Recent advances in terahertz light amplification by stimulated emission of radiation in optically pumped graphene are reviewed. We present, within a picosecond time scale, fast relaxation and relatively slow recombination dynamics of photogenerated electrons and holes in an exfoliated graphene under infrared pulse excitation. We conduct time-domain spectroscopic studies using an optical pump and terahertz probe with an optical probe technique and show that graphene sheet amplifies an incoming terahertz field. The graphene emission spectral dependency on laser pumping intensity shows a threshold-like behavior, testifying to the occurrence of the negative conductivity and the population inversion. The emission spectra clearly narrow at a longer terahertz probe delay time, giving an evidence that the quasi-Fermi energy moves closer to the equilibrium at this longer terahertz probe delay time.
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