Analysis of the modes of a core-shell plasmonic nanowire laser with a silver core

Considered is the two-dimensional (2-D) source-free problem of the H-polarized electromagnetic field in the presence of a silver circular cylindrical nanowire coated with a concentric layer of active material. We assume that the natural-mode frequency is real-valued and find it together with the corresponding threshold value of material gain in the active coating. To this end, we use the separation of variables and examine numerically independent characteristic equations for each azimuthal index. This study reveals that the considered nanowire laser can emit light on a number of modes of different nature including the localized surface plasmon (LSP) modes of all azimuthal orders. We consider dynamics of the lasing eigenvalues for varying radius of the core and thickness of the active silica shell on the plane (λ, γ). This dynamics is quite complicated.