Finite series algorithm design for lens-focused Laguerre–Gauss beams in the generalized Lorenz–Mie theory

Abstract

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.