Finite series expressions to evaluate the beam shape coefficients of a Laguerre-Gauss beam focused by a lens in an on-axis configuration

Rayleigh limit of generalized Lorenz-Mie theory for on-axis beams and its relationship with the dipole theory of forces. Part I: Non dark axisymmetric beams of the first kind, with the example of Gaussian beams

“…The fact that only low-order BSCs intervene in the optical forces on Rayleigh particles may be furthermore viewed as a consequence of the Van de Hulst principle of localization which, by the way, is at the origin of various localized approximations such as the ones used in the present paper, see [41] for a review, [53], [54] for complements, and [55], [56], [57], and references therein, for warnings against the use of localized approximations in the case of beams exhibiting an axicon angle and/or some amount of helicity.…”

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.…”