Abstract

We investigate the nonlinear transmission of a ~280-layer turbostratic graphene sheet for near-infrared amplifier laser pulses (775 nm, Ti:sapphire laser) with a duration of 150-fs and 20-fs. Saturable absorption is observed in both cases, however it is not very strong, amounting to ~13% transmittance change for the 20-fs (150-fs) pulses at a peak intensity of 30 GW/cm2 (4 GW/cm2). The dependence on incident peak intensity is reproduced well using a theoretical model for the time-dependent saturable absorption, where the excited carriers vacate the photo-excited energy range within 3-5 fs, which we attribute to energy redistribution due to carrier-carrier scattering. This is also supported by spectrally resolved measurements for the 20-fs pulses, which show a marked dependence of the degree of saturation on the photon energy. A key result is that the shorter pulses do not yield a lower saturation fluence, due to the combined effects of the broader excitation bandwidth, and the rapid and broad energy redistribution. We also predict the potential performance of multilayer graphene samples for removing pedestal and pre-pulse structure from ultrafast high-energy pulses.

© 2016 Optical Society of America

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2016 (1)

B. Semnani, A. H. Majedi, and S. Safavi-Naeini, “Nonlinear quantum optical properties of graphene,” J. Opt. 18(3), 035402 (2016).

2015 (3)

2014 (1)

F. Meng, M. D. Thomson, and H. G. Roskos, “Relativistic Doppler frequency upconversion of terahertz pulses reflecting from a photoinduced plasma front in silicon,” Phys. Rev. B 90(15), 155207 (2014).

2013 (1)

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4, 1987 (2013).

2012 (2)

C. C. Lee, J. M. Miller, and T. R. Schibli, “Doping-induced changes in the saturable absorption of monolayer graphene,” Appl. Phys. B 108(1), 129–135 (2012).

Z. Zheng, C. Zhao, S. Lu, Y. Chen, Y. Li, H. Zhang, and S. Wen, “Microwave and optical saturable absorption in graphene,” Opt. Express 20(21), 23201–23214 (2012).

2011 (7)

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. X. Shen, Q. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).

M. Amos, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. S. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11(7), 2622–2627 (2011).

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).

P. A. Obraztsov, M. G. Rybin, A. V. Tyurnina, S. V. Garnov, E. D. Obraztsova, A. N. Obraztsov, and Y. P. Svirko, “Broadband light-induced absorbance change in multilayer graphene,” Nano Lett. 11(4), 1540–1545 (2011).

L. G. Cançado, A. Jorio, E. H. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11(8), 3190–3196 (2011).

2010 (4)

G. Xing, H. Guo, X. Zhang, T. C. Sum, and C. H. A. Huan, “The Physics of ultrafast saturable absorption in graphene,” Opt. Express 18(5), 4564–4573 (2010).

M. D. Thomson, V. Blank, and H. G. Roskos, “Terahertz white-light pulses from an air plasma photo-induced by incommensurate two-color optical fields,” Opt. Express 18(22), 23173–23182 (2010).

W. D. Tan, C. Y. Su, R. J. Knize, G. Q. Xie, L. J. Li, and D. Y. Tang, “Mode locking of ceramic Nd:yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96(3), 031106 (2010).

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).

2009 (4)

C. L. Frewin, C. Coletti, C. Riedl, U. Starke, and S. E. Saddow, “A comprehensive study of hydrogen etching on the major SiC polytypes and crystal orientations,” Mater. Sci. Forum 615–617, 589–592 (2009).

M. Breusing, C. Ropers, and T. Elsaesser, “Ultrafast carrier dynamics in graphite,” Phys. Rev. Lett. 102(8), 086809 (2009).

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).

H. G. Yan, D. H. Song, K. F. Mak, I. Chatzakis, J. Maultzsch, and T. F. Heinz, “Time-resolved Raman spectroscopy of optical phonons in graphite: phonon anharmonic coupling and anomalous stiffening,” Phys. Rev. B 80(12), 121403 (2009).

2008 (5)

J. Bredenbeck, A. Ghosh, M. Smits, and M. Bonn, “Ultrafast two dimensional-infrared spectroscopy of a molecular monolayer,” J. Am. Chem. Soc. 130(7), 2152–2153 (2008).

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).

