Symmetric source implementation for ADI-FDTD

The alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is attractive for simulations involving highly refined grids due to its unconditional stability (Namiki, T. 2000; Zheng, F. et al., 2000; Darms, M. et al., 2002). It has been recently reported that the ADI-FDTD method may lead to asymmetrical results in the field distribution for a symmetric source (Darms et al., 2002; Zhao, A.P., 2002). We compare different excitation methods by testing the schemes for asymmetry and accuracy errors. We show that ADI-FDTD is perfectly symmetric if the excitation is applied inside the tridiagonal matrix and the source is correctly discretized within each time step.