Bessel-Gauss Beam Description in the Generalized Lorenz-Mie Theory: The Finite Series Method

Expansions over spherical harmonic functions are needed to describe electromagnetic beams in the Generalized Lorenz-Mie theory, the coefficients of which – the Beam Shape Coefficients (BSCs)- are related to the beam’s spatial shape. Bearing in mind applications in optical trapping, this work provides a set of finite series expressions for the BSCs, as an alternative exact method to analytically describe paraxial arbitrary order Bessel-Gauss beams. These beams are solutions to the Fresnel diffraction integral constructed from a Gaussianapodized Bessel beam. A comparison between finite series, 10-calized approximation (LA) and the time-consuming quadrature schemes are presented in terms of BSCs. It is shown that finite series and LA approaches agree with great precision. Taking into consideration its natural limitations, the LA approach computes BSCs with lower computational burden than the finite series, although the latter is an exact method which can also be extended to nonparaxial vector beams.