner distribution, [11] the tight focusing, [12] and the radiation force, [13] have been extensively investigated. Also, the propagation of Lorentz-Gauss beams has been widely examined in various media such as free space, [2,14] a turbulent atmosphere, [15] a uniaxial crystal, [16,17] a Kerr medium, [18] and a strongly nonlocal nonlinear medium.…”