C. Faugeras, A. Nerrière, M. Potemski, A. Mahmood, E. Dujardin, C. Berger, and W. A. de Heer, “Few-layer graphene on SiC, pyrolitic graphite, and graphene: a Raman scattering study,” Appl. Phys. Lett. 92(1), 011914 (2008).

P. A. George, J. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene,” Nano Lett. 8(12), 4248–4251 (2008).

2005 (3)

T. Kampfrath, L. Perfetti, F. Schapper, C. Frischkorn, and M. Wolf, “Strongly coupled optical phonons in the ultrafast dynamics of the electronic energy and current relaxation in graphite,” Phys. Rev. Lett. 95(18), 187403 (2005).

M. P. Kalashnikov, E. Risse, H. Schönnagel, and W. Sandner, “Double chirped-pulse-amplification laser: a way to clean pulses temporally,” Opt. Lett. 30(8), 923–925 (2005).

K.-H. Hong, B. Hou, J. A. Nees, E. Power, and G. A. Mourou, “Generation and measurement of >108 intensity contrast ratio in a relativistic kHz chirped-pulse amplified laser,” Appl. Phys. B 81(4), 447–457 (2005).

2004 (1)

G. Doumy, F. Quéré, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J. C. Gauthier, J.-P. Geindre, and T. Wittmann, “Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 026402 (2004).

1998 (2)

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69(3), 1207–1223 (1998).

J. Itatani, J. Faure, M. Nantel, G. Mourou, and S. Watanabe, “Suppression of the amplified spontaneous emission in chirped-pulse-amplification lasers by clean high-energy seed-pulse injection,” Opt. Commun. 148(1–3), 70–74 (1998).

1997 (1)

1994 (1)

Achete, C. A.

L. G. Cançado, A. Jorio, E. H. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11(8), 3190–3196 (2011).

Amos, M.

M. Amos, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).

Anderson, T.

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).

Audebert, P.

G. Doumy, F. Quéré, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J. C. Gauthier, J.-P. Geindre, and T. Wittmann, “Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 026402 (2004).

Backus, S.

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69(3), 1207–1223 (1998).

Bao, Q.

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. X. Shen, Q. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).

Basko, D. M.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).

Beere, H. E.

Berger, C.

C. Faugeras, A. Nerrière, M. Potemski, A. Mahmood, E. Dujardin, C. Berger, and W. A. de Heer, “Few-layer graphene on SiC, pyrolitic graphite, and graphene: a Raman scattering study,” Appl. Phys. Lett. 92(1), 011914 (2008).

Bezares, F. J.

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).

Bianco, F.

Blake, P.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).

Blank, V.

Bonaccorso, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).

Bonn, M.

J. Bredenbeck, A. Ghosh, M. Smits, and M. Bonn, “Ultrafast two dimensional-infrared spectroscopy of a molecular monolayer,” J. Am. Chem. Soc. 130(7), 2152–2153 (2008).

Booth, T. J.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).

Bredenbeck, J.

J. Bredenbeck, A. Ghosh, M. Smits, and M. Bonn, “Ultrafast two dimensional-infrared spectroscopy of a molecular monolayer,” J. Am. Chem. Soc. 130(7), 2152–2153 (2008).

Breusing, M.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).

M. Breusing, C. Ropers, and T. Elsaesser, “Ultrafast carrier dynamics in graphite,” Phys. Rev. Lett. 102(8), 086809 (2009).

Brida, D.

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4, 1987 (2013).

Caldwell, J. D.

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).

Cançado, L. G.

L. G. Cançado, A. Jorio, E. H. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11(8), 3190–3196 (2011).

Capaz, R. B.

L. G. Cançado, A. Jorio, E. H. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11(8), 3190–3196 (2011).

Castellano, F.

Cerullo, G.

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4, 1987 (2013).

Chandrashekhar, M.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

P. A. George, J. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene,” Nano Lett. 8(12), 4248–4251 (2008).

Chatzakis, I.

H. G. Yan, D. H. Song, K. F. Mak, I. Chatzakis, J. Maultzsch, and T. F. Heinz, “Time-resolved Raman spectroscopy of optical phonons in graphite: phonon anharmonic coupling and anomalous stiffening,” Phys. Rev. B 80(12), 121403 (2009).

