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We show that plasmons in two-dimensional graphene can have net gain atterahertz frequencies. The coupling of the plasmons to interband electron-holetransitions in population inverted graphene layers can lead to plasmonamplification through the process of stimulated emission. We calculate plasmongain for different electron-hole densities and temperatures and show that thegain values can exceed $10^{4}$ cm$^{-1}$ in the 1-10 terahertz frequencyrange, for electron-hole densities in the $10^{9}$-$10^{11}$ cm$^{-2}$ range,even when plasmon energy loss due to intraband scattering is considered.Plasmons are found to exhibit net gain for intraband scattering times shorterthan 100 fs. Such high gain values could allow extremely compact terahertzamplifiers and oscillators that have dimensions in the 1-10 $\mu$m range.

Plasmon Amplification through Stimulated Emission at Terahertz Frequencies in Graphene