On Methods Employing Auxiliary Sources for 2-D Electromagnetic Scattering by Noncircular Shapes

Methods employing auxiliary sources are applied to electromagnetic scattering problems by 2-D noncircular scatterers. Specific cases are considered for which the singularities of the analytic continuation of the scattered field into the interior of the scatterer can be analytically determined. Then, it is shown that the amplitudes (currents) of the sources diverge and oscillate when the auxiliary curve does not enclose these singularities. Still, the electric fields computed by means of the divergent and oscillatory currents are convergent and correct. The correctness of the computed fields is validated by comparison with the exact solutions (where possible) as well as with the numerical solutions computed via commercial field simulation software.