On the Use of the Geometric Mean in FDTD Near-to-Far-Field Transformations

Near-to-far-field transformations require the tangential electric and magnetic fields over a surface, which we call the integration boundary. However, the staggered nature of the finite-difference time-domain grid is problematic in that the electric and magnetic fields are not collocated in either space or time. For harmonic transformations, i.e., ones which rely upon a Fourier transform of the time-domain near-fields, one can account for the temporal offset with a simple phase correction in the frequency domain. To account for spatial offsets, previously an arithmetic mean of the time-domain fields to either side of the integration boundary has been used. Here we show that superior results are obtained by instead using a geometric mean of the harmonic fields to either side of the integration boundary.