Terahertz light amplification by stimulated emission of radiation in optically pumped graphene
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Terahertz light amplification by stimulated emission of radiation in optically pumped graphene Taiichi Otsuji1,3, Stephane Boubanga Tombet1, Akira Satou1,3, S. Chan2, and Victor Ryzhii1,3 1
RIEC, Tohoku University, Sendai, 980-8577, Japan NSF-PIRE Nano-Japan, University of Pennsylvania, Philadelphia, PA 19104, USA 3 JST-CREST, Tokyo, 102-0075, Japan 2
ABSTRACT 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. INTRODUCTION Graphene is a one-atom-thick planar sheet of a sp2-bonded honeycomb carbon crystal. Its gapless and linear energy spectra of electrons and holes lead to nontrivial features such as giant carrier mobility, ultra-broadband flat optical response, as well as negative dynamic conductivity in the terahertz spectral range [1-7]. The honeycomb symmetry of graphene leads to extremely high optical phonon energy (~198 meV at the zone center Γ and ~163 meV at the zone edges K and K’ for transverse mode) [8, 9]. Carrier-phonon interactions via intravalley, intervalley, intraband, and interband processes take the dominant roll to cool the elevated temperatures of photoelectrons and photoholes, which leads to extraordinary nonequilibrium energy relaxation processes in graphene. When graphene is pumped with an infrared photon energy electrons/holes are photogenerated via interband transitions as shown in figure 1. In case of room temperature environment and/or strong pumping, collective excitations due to the carrier-carrier (CC) scattering, e.g., intraband plasmons perform ultrafast carrier redistribution along the energy [1012]. Then optical phonons (OPs) are emitted by carriers on the high-energy tail of the carrier distributions [10-12]. This energy relaxation process accumulates the nonequilibrium carriers around the Dirac points. Due to a fast intraband relaxation (ps or less) and relatively slow interband recombination of photoelectrons/holes, one can obtain the population inversion under a sufficiently high pumping intensity [6, 7, 13]. The authors have first analytically found the possibility of terahertz gain in such a system under a cryogenic condition [6] and have recently numerically verified the occurrence of the terahertz negative dynamic conductivity even at h
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