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中文摘要：
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M^2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M^2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。
英文摘要：
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.
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