Plasmon Modes of Graphene-Disk at Dielectric Interface: Frequencies, Q-Factors, Refractive Index Sensitivities, and Lasing Thresholds

We derive analytical formulas for the natural frequencies, Q-factors, refractive index sensitivities, figures of merit, and lasing thresholds of the plasmon modes of a circular graphene disk lying on the material interface. The complex conductivity of graphene is modeled using the Kubo formulas, and the radiation losses are neglected. Our findings reveal that the frequencies for the nanosize disks are in the infrared, while for the microsize disks they are in the terahertz range. The characteristics of the plasmon modes can be controlled by graphene's chemical potential in a wide range.