Finite series expressions to evaluate the beam shape coefficients of a Laguerre–Gauss beam freely propagating.

On an infinite number of quadratures to evaluate beam shape coefficients in generalized Lorenz-Mie theory and the extended boundary condition method for structured EM beams

“…[23] to be complemented by [24], [25], [26], and …nite series which, after having been forgotten for several decades, has been recently used again due to the limitations encountered when dealing with localized approximations in the case of beams exhibiting axicon angles and/or topological charges, e.g. [27], [28], [29], and references therein. It is also possible to use an angular spectrum decomposition into elementary plane waves either (i) by computing the scattering response of each plane wave and summing up all the responses over the plane waves present in the decomposition, a process which requires the use of GLMT for each tilted plane wave, e.g.…”

Laser-light and Interactions with Particles (LIP), 2016

“…[25], [26], [27]. As a result, another technique known as the …nite series technique, invented in 1988 [28], [29] and given up the same year due to the success of localized approximations techniques, was born again in 2019 in the case of Laguerre-Gauss beams freely propagating [30], or focused by a lens [31]. The paper by Votto et al summarized in the present preface [32] implements the …nite series technique for Laguerre-Gauss beams focused by a lens, complements another paper [33] devoted to the case of Laguerre-Gauss beams freely propagating, and constitutes some kind of conclusion in the series told in the present paragraph.…”

Descrição de feixes de Bessel-Gauss e suas superposições do tipo >i<frozen wave>/i< na teoria generalizada de Lorenz-Mie

“…(4.136) a (4.138): Alternativamente, há uma forma mais direta para calcular os BSCs para modos TE e se baseia em propriedades de simetria destes coeficientes, no caso de feixes on-axis. Tais propriedades se resume, matematicamente, às condições [56]:…”

“…Outra técnica para calcular BSCs a partir de um feixe Maxwelliano é o método das Série Finitas (FS). Apesar de ser um método exato e de evitar integrações complexas em coordenada polar ele foi desenvolvido apenas para alguns feixes como feixes Gaussianos [54], laser-sheet [55] e recentemente, Laguerre-Gauss (LGB) [56,57], BBs [58] e BGBs [59], alguns deles de natureza escalar intrínseca.…”