Efficient modeling of dispersive materials via time-domain simulations of the Maxwell equations relies on the technique of auxiliary differential equations. In this approach, a material’s frequency-dependent permittivity is represented via a sum of rational functions, e.g., Lorentz poles, and the associated free parameters are determined by fitting to experimental data. In the present work, we present a modified approach for plasmonic materials that requires considerably fewer fit parameters than traditional approaches. Specifically, we consider the underlying microscopic theory and, in the frequency domain, separate the hydrodynamic contributions of the quasi-free electrons in partially filled bands from the interband transitions. As an illustration, we apply our approach to gold and demonstrate how to treat the interband transitions within the effective model via connecting to the underlying electronic band structure, thereby assigning physical meaning to the remaining fit parameters. Finally, we show how to utilize this approach within the technique of auxiliary differential equations. Our approach can be extended to other plasmonic materials and leads to efficient time-domain simulations of plasmonic structures for frequency ranges where interband transitions have to be considered.

通过麦克斯韦方程的时域模拟对色散材料进行有效建模依赖于辅助微分方程技术。在这种方法中，材料的频率相关介电常数通过有理函数（例如洛伦兹极）之和来表示，并且相关的自由参数通过拟合实验数据来确定。在目前的工作中，我们提出了一种等离子体材料的改进方法，与传统方法相比，该方法需要的拟合参数要少得多。具体来说，我们考虑潜在的微观理论，并在频域中将部分填充带中的准自由电子的流体动力学贡献与带间跃迁分开。作为说明，我们将我们的方法应用于黄金，并演示如何通过连接到底层电子能带结构来处理有效模型内的带间跃迁，从而为其余拟合参数分配物理意义。最后，我们展示了如何在辅助微分方程技术中利用这种方法。我们的方法可以扩展到其他等离子体材料，并可以在必须考虑带间跃迁的频率范围内对等离子体结构进行有效的时域模拟。