Modes of core–shell silver wire plasmonic nanolaser beyond Drude formula

Abstract

We consider the two-dimensional problem of a nonattenuating H-polarized electromagnetic field that can exist in the presence of a circular cylindrical nanowire (core) made of silver and coated with a concentric layer of active material (shell). Assuming that the natural-mode frequency is real-valued, we search for it together with the associated threshold value of material gain in the coating. Using the separation of variables, we arrive at a set of independent characteristic equations for each azimuthal index and seek their roots numerically. Here, it is important to use an adequate description of the metal core dielectric function. We observe that the well-known Drude formula not only leads to predictable errors in the lasing wavelengths but additionally, fails to reveal the complete composition of the modal spectrum. Known examples of sophisticated Drude-like formulas help overcome these drawbacks; however, these formulas suffer from negative absorption in silver in part of the visible range. Therefore, the use of experimental data for the metal dielectric function is mandatory. Our analysis reveals that, in each azimuthal order, the considered nanowire laser can emit light on several localized surface plasmon modes and the shell modes.