Padé resummation of divergent Born series and its motivation by analysis of poles

Abstract

The Born series is in principle a powerful way to solve electromagnetic scattering problems. Higherorder terms can be computed recurrently until the desired accuracy is obtained. In practice, however, the series solution often diverges, which severely limits its use. We discuss how Padé approximation can be applied to the Born series to tame its divergence. We apply it to the scalar problem of scattering by a cylinder, which has an analytical solution that we use for comparison. Furthermore, we improve our understanding of the divergence problem by analyzing the poles in the analytical solution. This helps build the case for the use of Padé approximation in electromagnetic scattering problems. Additionally, the poles reveal the region of convergence of the Born series for this problem, which agrees with actual calculations of the Born series.