Scattering pattern in 3D. Model a spherical PEC scatterer in a 3D Cartesian simulation, using UPML or CPML boundaries and a total-field / scattered-field formulation surrounding the scatterer.
(a) Make the scatterer exactly 1 wavelength in radius. Launch a plane wave from one side of the space at the TF/SF boundary, and measure the scattering pattern in 3D just inside the PML by monitoring a large number of points in 3D. Compare the resulting scattering pattern to the theoretical approximation from the Mie solution (see, for example, Balanis [7] or Stratton [8]).
(b) Modify the scatterer to be either one-half wavelength or two wavelengths in radius; how does the scattering pattern change?
(c) Make the scatterer a dielectric with r = 4 and compare the scattering patterns to those found for the PEC scatterer above.