Chen, W.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. S. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11(7), 2622–2627 (2011).

Chen, Y.

Z. Zheng, C. Zhao, S. Lu, Y. Chen, Y. Li, H. Zhang, and S. Wen, “Microwave and optical saturable absorption in graphene,” Opt. Express 20(21), 23201–23214 (2012).

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

Chun, H.

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).

Coletti, C.

F. Bianco, V. Miseikis, D. Convertino, J.-H. Xu, F. Castellano, H. E. Beere, D. A. Ritchie, M. S. Vitiello, A. Tredicucci, and C. Coletti, “THz saturable absorption in turbostratic multilayer graphene on silicon carbide,” Opt. Express 23(9), 11632–11640 (2015).

C. L. Frewin, C. Coletti, C. Riedl, U. Starke, and S. E. Saddow, “A comprehensive study of hydrogen etching on the major SiC polytypes and crystal orientations,” Mater. Sci. Forum 615–617, 589–592 (2009).

Convertino, D.

Currie, M.

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).

Dawlaty, J.

P. A. George, J. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene,” Nano Lett. 8(12), 4248–4251 (2008).

Dawlaty, J. M.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

de Heer, W. A.

C. Faugeras, A. Nerrière, M. Potemski, A. Mahmood, E. Dujardin, C. Berger, and W. A. de Heer, “Few-layer graphene on SiC, pyrolitic graphite, and graphene: a Raman scattering study,” Appl. Phys. Lett. 92(1), 011914 (2008).

De Silvestri, S.

Doumy, G.

G. Doumy, F. Quéré, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J. C. Gauthier, J.-P. Geindre, and T. Wittmann, “Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 026402 (2004).

Dujardin, E.

C. Faugeras, A. Nerrière, M. Potemski, A. Mahmood, E. Dujardin, C. Berger, and W. A. de Heer, “Few-layer graphene on SiC, pyrolitic graphite, and graphene: a Raman scattering study,” Appl. Phys. Lett. 92(1), 011914 (2008).

Durfee, C. G.

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69(3), 1207–1223 (1998).

Elsaesser, T.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).

M. Breusing, C. Ropers, and T. Elsaesser, “Ultrafast carrier dynamics in graphite,” Phys. Rev. Lett. 102(8), 086809 (2009).

Fan, D. Y.

Faugeras, C.

C. Faugeras, A. Nerrière, M. Potemski, A. Mahmood, E. Dujardin, C. Berger, and W. A. de Heer, “Few-layer graphene on SiC, pyrolitic graphite, and graphene: a Raman scattering study,” Appl. Phys. Lett. 92(1), 011914 (2008).

Faure, J.

J. Itatani, J. Faure, M. Nantel, G. Mourou, and S. Watanabe, “Suppression of the amplified spontaneous emission in chirped-pulse-amplification lasers by clean high-energy seed-pulse injection,” Opt. Commun. 148(1–3), 70–74 (1998).

Feng, X.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. S. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11(7), 2622–2627 (2011).

Ferencz, K.

Ferrari, A. C.

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4, 1987 (2013).

L. G. Cançado, A. Jorio, E. H. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11(8), 3190–3196 (2011).

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).

Ferreira, E. H.

L. G. Cançado, A. Jorio, E. H. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11(8), 3190–3196 (2011).

Frewin, C. L.

C. L. Frewin, C. Coletti, C. Riedl, U. Starke, and S. E. Saddow, “A comprehensive study of hydrogen etching on the major SiC polytypes and crystal orientations,” Mater. Sci. Forum 615–617, 589–592 (2009).

Frischkorn, C.

T. Kampfrath, L. Perfetti, F. Schapper, C. Frischkorn, and M. Wolf, “Strongly coupled optical phonons in the ultrafast dynamics of the electronic energy and current relaxation in graphite,” Phys. Rev. Lett. 95(18), 187403 (2005).

Fuse, K.

M. Amos, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).

Garnov, S. V.

P. A. Obraztsov, M. G. Rybin, A. V. Tyurnina, S. V. Garnov, E. D. Obraztsova, A. N. Obraztsov, and Y. P. Svirko, “Broadband light-induced absorbance change in multilayer graphene,” Nano Lett. 11(4), 1540–1545 (2011).

