Conductive mixed-order generalized dispersion model for noble metals in the optical regime

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^st 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.