Inadequacy of the Drude formula in the simulation of a siver nanowire laser

We consider the two-dimensional (2-D) problem of the H-polarized electromagnetic field that can exist in the presence of a circular cylindrical nanowire made of silver, coated with a concentric layer of active material. Assuming that the natural-mode frequency is real-valued, we look for it together with the associated threshold value of material gain in the coating. Using the separation of variables, we arrive at the set of independent characteristic equations for each azimuthal index. We seek the roots of them numerically. Here, we observe that the well-known Drude formula leads to heavy errors in both the composition of modal spectrum and its characterization. Known examples of sophisticated Drude-like formulas suffer of negative absorption in silver in a part of the visible range. Therefore we use the experimental data for the silver dielectric function. This analysis reveals that the considered nanowires laser can emit light on both localized surface plasmon (LSP) modes and on the coating modes, in each azimuthal order.