Gauthier, J. C.

G. Doumy, F. Quéré, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J. C. Gauthier, J.-P. Geindre, and T. Wittmann, “Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 026402 (2004).

Geim, A. K.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).

Geindre, J.-P.

G. Doumy, F. Quéré, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J. C. Gauthier, J.-P. Geindre, and T. Wittmann, “Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 026402 (2004).

George, P.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

George, P. A.

P. A. George, J. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene,” Nano Lett. 8(12), 4248–4251 (2008).

Ghosh, A.

J. Bredenbeck, A. Ghosh, M. Smits, and M. Bonn, “Ultrafast two dimensional-infrared spectroscopy of a molecular monolayer,” J. Am. Chem. Soc. 130(7), 2152–2153 (2008).

Gobert, O.

G. Doumy, F. Quéré, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J. C. Gauthier, J.-P. Geindre, and T. Wittmann, “Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 026402 (2004).

Gold, D. M.

Grigorenko, A. N.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).

Guo, H.

Guo, Z. N.

Han, S.

F. Zhang, S. Han, Y. Liu, Z. Wang, and X. Xu, “Dependence of the saturable absorption of graphene upon excitation photon energy,” Appl. Phys. Lett. 106(9), 091102 (2015).

Hasan, T.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).

Heinz, T. F.

H. G. Yan, D. H. Song, K. F. Mak, I. Chatzakis, J. Maultzsch, and T. F. Heinz, “Time-resolved Raman spectroscopy of optical phonons in graphite: phonon anharmonic coupling and anomalous stiffening,” Phys. Rev. B 80(12), 121403 (2009).

Hong, K.-H.

K.-H. Hong, B. Hou, J. A. Nees, E. Power, and G. A. Mourou, “Generation and measurement of >108 intensity contrast ratio in a relativistic kHz chirped-pulse amplified laser,” Appl. Phys. B 81(4), 447–457 (2005).

Hou, B.

K.-H. Hong, B. Hou, J. A. Nees, E. Power, and G. A. Mourou, “Generation and measurement of >108 intensity contrast ratio in a relativistic kHz chirped-pulse amplified laser,” Appl. Phys. B 81(4), 447–457 (2005).

Huan, C. H. A.

Huang, H.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. S. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11(7), 2622–2627 (2011).

Itatani, J.

J. Itatani, J. Faure, M. Nantel, G. Mourou, and S. Watanabe, “Suppression of the amplified spontaneous emission in chirped-pulse-amplification lasers by clean high-energy seed-pulse injection,” Opt. Commun. 148(1–3), 70–74 (1998).

Ji, W.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. S. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11(7), 2622–2627 (2011).

Jorio, A.

L. G. Cançado, A. Jorio, E. H. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11(8), 3190–3196 (2011).

Kalashnikov, M. P.

Kampfrath, T.

T. Kampfrath, L. Perfetti, F. Schapper, C. Frischkorn, and M. Wolf, “Strongly coupled optical phonons in the ultrafast dynamics of the electronic energy and current relaxation in graphite,” Phys. Rev. Lett. 95(18), 187403 (2005).

Kapteyn, H. C.

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69(3), 1207–1223 (1998).

Kim, Y. J.

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4, 1987 (2013).

Knize, R. J.

W. D. Tan, C. Y. Su, R. J. Knize, G. Q. Xie, L. J. Li, and D. Y. Tang, “Mode locking of ceramic Nd:yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96(3), 031106 (2010).

Knorr, A.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).

Krausz, F.

Kuehn, S.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).

Kulmala, T. S.

L. G. Cançado, A. Jorio, E. H. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11(8), 3190–3196 (2011).

Lee, C. C.

C. C. Lee, J. M. Miller, and T. R. Schibli, “Doping-induced changes in the saturable absorption of monolayer graphene,” Appl. Phys. B 108(1), 129–135 (2012).

Li, L. J.

W. D. Tan, C. Y. Su, R. J. Knize, G. Q. Xie, L. J. Li, and D. Y. Tang, “Mode locking of ceramic Nd:yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96(3), 031106 (2010).

Li, Y.

Liu, Y.

F. Zhang, S. Han, Y. Liu, Z. Wang, and X. Xu, “Dependence of the saturable absorption of graphene upon excitation photon energy,” Appl. Phys. Lett. 106(9), 091102 (2015).

