A Highly Accurate FDTD Model for Simulating Lorentz Dielectric Dispersion
A Highly Accurate FDTD Model for Simulating Lorentz Dielectric Dispersion
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DOI：
10.1109/lpt.2009.2031818
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发表时间：
2009-09
影响因子：
2.6
通讯作者：
Zhili Lin;P. Ou;Yudong Jia;Chunxi Zhang
中科院分区：
文献类型：
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作者：
Zhili Lin;P. Ou;Yudong Jia;Chunxi Zhang
提出了一种用于时域有限差分 (FDTD) 方法的高精度且数值稳定的洛伦兹介电色散模型。基于麦克劳林级数展开（MSE）方法对所提出模型的系数进行了优化推导，结果表明该模型在实现洛伦兹介电色散方面比其他四种已报道的模型要好得多，相对介电常数的误差要低几个数量级。当将该模型结合到示例洛伦兹介质的实用二阶和四阶精确 FDTD 算法中时，还分析了该模型的稳定性和性能。有趣的是，我们发现所有提到的模型由于其固有的数值色散较大，在二阶算法中表现出几乎相同的性能，并且所提出的 MSE 模型的优越性开始在高阶（例如四阶 FDTD 算法）中显现出来，如控制数值色散方程所暗示的那样。
A highly accurate and numerically stable model of Lorentz dielectric dispersion for the finite-difference time-domain (FDTD) method is presented. The coefficients of the proposed model are optimally derived based on the Maclaurin series expansion (MSE) method and it is shown that the model is much better than the other four reported models in implementing the Lorentz dielectric dispersion with error of relative permittivity several orders lower. The model's stability and performance are also analyzed when it is incorporated into the practical second- and fourth-order accurate FDTD algorithms for an exemplified Lorentz medium. Interestingly, we find that all the mentioned models show nearly the same performance in the second-order algorithm due to its large intrinsic numerical dispersion and the superiority of the proposed MSE model begins to be manifested in the higher-order, say, fourth-order FDTD algorithms as implied by the governing numerical dispersion equations.