Computation of a branch-cut integral arising in transient electromagnetic scattering by a perfectly conducting cylinder

摘要

The paper addresses the rigorous computation of a branch-cut integral that arises in the transient electromagnetic scattering by a perfectly conducting cylinder subject to line source excitation. The branch-cut integral is formulated according to the singularity expansion method (SEM) representation of circumnavigating creeping waves, proposed in a recent paper by Heyman and Felsen (1986). The branch-cut integral decays exponentially and its contribution is negligible in comparison with that of the natural resonant mode. A useful byproduct of this computation is an algorithm to compute accurately the zeros of Hankel functions (and their derivatives) in the complex order-plane. These zeros occur frequently in electromagnetic and acoustic scattering by impenetrable cylinders as poles of creeping waves. The accuracy of the computed zeros is checked with approximate small- and large-argument approximations.