High-order approximations to the Mie–series for electromagnetic scattering in three dimensions

Approximations to the Mie–series are fundamental in many applications. In particular, for validation of efficient electromagnetic scattering algorithms (to compute the radar cross section of three dimensional targets) or to understand the electromagnetic scattering by rain drops, it is important to evaluate the Mie–series with accuracy close to machine precision. In this paper, we propose a quadrature based algorithm to approximate the Mie–series to very high–order accuracy, and demonstrate that the approach leads to better approximations than obtained using a industrial standard Mie–series scattering code. Key–Words: Mie–series, electromagnetics, scattering, radar cross section, quadrature