Resonant amplification of surface plasmon polaritons with an electric current in a single-walled carbon nanotube lying on a spatially modulated substrate

We discuss the possibility of using a direct electric current pump in order to amplify a mid-infrared surface plasmon polariton (SPP) in a single-walled carbon nanotube (CNT) deposited on a substrate. Amplification is achieved providing that the phase velocity of the SPP and the drift velocity of the charge carriers in the nanotube are matched. Calculating the amplification characteristics involves numerical simulations that allow to account for the influence of the substrate on the dispersion and inhomogeneity of the plasmon mode field distribution across the CNT. The spectral behaviour of an amplified SPP is shown to exhibit a high sensitivity to variations of the refractive index of the substrate supporting the CNT. We propose a design for the resonant amplification of SPPs with a DC current pump, in which a distributed resonator is obtained with a periodical modulation of the refractive index of the substrate. (paper)