Advancements in the finite series method of the generalized Lorenz-Mie theory

• Ano de defesa: 2024
• Autor(a) principal: Votto, Luiz Felipe Machado
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: espalhamento; finite series; generalized Lorenz-Mie theory; lasers; Mie theory; scattering; série finita; teoria de Mie; teoria generalizada de Lorenz-Mie
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/18/18155/tde-13092024-083840/

The finite series method of the generalized Lorenz-Mie theory has been put aside for decades since its inception due to its apparent lack of flexibility when applied to each new type of electromagnetic field. The strong points of the method were still unclear up until now. This study features a collection of papers published in scientific journals displaying the most recent applications of the finite series method and their implications. Generally, the focus was the representation of the scattering of laser beams, modeled as solutions to the paraxial wave equation, by spherical obstacles. Several families of higher-order solutions, such as Laguerre-Gaussian, Bessel-Gaussian, Hermite-Gaussian, and Ince-Gaussian modes, were included in the formalism of the generalized Lorenz-Mie theory with their beam shape coefficients given by closed-form expressions. The performance of the finite series method was shown to be better than other usual methods in such cases. In the process of implementing the finite series method, a phenomenon that was unaccounted for took place – the issue of the blowing-up coefficients. During this investigation, it was possible to determine that the blowing-ups had two origins. First, the finite series coefficients are susceptible to catastrophic error propagation when the numerical representation has low precision. Second, the actual physical formulation of scalar paraxial beams translated to a diverging model when put in terms of solutions to Maxwells equations. The blowing-up phenomenon has been proven to originate from the actual mathematical scheme that describes the incident fields since the finite series beam shape coefficients of a fundamental Gaussian beam are shown to be given by a family of special functions known as the generalized Bessel polynomials.