Abstract
The finite-difference time-domain (FDTD) method has been popularly utilized to analyze the electromagnetic (EM) wave propagation in dispersive media. Various dispersion models were introduced to consider the frequency-dependent permittivity, including Debye, Drude, Lorentz, quadratic complex rational function, complex-conjugate pole-residue, and critical point models. The Newmark-FDTD method was recently proposed for the EM analysis of dispersive media and it was shown that the proposed Newmark-FDTD method can give higher stability and better accuracy compared to the conventional auxiliary differential equation- (ADE-) FDTD method. In this work, we extend the Newmark-FDTD method to modified Lorentz medium, which can simply unify aforementioned dispersion models. Moreover, it is found that the ADE-FDTD formulation based on the bilinear transformation is exactly the same as the Newmark-FDTD formulation which can have higher stability and better accuracy compared to the conventional ADE-FDTD. Numerical stability, numerical permittivity, and numerical examples are employed to validate our work.
Highlights
The finite-difference time-domain (FDTD) method has been widely utilized to analyze various electromagnetic wave (EM) problems owing to its simplicity, robustness, and accuracy [1,2,3]
The Newmark-FDTD method is applied to modified Lorentz dispersion model which can systematically unify various existing dispersion models
It is found that the Newmark-FDTD is equivalent to the auxiliary differential equation- (ADE-)FDTD with the bilinear transformation (BT) in terms of update formulation, numerical stability, and numerical accuracy
Summary
The finite-difference time-domain (FDTD) method has been widely utilized to analyze various electromagnetic wave (EM) problems owing to its simplicity, robustness, and accuracy [1,2,3]. The Newmark time-stepping algorithm was applied to the dispersive FDTD modeling of Debye, Drude, Lorentz, and QCRF dispersion models [17, 18]. The Newmark-FDTD method is successfully extended to the modified Lorentz dispersion model. It is found that the formulation of the ADE-FDTD method based on the bilinear transformation (BT) [20,21,22] leads to the same formulation of the Newmark-FDTD method. The ADE-FDTD formulations with BT for Debye, Drude, Lorentz, and QCRF dispersion models are considered and it will be shown that the resulting FDTD formulations are equivalent to the Newmark-FDTD counterparts. The Newmark time-stepping algorithm is reviewed and the Newmark-FDTD formulation is derived for modified Lorentz medium. Numerical examples involving homogenous one-dimensional (1D) structure and three-dimensional (3D) plasmonic nanosphere are used to validate our work
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