On the validity of the use of a localized approximation for helical beams. II. Numerical aspects

The description of an electromagnetic beam for use in light scattering theories may be carried out by using an expansion over vector spherical wave functions with expansion coefficients expressed in terms of Beam Shape Coefficients (BSCs). A celebrated method to evaluate these BSCs has been the use of a localized approximation. In Part I of the present work devoted to formal aspects of the issue, we have demonstrated, using what is known as the N-procedure, that the use of a localized approximation is likely to be of limited validity in the case of helical beams exhibiting a nonzero topological charge. In the present Part II devoted to numerical aspects, we confirm the previous statement by relying on the comparison between exact and localized values of the BSCs in the case of Laguerre-Gauss beams. As a by-product we shall exhibit new examples of helical beams which are nonvortex beams.