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Graphene exhibits excellent ultrafast optical properties due to its unique electronic structure. In this paper we investigate theoretically the ultrafast dynamic optical properties of graphene based on the Bloch-equations, and introduce the theoretical model of graphene. First, we give the energy which has a linear relationship with the wave vector k. The behavior of electrons in the vicinity of the two Dirac points can be described by the massless Dirac-equation, thus we have the Dirac equation of graphene. Second, we discuss the interaction between graphene and light field. The Bloch-equations of graphene are obtained through the Heisenberg equation and then we discuss the photon carriers,electric polarization and optical current change over time by analyzing the Bloch-equations. It is found that the nonequilibrium carriers in graphene induced by a terahertz field can be built in 20-200 fs due to the Pauli blocking and the conservation of energy principle. The photon carrier density will increase with the frequency of enhanced light field. Thus an optical current can be created rapidly within 1 ps. A graphene system responds linearly to the external optical field for 2evFE0tħ, while the graphene systems respond nonlinearly to the external optical field, where E0 and are respectively the intensity and the frequency of the light, t is the time and vF the Dirac velocity in graphene. The electric polarization and optical current increase with increasing photon energies. These theoretical results are in agreement with recent experimental findings and indicate that graphene exhibits important features and has practical applications in the ultrafast optic filed, especially in terahertz field.
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Keywords:
- graphene /
- ultrafast dynamic /
- optical /
- Bloch-equation
[1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
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[28] Breusing M, Kuehn S, Winzer T, Malic E, Milde F, Severin N, Rabe J P, Ropers C, Knorr A, Elsaesser T 2011 Phys. Rev. B 83 153410
[29] Xu W, Dong H M, Li L L, Yao J Q, Vasilopoulos P, Peeters F M 2010 Phys. Rev. B 82 125304
[30] Dong H M, Han K, Xu W 2014 Journal of Applied Physics 115 063503
[31] Dong H M 2013 Acta Phys. Sin. 62 237804 (in Chinese) [董海明 2013 62 237804]
[32] Ang Y S, Chen Q J, Zhang C 2015 Front. Optoelectron. 8 3
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[1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
[2] Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich V V, Morozov S V, Geim A K 2005 Science 102 10451
[3] Geim A K, MacDonald A H 2007 Phys. Today 60 35
[4] Williams J R, Di C L, Marcus C M 2007 Science 317 638
[5] Nomura K, Mac A H 2006 Phys. Rev. Lett. 96 6602
[6] Brink J 2007 Nat. Nanotechnol. 2 199
[7] Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201
[8] Novoselov K S, Jiang Z, Zhang Y, Morozov S V, Stormer H L, Zeitler U, Maan J C, Boebinger G S, Kim P, Geim A K 2007 Science 315 1379
[9] Heersche H B, Jarillo H P, Oostinga J B, Vandersypen L M K, Morpurgo A F 2007 Solid State Commun 143 72
[10] Vozmediano M A H, Lopez-Saneho M P, Stauber T, Guinea F 2005 Phys. Rev. B 72 5121
[11] Dragoman M, Dragoman D, Deligiorgis G, Konstantinidis G, Neculoiu D, Cismaru A, Plana R 2009 J. Appl. Phys. 106 044312
[12] Xia F N, Mueller T, Lin Y M, Valdes-Garcia A, Avouris P 2009 Nat. Nanotechnol. 4 839
[13] Kim K, Choi J Y, Kim T, Cho S H, Chung H J 2011 Nature 479 338
[14] Fang Z Y, Wang Y M, Schlather A E, Liu Z, Ajayan P M, F. Javier Garcia de Abajo, Nordlander P, Zhu X, Halas N J 2014 Nano Lett. 14 299
[15] Fang Z Y, Liu Z, Wang Y M, Ajayan P M, Nordlander P, Halas N J 2012 Nano Letters 12 3808
[16] Fang Z Y, Thongrattanasiri S, Schlather A, Liu Z, Ma L L, Wang Y M, Ajayan P M, Nordlander P, Halas N J, F. v Javier Garc. ade Abajo 2013 ACS Nano 7 2388
[17] Yan B, Yang X X, Fang J Y, Huang Y D, Qin H, Qin S Q 2015 Chin. Phys. B 24 015023
[18] Hendry E, Hale P J, Moger J and Savchenko A K 2010 Phys. Rev. Lett. 105 097401
[19] Bao Q L, Zhang H, Wang Y, Ni Z H, Yan Y L, Shen Z X, Loh K P, Tang D Y 2009 Adv. Funct. Mater. 19 3077
[20] Ruzicka B A, Wang S, Liu J W, Loh K P, Wu J Z, Zhao H 2012 Optics Materials Express 2 708
[21] Dawlaty J M, Shivaraman S, Chandrashekhar M, Rana F, Spencer M G 2008 Applied Physics Letters 92 042116
[22] Liu Z B, Zhao X, Zhang X L, Yan X Q, Wu Y P, Chen Y S, Tian J G 2011 The Journal of Physical Chemistry Letters 2 1972
[23] Xing G H, Guo H C, Zhang X H, Sum T C, Huan C H A 2010 Optics Express 18 4564
[24] Brida D, Manzoni C, Cerullo G, Tomadin A, Polini M, Nair R R, Geim A K, Novoselov K S, Milana S, Lombardo A, Ferrari A C 2012 Conference on Lasers and Electro-Optics San Jose, California United States, May 60-11, 2012 pQTh3H.1
[25] Sun D, Divin C, Mihnev M, Winzer T, Malic E, Knorr A, Sipe J E, Berger C, Heer W A D, First P N, Norris T B 2012 New Journal of Physics 14 105012
[26] Søren Ulstrup, Johannsen J C, Crepaldi A, Cilento F, Zacchigna M, Cacho C, Chapman R T, Springate E, Fromm F, Raidel C, Seyller T, Parmigiani F, Grioni M Hofmann P 2015 J. Phys.: Condensed Matter 27 164206
[27] Liu M, Yin X B, Ulin-Avila E, Geng B S, Zentgraf T, Ju L, Wang F, Zhang X 2011 Nature 474 64
[28] Breusing M, Kuehn S, Winzer T, Malic E, Milde F, Severin N, Rabe J P, Ropers C, Knorr A, Elsaesser T 2011 Phys. Rev. B 83 153410
[29] Xu W, Dong H M, Li L L, Yao J Q, Vasilopoulos P, Peeters F M 2010 Phys. Rev. B 82 125304
[30] Dong H M, Han K, Xu W 2014 Journal of Applied Physics 115 063503
[31] Dong H M 2013 Acta Phys. Sin. 62 237804 (in Chinese) [董海明 2013 62 237804]
[32] Ang Y S, Chen Q J, Zhang C 2015 Front. Optoelectron. 8 3
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