A framework for the finite series method of the generalized Lorenz-Mie theory and its application to freely-propagating Laguerre-Gaussian beams

Author(s)

Votto, Luiz Felipe Machado ; Gouesbet, Gerard ; Ambrosio, Leonardo Andre

• Document type: Journal article
• Source: JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER; v. 309, p. 9-pg., 2023-06-24.

Abstract

In face of a revival of interest in the finite series (FS) method due to recent developments upon gener-alized Lorenz-Mie theories (GLMTs), a more general, understandable, and systematic formulation is pro-posed. Possibly due to an apparent lack of flexibility in the FS method's earlier statements, there has been a void in its use since the 1990s. Particularly, the method demands some degree of mathematical labor each time it is applied to a different kind of field profile. Furthermore, the algebraic complexity of its earlier occurrences might also have weighted upon the method's historical shunning. Dissecting the later works reclaiming the FS, several possibilities for generalization, simplification, and organization were found. Accordingly, with the intent to render the method more approachable and to encourage its use, this work derives an alternative path suitable for both understanding and implementation. Applying the procedure, expressions for the beam shape coefficients of freely propagating Laguerre-Gaussian beams are obtained in closed form in a more straightforward manner when compared to previous formulations - this time not relying on recursions. (c) 2023 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 21/06121-0 - Electromagnetic wave propagation through complex structures
• Grantee: Ben-Hur Viana Borges
• Support Opportunities: Regular Research Grants
• FAPESP's process: 20/05280-5 - Frozen wave-type structured beams: theoretical and experimental aspects in 2D and 3D imaging, optical tweezers and in photophoretic traps for application in optical trapping displays
• Grantee: Leonardo Andre Ambrosio
• Support Opportunities: Regular Research Grants