Apparent 3-D finite-difference Green's function anomalies are features, not artefacts
We have previously reported on the use of Zeil-berger's algorithm to construct a third-order recurrence scheme with polynomial coefficients of the sixth degree, by which 2-D finite-difference time-domain (FDTD) Green's function sequences can be generated on-the-fly. For 3-D cubic lattices, we have managed to find recurrence schemes for lattice points along the symmetry directions. In the non-diagonal symmetry directions, an apparently strong secondary signal peak occurs. A group-delay analysis associated with the characteristic variety of a spectral integral representation for the FDTD Green's function leads to curves that coincide with the ones in its spectrogram resulting from a Gabor transformation, indicating that the anomalies are rapidly oscillating local features rather than artefacts.