Limitations on using the staircased FDTD method when modeling narrow-angled TEM horn antennas

It has been shown (Cangellaris and Wright, 1991; Holland 1993) that a finite-difference time domain (FDTD) scheme employing a traditional orthogonal grid Yee mesh can often produce erroneous results due to the limitations of "staircasing". While these results suggest and show there are limitations in using staircased models in the FDTD method, no practical guidelines for a user of the FDTD method were given. In this paper, it is shown that when modeling narrow-angled TEM horn antennas using the orthogonal grid Yee approach, one must insure that the maximum length of the FDTD staircase is much less than one half a wavelength at the highest frequency of interest of the incident pulse to obtain accurate results. The example studied further validates a similar conclusion which the present authors first observed when analyzing metallic bow-tie antennas (Shlager et al., 1994).