Generalized Stability Criterion of 3-D FDTD Schemes for Doubly Lossy Media

This paper presents the generalized stability criterion of 3-D finite-difference time-domain (FDTD) schemes for doubly lossy media, where both electric and magnetic conductivities coexist. The generalized stability criterion is applicable for all 3-D FDTD schemes, such as time-average (TA), time-forward (TF), time-backward (TB) and exponential time differencing (ETD). It is reducible to either electrically lossy, magnetically lossy or lossless media. The stability criterion for perfectly matched layer (PML) matching condition can also be obtained as a special case to the doubly lossy media. It is shown that, for doubly lossy media, the stability criterion for ETD and TF becomes even more relaxed, and for TB, even more stringent compared to either electrically lossy, magnetically lossy or lossless media. On the other hand, the stability criterion for TA remains unchanged even in doubly lossy media. As numerical demonstration, the tunneling of electromagnetic wave through a very thin doubly lossy conductor is simulated. Numerical experiments further show the maximum allowed time step as dictated by the derived stability criterion for different schemes.