中文摘要：

An orthonormal beam family of super Lorentz–Gauss(SLG) beam model is proposed to describe the higher-order mode beams with high divergence,which are generated by a high power diode laser.Here we consider the simplest case of the SLG beams,where there are four mutually orthogonal SLG beams,namely SLG00,SLG01,SLG10,and SLG11beams.The SLG00beam is just the Lorentz–Gauss beam.Based on the Collins integral formula and the Hermite–Gaussian expansion of a Lorentz function,an analytical expression for the Wigner distribution function(WDF) of an SLG11beam through a paraxial ABCD optical system is derived.The properties of the WDF of an SLG11beam propagating in free space are demonstrated.The normalized WDFs of an SLG11beam at the different spatial points are depicted in several observation planes.The influence of the beam parameter on the WDF of an SLG11beam in free space is analyzed at different propagation distances.The second-order moments of the WDF of an SLG11beam in free space are also examined.This research reveals the propagation properties of an SLG11beam from another perspective.The WDFs of SLG01and SLG10beams can be easily obtained by using the WDFs of Lorentz–Gauss beam and the SLG11beam.

英文摘要：

An orthonormal beam family of super Lorentz-Gauss （SLG） beam model is proposed to describe the higher-order mode beams with high divergence, which are generated by a high power diode laser. Here we consider the simplest case of the SLG beams, where there are four mutually orthogonal SLG beams, namely SLG00, SLG01, SLG10, and SLGll beams. The SLG00 beam is just the Lorentz-Gauss beam. Based on the Collins integral formula and the Hermite-Gaussian expansion of a Lorentz function, an analytical expression for the Wigner distribution function （WDF） of an SLG11 beam through a paraxial ABCD optical system is derived. The properties of the WDF of an SLG11 beam propagating in free space are demonstrated. The normalized WDFs of an SLG11 beam at the different spatial points are depicted in several observation planes. The influence of the beam parameter on the WDF of an SLGI 1 beam in free space is analyzed at different propagation distances. The second-order moments of the WDF of an SLG11 beam in free space are also examined. This research reveals the propagation properties of an SLGll beam from another perspective. The WDFs of SLG01 and SLG10 beams can be easily obtained by using the WDFs of Lorentz-Gauss beam and the SLG11 beam.