A discussion of efficient methods for including thin material sheets in the FDTD technique

Two approaches (which were applied to a parallel plate waveguide) for including thin material sheets in the finite-difference time-domain (FDTD) technique are compared. The first approach by J.G. Maloney and G.S. Smith (see IEEE Trans. Antennas Propag., vol.AP-40, no.3, 1992) uses a special FDTD cell to handle the sheet. Throughout the cell the component of the electric field tangential to the sheet is assumed to be constant. However, the component of the electric field normal to the sheet assumes different constant values in the sheet and in the space adjacent to the sheet. The discontinuity of the normal component of the electric field at the surface of the sheet allows for the presence of surface charge. In the second approach by P.A. Tirkas and K.R. Demarest (see IEEE Trans. Antennas Propag., vol.AP-39, no.9, p.1338, 1991) the component of the electric field tangential to the sheet is also assumed to be constant, but the component of the electric displacement normal to the sheet is assumed to vary linearly across the cell. This makes the normal component of the electric field jump by the ratio of the dielectric constants at the surface of the sheet. There are some subtle differences in the two approaches; these may make one prefer one of the approaches over the other for a particular application.<>