Mai Wending, Campbell Sawyer D, Werner Douglas H
Opt Express. 2021 Sep 13;29(19):30520-30531. doi: 10.1364/OE.435297.
Various dispersion models can be expressed as special cases of the Generalized Dispersion Model (GDM), which is composed of a series of Padé polynomials. While important for its broad applicability, we found that some materials with Drude dispersive terms can be accurately modeled by mixing a 1 order Padé polynomial with an extra conductivity term. This conductivity term can be separated from the auxiliary differential equation (ADE). Therefore, the proposed mixed-order model can achieve the same accuracy with fewer unknowns, thus realizing higher computational efficiency and lower memory consumption. For examples, we derive the model parameters and corresponding numerical errors for noble metals including Au, Ag, and Al in the optical regime. Finally, the proposed model's efficiency improvements are validated through implementation within a Discontinuous Galerkin Time Domain (DGTD) framework. The proposed model can achieve up to 12.5% efficiency improvement in theory compared to the conventional GDM with the same accuracy. A numerical example validates that, in practice, 9% memory reduction and 11% acceleration can be realized.
各种色散模型都可以表示为广义色散模型（GDM）的特殊情况，广义色散模型由一系列帕德多项式组成。虽然其广泛的适用性很重要，但我们发现，对于一些具有德鲁德色散项的材料，可以通过将一阶帕德多项式与一个额外的电导率项混合来进行精确建模。这个电导率项可以从辅助微分方程（ADE）中分离出来。因此，所提出的混合阶模型可以用更少的未知数达到相同的精度，从而实现更高的计算效率和更低的内存消耗。例如，我们推导了包括金、银和铝在内的贵金属在光学波段的模型参数和相应的数值误差。最后，通过在时域间断伽辽金（DGTD）框架内的实现，验证了所提出模型的效率提升。与具有相同精度的传统GDM相比，所提出的模型在理论上可以实现高达12.5%的效率提升。一个数值例子验证了，在实际中，可以实现9%的内存减少和11%的加速。
