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Terahertz-wave generation using graphene Taiichi Otsuji1,3, Stephane Boubanga Tombet1, Akira Satou1,3, Maxim Ryzhii2,3, and Victor Ryzhii2,3 1

RIEC, Tohoku University, Sendai, 980-8577, Japan CNEL, University of Aizu, Aizu Wakamatsu, 965-8580, Japan 3 JST-CREST, Tokyo, 102-0075, Japan 2

ABSTRACT In this paper recent advances in terahertz-wave generation in graphene are reviewed. First, fundamental basis of the optoelectronic properties of graphene is introduced. Second, nonequilibrium carrier relaxation and recombination dynamics in optically or electrically pumped graphene is described to introduce a possibility of negative dynamic conductivity in a wide terahertz range. Third, recent theoretical advances toward the creation of current-injection graphene terahertz lasers are described. Fourth, unique terahertz dynamics of the twodimensional plasmons in graphene are described. Finally, the advantages of graphene materials and devices for terahertz-wave generation are summarized. INTRODUCTION Graphene, a one-atom-thick planar sheet of sp2-hybridized orbital bonded honeycomb carbon crystal, has attracted considerable attention due to its unique carrier transport and optical properties [1-5]. Figure 1 depicts the energy band structures and dispersion relations for graphene. The conduction band and the valence band of graphene take symmetrical corn shape around the K and K’ points and contact each other at the K and K’ points. Electrons and holes in graphene hold a linear dispersion relation with zero bandgap, resulting in peculiar features like massless relativistic Fermions with back-scattering-free ultrafast transport [2-9] as well as the negative-dynamic conductivity in the terahertz spectral range under optical or electrical pumping [10-12].

Figure 1. Lattice and energy band structures of graphene.

When we consider the nonequilibrium carrier relaxation/recombination dynamics of optically pumped graphene, a very fast energy relaxation of photoexcited electrons/holes via the optical phonon emission and a relatively slow recombination will lead to the population inversion in the wide terahertz range under sufficiently high pumping intensity. This will make it possible to obtain the negative dynamic conductivity or gain in the terahertz spectral range [1012]. The authors recently succeeded in observation of amplified stimulated terahertz emission in exfoliated monolayer graphene and/or heteroepitaxial multilayer graphene pumped by an infrared femtosecond pulse laser at room temperature, testifying to the occurrence of the terahertz negative conductivity [13, 14]. Such an active mechanism can be utilized for creating the graphene-based coherent laser sources of terahertz radiation [12, 15-17]. The authors have first analytically found the possibility of terahertz gain in such systems under a cryogenic condition [9] and have recently numerically verified the occurrence of the terahertz gain even at 300K [18-20]. Optical pumping with rather high photon energy of the order of “~eV” significantly heats the carriers, wh