Numerical Stability of Modified Lorentz FDTD Unified From Various Dispersion Models.

Abstract

The finite-difference time-domain (FDTD) method has been widely used to analyze electromagnetic wave propagation in complex dispersive media. Until now, there are many reported dispersion models including Debye, Drude, Lorentz, complex-conjugate pole-residue (CCPR), quadratic complex rational function (QCRF), and modified Lorentz (mLor). The mLor FDTD is promising since the mLor dispersion model can simply unify other dispersion models. To fully utilize the unified mLor FDTD method, it is of great importance to investigate its numerical stability in the aspects of the original dispersion model parameters. In this work, the numerical stability of the mLor FDTD formulation unified from the aforementioned dispersion models is comprehensively studied. It is found out that the numerical stability conditions of the original model-based FDTD method are equivalent to its unified mLor FDTD counterparts. However, when unifying the mLor FDTD formulation for the QCRF model, a proper Courant number should be used. Otherwise, its unified mLor FDTD simulation may suffer from numerical instability, different from other dispersion models. Numerical examples are performed to validate our investigations.