中文摘要：

由于金属材料的介电常数为复数，直接利用时域有限差分方法（FDTD）处理金属材料电磁波问题时，会导致计算结果的发散及不稳定问题．本文采用各向同性有损耗金属材料介电常数的Drude色散模型，利用电位移矢量作为辅助中间变量，推导出了各向同性色散金属材料的辅助差分FDTD迭代公式．利用该辅助迭代公式计算了金属Au光栅与平面电磁波的相互作用，结果表明该方法解决了数值计算中的不稳定问题，模拟效果较好．

英文摘要：

When processing electromagnetic problems of metallic material using FDTD method, the numerical results are not convergent or stable because permittivity of metallic material is plural. In this paper, a Drude dispersive model for the plural of isotropic lossy metallic material was adopted. Auxiliary differential equations for FDTD algorithm were derived with electric displacement vector D being used as an auxiliary transitional variable. The interaction between Au grating and Plane Electromagnetic waves was simulated using these auxiliary differential FDTD equations. The simulated results showed that this method could solve the numerical instability problem and the simulation results were accurate.