In continuation to a series of works on the elaboration of Finite Series (FS) methods for helical beams under the Generalized Lorenz–Mie Theory’s formalism, this paper consists of a thorough study of the mathematical and computational nuances which arise from implementing the recently deduced FS method for Lens–Focused Laguerre–Gaussian beams. This family of beams, as in most brought under the FS procedure, has its features which result in unique implications to the algorithm’s design, implementation and analysis. Then, results are compared in terms of accuracy and time-performance with the ones obtained from two other known methods - quadratures and the Integral Localized Approximation. It is then concluded that a properly implemented FS algorithm should generally be the most preferable of the three since it converges to exact solutions within acceptable time costs.

在对广义洛伦兹-米氏理论形式主义下的螺旋梁的有限系列（FS）方法进行详细阐述的一系列工作的基础上，本文全面研究了因实施最新推导的FS而产生的数学和计算上的细微差别透镜聚焦拉盖尔-高斯光束的方法。在FS程序中，大多数光束都具有其特征，这些特征会对算法的设计，实现和分析产生独特的影响。然后，将结果在准确性和时间性能方面与从其他两种已知方法-正交和积分局部近似中获得的结果进行比较。