Electromagnetic analysis of a silver nanowire laser with a concentric active region

Plasmon-assisted nanolasers are actively considered today as miniature sources of light for advanced photonics applications. We study the lasing modes a circular cylindrical nanowire made of silver, coated with a concentric layer of active material. The electromagnetic problem is two-dimensional (2-D) and implies the H-polarization regime where localized surface-plasmon (LSP) modes exist on metal wires. We assume that the lasing-mode frequency is real-valued and consider it as an eigenvalue, together with the associated threshold value of material gain in the coating. Separation of variables in the polar coordinates enables us to derive independent characteristic equations for each azimuthal index and look for their roots numerically. In this analysis, we can see that the well-known Drude formula for the dielectric function of silver leads to heavy errors in determination of the lasing wavelengths and even in the composition of modal spectrum. Moreover, sophisticated formulas aimed at improving the Drude model produce non-physical 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, in each azimuthal order, both the LSP modes and on the coating modes may have comparable values of threshold gain.