Loh, K. P.

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. X. Shen, Q. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).

Lombardo, A.

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4, 1987 (2013).

L. G. Cançado, A. Jorio, E. H. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11(8), 3190–3196 (2011).

Lu, S.

Lu, S. B.

Mahmood, A.

C. Faugeras, A. Nerrière, M. Potemski, A. Mahmood, E. Dujardin, C. Berger, and W. A. de Heer, “Few-layer graphene on SiC, pyrolitic graphite, and graphene: a Raman scattering study,” Appl. Phys. Lett. 92(1), 011914 (2008).

Majedi, A. H.

B. Semnani, A. H. Majedi, and S. Safavi-Naeini, “Nonlinear quantum optical properties of graphene,” J. Opt. 18(3), 035402 (2016).

Mak, K. F.

H. G. Yan, D. H. Song, K. F. Mak, I. Chatzakis, J. Maultzsch, and T. F. Heinz, “Time-resolved Raman spectroscopy of optical phonons in graphite: phonon anharmonic coupling and anomalous stiffening,” Phys. Rev. B 80(12), 121403 (2009).

Malic, E.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).

Manzoni, C.

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4, 1987 (2013).

Martin, P.

G. Doumy, F. Quéré, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J. C. Gauthier, J.-P. Geindre, and T. Wittmann, “Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 026402 (2004).

Maultzsch, J.

H. G. Yan, D. H. Song, K. F. Mak, I. Chatzakis, J. Maultzsch, and T. F. Heinz, “Time-resolved Raman spectroscopy of optical phonons in graphite: phonon anharmonic coupling and anomalous stiffening,” Phys. Rev. B 80(12), 121403 (2009).

Meng, F.

F. Meng, M. D. Thomson, and H. G. Roskos, “Relativistic Doppler frequency upconversion of terahertz pulses reflecting from a photoinduced plasma front in silicon,” Phys. Rev. B 90(15), 155207 (2014).

Miao, L. L.

Milana, S.

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4, 1987 (2013).

Milde, F.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).

Miller, J. M.

C. C. Lee, J. M. Miller, and T. R. Schibli, “Doping-induced changes in the saturable absorption of monolayer graphene,” Appl. Phys. B 108(1), 129–135 (2012).

Miseikis, V.

Mourou, G.

J. Itatani, J. Faure, M. Nantel, G. Mourou, and S. Watanabe, “Suppression of the amplified spontaneous emission in chirped-pulse-amplification lasers by clean high-energy seed-pulse injection,” Opt. Commun. 148(1–3), 70–74 (1998).

Mourou, G. A.

K.-H. Hong, B. Hou, J. A. Nees, E. Power, and G. A. Mourou, “Generation and measurement of >108 intensity contrast ratio in a relativistic kHz chirped-pulse amplified laser,” Appl. Phys. B 81(4), 447–457 (2005).

Moutinho, M. V. O.

L. G. Cançado, A. Jorio, E. H. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11(8), 3190–3196 (2011).

Murnane, M. M.

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69(3), 1207–1223 (1998).

Nair, R. R.

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4, 1987 (2013).

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).

Nantel, M.

J. Itatani, J. Faure, M. Nantel, G. Mourou, and S. Watanabe, “Suppression of the amplified spontaneous emission in chirped-pulse-amplification lasers by clean high-energy seed-pulse injection,” Opt. Commun. 148(1–3), 70–74 (1998).

Nees, J. A.

K.-H. Hong, B. Hou, J. A. Nees, E. Power, and G. A. Mourou, “Generation and measurement of >108 intensity contrast ratio in a relativistic kHz chirped-pulse amplified laser,” Appl. Phys. B 81(4), 447–457 (2005).

Nerrière, A.

C. Faugeras, A. Nerrière, M. Potemski, A. Mahmood, E. Dujardin, C. Berger, and W. A. de Heer, “Few-layer graphene on SiC, pyrolitic graphite, and graphene: a Raman scattering study,” Appl. Phys. Lett. 92(1), 011914 (2008).

Ni, Z.

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. X. Shen, Q. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).

Nisoli, M.

Novoselov, K. S.

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4, 1987 (2013).

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).

Obraztsov, A. N.

