Frequencies and Thresholds of Transversal Plasmon Modes of the Laser Shaped as a Circular Quantum Wire Wrapped in Graphene Cover

We use the Lasing Eigenvalue Problem (LEP) approach to study the source-free problem of the electromagnetic field in the presence of a circular quantum wire (QW) wrapped in graphene cover. Our instrument is the method of separation of variables and the Kubo formalism for the graphene conductivity. We analyze the lasing conditions for the plasmon modes of such a laser with microsize and nanosize QW diameters. We find eigenvalue pairs, i.e. the frequencies and the threshold values of the QW gain index for several plasmon modes and investigate their dependences on the QW and graphene parameters.