Convergence of Mie theory series: criteria for far-field and near-field properties

We investigate the convergence of the series arising in Mie theory for the solution of electromagnetic scattering by a sphere. In contrast with previous studies that focused only on the scattering cross section, we here consider a wide spectrum of relevant properties, including scattering, extinction, and absorption cross sections, complex scattering amplitudes (i.e., radiation profile), and near-field properties such as surface electric field and average surface field intensity. The scattering cross section is shown to exhibit the fastest convergence, indicating that existing convergence criteria based on this property are not suitable for the majority of other relevant characteristics computed from Mie theory. Criteria are therefore proposed for those properties.