P. A. Obraztsov, M. G. Rybin, A. V. Tyurnina, S. V. Garnov, E. D. Obraztsova, A. N. Obraztsov, and Y. P. Svirko, “Broadband light-induced absorbance change in multilayer graphene,” Nano Lett. 11(4), 1540–1545 (2011).

Obraztsov, P. A.

P. A. Obraztsov, M. G. Rybin, A. V. Tyurnina, S. V. Garnov, E. D. Obraztsova, A. N. Obraztsov, and Y. P. Svirko, “Broadband light-induced absorbance change in multilayer graphene,” Nano Lett. 11(4), 1540–1545 (2011).

Obraztsova, E. D.

P. A. Obraztsov, M. G. Rybin, A. V. Tyurnina, S. V. Garnov, E. D. Obraztsova, A. N. Obraztsov, and Y. P. Svirko, “Broadband light-induced absorbance change in multilayer graphene,” Nano Lett. 11(4), 1540–1545 (2011).

Perdrix, M.

G. Doumy, F. Quéré, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J. C. Gauthier, J.-P. Geindre, and T. Wittmann, “Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 026402 (2004).

Peres, N. M. R.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).

Perfetti, L.

T. Kampfrath, L. Perfetti, F. Schapper, C. Frischkorn, and M. Wolf, “Strongly coupled optical phonons in the ultrafast dynamics of the electronic energy and current relaxation in graphite,” Phys. Rev. Lett. 95(18), 187403 (2005).

Polavarapu, L.

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. X. Shen, Q. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).

Polini, M.

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4, 1987 (2013).

Popa, D.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).

Potemski, M.

C. Faugeras, A. Nerrière, M. Potemski, A. Mahmood, E. Dujardin, C. Berger, and W. A. de Heer, “Few-layer graphene on SiC, pyrolitic graphite, and graphene: a Raman scattering study,” Appl. Phys. Lett. 92(1), 011914 (2008).

Power, E.

K.-H. Hong, B. Hou, J. A. Nees, E. Power, and G. A. Mourou, “Generation and measurement of >108 intensity contrast ratio in a relativistic kHz chirped-pulse amplified laser,” Appl. Phys. B 81(4), 447–457 (2005).

Privitera, G.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).

Qi, X.

Quéré, F.

G. Doumy, F. Quéré, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J. C. Gauthier, J.-P. Geindre, and T. Wittmann, “Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 026402 (2004).

Rabe, J. P.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).

Rana, F.

P. A. George, J. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene,” Nano Lett. 8(12), 4248–4251 (2008).

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

Riedl, C.

C. L. Frewin, C. Coletti, C. Riedl, U. Starke, and S. E. Saddow, “A comprehensive study of hydrogen etching on the major SiC polytypes and crystal orientations,” Mater. Sci. Forum 615–617, 589–592 (2009).

Risse, E.

Ritchie, D. A.

Robinson, J.

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).

Ropers, C.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).

M. Breusing, C. Ropers, and T. Elsaesser, “Ultrafast carrier dynamics in graphite,” Phys. Rev. Lett. 102(8), 086809 (2009).

Roskos, H. G.

F. Meng, M. D. Thomson, and H. G. Roskos, “Relativistic Doppler frequency upconversion of terahertz pulses reflecting from a photoinduced plasma front in silicon,” Phys. Rev. B 90(15), 155207 (2014).

M. D. Thomson, V. Blank, and H. G. Roskos, “Terahertz white-light pulses from an air plasma photo-induced by incommensurate two-color optical fields,” Opt. Express 18(22), 23173–23182 (2010).

Rybin, M. G.

P. A. Obraztsov, M. G. Rybin, A. V. Tyurnina, S. V. Garnov, E. D. Obraztsova, A. N. Obraztsov, and Y. P. Svirko, “Broadband light-induced absorbance change in multilayer graphene,” Nano Lett. 11(4), 1540–1545 (2011).

Saddow, S. E.

C. L. Frewin, C. Coletti, C. Riedl, U. Starke, and S. E. Saddow, “A comprehensive study of hydrogen etching on the major SiC polytypes and crystal orientations,” Mater. Sci. Forum 615–617, 589–592 (2009).

Safavi-Naeini, S.

