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Results from the electromagnetic modeling of the threshold conditions of hybrid plasmon modes of a laser based on a silver nanotube with an active core and covered with an active shell are presented. We study the modes of such a nanolaser that have their emission wavelengths in the visible-light range. Our analysis uses the mathematically grounded approach called the lasing eigenvalue problem (LEP) for the set of the Maxwell equations and the boundary and radiation conditions. As we study the modes exactly at the threshold, there is no need to invoke nonlinear and quantum models of lasing. Instead, we consider a laser as an open plasmonic resonator equipped with an active region. This allows us to assume that at threshold the natural-mode frequency is real-valued, according to the situation where the losses, in the metal and for the radiation, are exactly balanced with the gain in the active region. Then the emission wavelength and the associated threshold gain can be viewed as parts of two-component eigenvalues, each corresponding to a certain mode. In the configuration considered, potentially there are three types of modes that can lase: the hybrid localized surface plasmon (HLSP) modes of the metal tube, the core modes, and the shell modes. The latter two types can be kept off the visible range in thin enough configurations. Keeping this in mind, we focus on the HLSP modes and study how their threshold gain values change with variations in the geometrical parameters of the nanotube, the core, and the shell. It is found that essentially a single-mode laser can be designed on the difference-type HLSP mode of the azimuth order m = 1, shining in the orange or red spectral region. Furthermore, the threshold values of gain for similar HLSP modes of order m = 2 and 3 can be several times lower, with emission in the violet or blue parts of the spectrum.

Electromagnetic analysis of the lasing thresholds of hybrid plasmon modes of a silver tube nanolaser with active core and active shell