Numerical Methods for Solving the Problem of Electromagnetic Scattering by a Thin Finite Conducting Wire

Scattering, absorption and extinction by a thin finite length conducting wire are computed numerically by solving the generalized Pocklington integro-differential equation using two approaches: the method of moments (MoM) with short range pulse basis functions via the point matching scheme and the Galerkin method with long range basis functions (Legendre polynomials modified to satisfy the boundary conditions of the problem). A new development included in the computations reported here involves a more accurate rendering of wires with lower aspect (length-to-diameter) ratios. Both methods converge to the same answer and satisfy the energy balance to within one percent. A comparison is made with an existing analytical theory by Waterman and Pedersen. This theory solves a more approximate form of the Pocklington equation and is found to have anomalies for some cases. The solutions of this paper agree with the analytical theory for very thin wires, and the results yield a small but significant amplitude and resonance shift for lower aspect ratios. All three solutions are in agreement with the numerous available experimental results to within the experimental errors. The numerical approaches provide a complete direct solution to the problem and remove all the anomalies which occurred in the analytical theory by Waterman and Pedersen.