markFDTD: Two Dimensional FDTD Total Scattered Field Formulation

The simulation of plane waves is often of interest in computational electromagnetics. Many problems, such as the calculation of radar cross sections, deal with plane waves. Furthermore, after a distance on the order of tens of wavelengths, the field from most antennas can be approximated as a plane wave.

In order to simulate a plane wave in a 2D FDTD program, the problem space will be divided up into two regions, the total field and the scattered field. There are two primary reasons for doing this: (1) The propagating plane wave should not interact with the absorbing boundary conditions; (2) the load on the absorbing boundary conditions should be minimized. These boundary conditions are not perfect, i.e. a certain portion of the impinging wave is reflected back into the problem space. By subtracting the incident field, the amount of the radiating field hitting the boundary is minimized, thereby reducing the amount of error.

Figure 1 illustrates how this is accomplished.

First note that there is an auxiliary one-dimensional buffer called the incident array. Because this is a one-dimensional array, it is easy to generate a plane wave: a source point is chosen and the incident Ez field is just added at that point. Then a plane wave propagates away in both directions. Since it is a one-dimensional array, the boundary conditions are perfect.

The program fd2d_003 implements these algorithms with an incident plane wave. Fig.2 and Fig.3 illustrates the propagation of a Gaussian pulse through the problem space at 0 and 90 degree respectively.