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.

中文翻译：

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修正的Lorentz色散介质的Newmark-FDTD公式及其与双线性变换的辅助微分方程-FDTD的等价关系

有限差分时域（FDTD）方法已广泛用于分析电磁波在分散介质中的传播。引入了多种色散模型来考虑频率相关的介电常数，包括德拜，德鲁德，洛伦兹，二次复有理函数，复共轭极残差和临界点模型。最近提出了对分散介质进行电磁分析的Newmark-FDTD方法，结果表明，与传统的辅助微分方程（ADE-）FDTD方法相比，所提出的Newmark-FDTD方法具有更高的稳定性和更好的精度。在这项工作中，我们将Newmark-FDTD方法扩展到改良的Lorentz介质，该介质可以简单地统一上述色散模型。此外，结果发现，基于双线性变换的ADE-FDTD配方与Newmark-FDTD配方完全相同，与传统的ADE-FDTD相比，具有更高的稳定性和更好的准确性。数值稳定性，数值介电常数和数值示例可用来验证我们的工作。