Dispersion analysis of FDTD schemes for doubly lossy media

Abstract

This paper presents the 3-D dispersion analysis of finitedifference time-domain (FDTD) schemes for doubly lossy media, where both electric and magnetic conductivities are nonzero. Among the FDTD schemes presented are time-average (TA), time-forward (TF), time-backward (TB) and exponential time differencing (ETD). It is first shown that, unlike in electrically lossy media, the attenuation constant in doubly lossy media can be larger than its phase constant. This further calls for careful choice of cell size such that both wavelength and skin depth of the doubly lossy media are properly resolved. From the dispersion analysis, TF generally displays higher phase velocity and attenuation errors due to its first-order temporal accuracy nature compared to second-order ETD and TA. Although both have second-order temporal accuracy, ETD has generally lower phase velocity and attenuation errors than TA. This may be attributed to its closer resemblance to the solution of first-order differential equation. Numerical FDTD simulations in 1-D and 3-D further confirm these findings.