On radial quadrature method applied to spherical wave expansion of Gaussian beams

The radial quadrature method is proposed recently for evaluating the beam shape coefficients (BSCs) of shaped beams, in which the BSCs are expressed in terms of integrals, infinite series and finite series as well. Previous study reveals that the BSCs expressed in finite series agree exactly with those obtained in the finite series technique and show blowing-ups for high-order partial waves, while the BSCs expressed in infinite series do not blow up. The paper presented here uncovers the reason behind these phenomena. It is found that the radial quadrature suppresses significantly the evanescent waves in the BSC evaluation.