Fourier Methods Applicable in the Numerical Solution of Electromagnetic Time-Domain Scattering Problems

Abstract

In transient electromagnetic scattering problems, Fourier or Laplace transformations are employed to attain a spectral decomposition in terms of solutions of reduced problems of a lower dimensionality. The resulting inversion integrals are evaluated either by contour deformation into the complex frequency or order plane, or by the direct evaluation of one or more Fourier or Bromwich inversion integrals. The modal representations resulting from the former approach provide a detailed physical insight into the scattering process; the latter approach is more suitable for an efficient computation of the desired time-domain solution. Both approaches are illustrated for the “tutorial” scattering problem of transient scattering by a radially inhomogeneous, lossy dielectric circular cylinder embedded in a homogeneous, lossless dielectric. Numerical results are presented and discussed.