Lasing thresholds of plasmonic modes of a silver tube nanolaser with active shell and core

We considered the source-free problem of the H-polarized field in the presence of a circular silver nanotube with inner active core coated with a concentric layer of the same active material. In the analysis, we used mathematically grounded Lasing Eigenvalue Problem, according to which we assumed that at the threshold the natural-mode frequency is real-valued. We looked for it together with the corresponding threshold value of material gain in the active regions. To build characteristic equations for each azimuth index, we used the separation of variables. We found surface plasmon modes of such nanolaser, classified them, and studied the dependences of modal thresholds and wavelengths on the core, tube and shell thicknesses.