Review of an FDTD TF/SF Formulation Based on Auxiliary 1-D grids

Several new techniques have been recently proposed to reduce the error in total/scattered field (TF/SF) formulations for simulating plane waves with the finite difference time domain (FDTD) method. In this paper, we re-examine a conceptually simple method based on multiple auxiliary one-dimensional (1-D) grids, which was previously used to model propagation in layered media. We show that the method can lead to less than -120 dB leakage errors in the scattered field region, which are comparable to results from other recently proposed methods. A simple explanation for this very good performance is provided, relating it to the numerical dispersion matching technique. Extension of the method to three dimensional (3-D) geometries is also discussed.