非傍轴矢量拉盖尔-高斯光束的二阶矩表示  

The second-order moment representation of nonparaxial vectorial Laguerre-Gaussian beams

作　　者：康小平[1,2] 吕百达[1] 

机构地区：[1]四川大学激光物理与化学研究所 [2]琼州大学物理系,五指山572200

出　　处：《物理学报》2006年第9期4563-4568,共6页Acta Physica Sinica

基　　金：国家高技术研究发展计划(批准号:A823070);国家自然科学基金(批准号:10574097);海南省自然科学基金(批准号:80598)资助的课题.~~

摘　　要：基于Porras提出的光传输的非傍轴矢量矩理论,推导出初始圆偏振的非傍轴矢量拉盖尔-高斯(LG)光束的特征参数,包括束宽、远场发散角和M2因子等的公式,并表示为级数求和形式.非傍轴矢量高斯光束公式作为特例给出.研究表明,基于二阶矩定义的束宽按双曲线规律传输,当w0/λ→0(w0为束宽,λ为波长)时,远场发散角θ趋于90°,大于非傍轴标量理论预示的值63.435°.非傍轴矢量LG光束的M2因子不仅与模指数p有关,而且还与w0/λ有关.最后,对非傍轴矢量LG光束和非傍轴标量LG光束的传输作了比较,结果表明在w0/λ较小时,矢量效应对远场发散角的影响十分显著.对θ→90°引起的问题和非傍轴矢量矩理论的适用范围,以及解决问题的可能途径作了分析和讨论.Based on the nonparaxial vectorial moment theory of light beam propagation proposed by Porras, the characteristic parameters, such as the beam width, far-field divergence angle and ME factor of nonparaxial vectorial Laguerre-Gaussian （LG） beams with initial circular polarization, are derived and expressed in terms of a series sum. The nonparaxial vectorial Gaussian beam is treated as a special case of our result. It is shown that the second-order-moment based beam width propagates according to the hyperbolic law, and for w0/λ→0 （ w0-waist width, λ-wavelength） the far-field divergence angle θ approaches 90°, which is larger than 63.435° predicated by the nonparaxial scalar theory. The ME factor of nonparaxial vectorial LG beams depends not only on the mode index p, but also on the w0/λ. Finally, comparison between the propagation of nonparaxial vectorial LG beams and that of nonparaxial scalar LG beams indicates that the far-field divergence angle is greatly influenced by the vectorial effect when Wo/X is relatively small. The problem which results from θ→90° and the applicability of the nonparaxial vectorial moment theory as well as the possible method for solving the problem are discussed.

关 键 词：非傍轴矢量拉盖尔 高斯光束 圆偏振 非傍轴矢量矩理论 光束参数 

分 类 号：O436[机械工程—光学工程]