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 ...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 SLC01 beam, the kurtosis parameters of the SLG10 and SLGll 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.展开更多
Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometric- Gaussian type-II beams passing through an ABCD system, the kurtosis parameter is derived analytically...Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometric- Gaussian type-II beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre-Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.10974179)the Natural Science Foundation of Zhejiang Province,China(Grant No.Y1090073)
文摘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 SLC01 beam, the kurtosis parameters of the SLG10 and SLGll 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.
文摘Based on the irradiance moment definition and the analytical expression of waveform propagation for hypergeometric- Gaussian type-II beams passing through an ABCD system, the kurtosis parameter is derived analytically and illustrated numerically. The kurtosis parameters of the Gaussian beam, modified Bessel modulated Gaussian beam with quadrature radial and elegant Laguerre-Gaussian beams are obtained by treating them as special cases of the present treatment. The obtained results show that the kurtosis parameter depends on the change of the beam order m and the hollowness parameter p, such as its decrease with increasing m and increase with increasing p.
