Blowing-ups of beam shape coefficients of Gaussian beams using finite series in generalized Lorenz-Mie theory

Compact closed-form expressions of the beam shape coefficients (BSCs) of Gaussian beams are obtained in the generalized Lorenz-Mie theory through the finite series (FS) method. As a result, such expressions have made it possible to more deeply understand the behaviour of the BSCs and, therefore, the scattering of Gaussian beams beyond the paraxial approximation. The blowing up, in particular, of FS BSCs which has been observed for several paraxial beams is now mathematically justified as a phenomenon that is independent of numerical precision. Furthermore, numerical results demonstrate how such blow ups are related to the ratio between the beam waist radius and its wavelength.