  It is evidenced by numerical calculations that optically pumped graphene is
suitable for compensating inherent loss in terahertz (THz) metamaterials. In a
first step, the complex conductivity of graphene under optical pumping is
calculated and the proper conditions for terahertz amplification in single
layer graphene are determined. It is shown that amplification in graphene
occurs for temperatures up to room temperature and for moderate pump
intensities when pumped at a telecommunication wavelength
$\lambda=1.5~\mathrm{\mu m}$. Furthermore, the amplification properties of
graphene are evaluated and discussed at a temperature as low as
$T=77~\mathrm{K}$ and a pump intensity $I=300~\mathrm{mW/mm^2}$ to investigate
the coupling between graphene and a plasmonic split ring resonator (SRR)
metamaterial. The contributions of ohmic and dielectric loss mechanisms are
studied by full wave simulations. As a result, it is found that the loss of a
split-ring resonator metamaterial can be compensated by optically stimulated
amplification in graphene. Moreover, it is shown that a hybrid material
consisting of asymmetric split-ring resonators and optically pumped graphene
can exceed the laser threshold condition and can emit coherent THz radiation at
minimum output power levels of $6 0~\mathrm{nW/mm^2}$. The use of optically
pumped graphene is well suited for loss compensation in THz metamaterials and
paves the way to new kinds of coherent THz sources.
