On Using a Closed Box as the Integration Surface With the FDTD Method

This paper disproves an hypothesis that this author had made in an earlier paper from the observation that the values of the plane wave scattering coefficients computed with his numerical method could vary substantially with the physical separation distance between the integration box and the scatterer enclosed within the box. This variation was observed when the edges and corners of the integration box were strongly illuminated with the scattered field. It was hypothesized that this variation was due to the use of a box as the integration surface because a box is not the smooth integration surface that is supposed to be needed for the application of Huygens´ principle on which is based the computation of the far-field values with the steady-state near-to-far field transformation. In this paper, it is found by reconstructing the spatial field distribution that corresponds to the error spectrum, and noting that this distribution is not confined to the edges and corners of the integration box, that the use of the box is not the cause for the variation and thus, that the hypothesis is false. It turned out that the variation nearly disappeared when the FDTD mesh size was of the order of 100 cells per wavelength. It is shown that the variation was due to the second-order accuracy of the FDTD stencil.