Near-to-Far Field Transformation in FDTD: A Comparative Study of Different Interpolation Approaches

Equivalence theorems in electromagnetic field theory stipulate that farfield radiation pattern/scattering profile of a source/scatterer can be evaluated from fictitious electric and magnetic surface currents on an equivalent imaginary surface enclosing the source/scatterer. These surface currents are in turn calculated from tangential (to the equivalent surface) magnetic and electric fields, respectively. However, due to the staggered-in-space placement of electric and magnetic fields in FDTD Yee cell, selection of a single equivalent surface harboring both tangential electric and magnetic fields is not feasible. The work-around is to select a closed surface with tangential electric (or magnetic) fields and interpolate the neighboring magnetic (or electric) fields to bring approximate magnetic (or electric) fields onto the same surface. Interpolation schemes available in the literature include averaging, geometric mean and the mixed-surface approach. In this work, we compare FDTD farfield scattering profiles of a dielectric cube calculated from surface currents that are obtained using various interpolation techniques. The results are benchmarked with those obtained from integral equation solvers available in the commercial packages FEKO and HFSS.