B. Semnani, A. H. Majedi, and S. Safavi-Naeini, “Nonlinear quantum optical properties of graphene,” J. Opt. 18(3), 035402 (2016).

Sandner, W.

Sartania, S.

Schapper, F.

T. Kampfrath, L. Perfetti, F. Schapper, C. Frischkorn, and M. Wolf, “Strongly coupled optical phonons in the ultrafast dynamics of the electronic energy and current relaxation in graphite,” Phys. Rev. Lett. 95(18), 187403 (2005).

Schibli, T. R.

C. C. Lee, J. M. Miller, and T. R. Schibli, “Doping-induced changes in the saturable absorption of monolayer graphene,” Appl. Phys. B 108(1), 129–135 (2012).

Schönnagel, H.

Semnani, B.

B. Semnani, A. H. Majedi, and S. Safavi-Naeini, “Nonlinear quantum optical properties of graphene,” J. Opt. 18(3), 035402 (2016).

Severin, N.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).

Shen, Z. X.

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. X. Shen, Q. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).

Shivaraman, S.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

P. A. George, J. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene,” Nano Lett. 8(12), 4248–4251 (2008).

Smits, M.

J. Bredenbeck, A. Ghosh, M. Smits, and M. Bonn, “Ultrafast two dimensional-infrared spectroscopy of a molecular monolayer,” J. Am. Chem. Soc. 130(7), 2152–2153 (2008).

Song, D. H.

H. G. Yan, D. H. Song, K. F. Mak, I. Chatzakis, J. Maultzsch, and T. F. Heinz, “Time-resolved Raman spectroscopy of optical phonons in graphite: phonon anharmonic coupling and anomalous stiffening,” Phys. Rev. B 80(12), 121403 (2009).

Spencer, M. G.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

P. A. George, J. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene,” Nano Lett. 8(12), 4248–4251 (2008).

Spielmann, Ch.

Starke, U.

C. L. Frewin, C. Coletti, C. Riedl, U. Starke, and S. E. Saddow, “A comprehensive study of hydrogen etching on the major SiC polytypes and crystal orientations,” Mater. Sci. Forum 615–617, 589–592 (2009).

Stauber, T.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).

Stavale, F.

L. G. Cançado, A. Jorio, E. H. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11(8), 3190–3196 (2011).

Strait, J.

P. A. George, J. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene,” Nano Lett. 8(12), 4248–4251 (2008).

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

Su, C. Y.

W. D. Tan, C. Y. Su, R. J. Knize, G. Q. Xie, L. J. Li, and D. Y. Tang, “Mode locking of ceramic Nd:yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96(3), 031106 (2010).

Sum, T. C.

Sun, Z.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).

Svelto, O.

Svirko, Y. P.

P. A. Obraztsov, M. G. Rybin, A. V. Tyurnina, S. V. Garnov, E. D. Obraztsova, A. N. Obraztsov, and Y. P. Svirko, “Broadband light-induced absorbance change in multilayer graphene,” Nano Lett. 11(4), 1540–1545 (2011).

Szipocs, R.

Tadjer, M.

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).

Tan, W. D.

W. D. Tan, C. Y. Su, R. J. Knize, G. Q. Xie, L. J. Li, and D. Y. Tang, “Mode locking of ceramic Nd:yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96(3), 031106 (2010).

Tang, D. Y.

S. B. Lu, L. L. Miao, Z. N. Guo, X. Qi, C. J. Zhao, H. Zhang, S. C. Wen, D. Y. Tang, and D. Y. Fan, “Broadband nonlinear optical response in multi-layer black phosphorus: an emerging infrared and mid-infrared optical material,” Opt. Express 23(9), 11183–11194 (2015).

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. X. Shen, Q. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).

W. D. Tan, C. Y. Su, R. J. Knize, G. Q. Xie, L. J. Li, and D. Y. Tang, “Mode locking of ceramic Nd:yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96(3), 031106 (2010).

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).

Thomson, M. D.

F. Meng, M. D. Thomson, and H. G. Roskos, “Relativistic Doppler frequency upconversion of terahertz pulses reflecting from a photoinduced plasma front in silicon,” Phys. Rev. B 90(15), 155207 (2014).

M. D. Thomson, V. Blank, and H. G. Roskos, “Terahertz white-light pulses from an air plasma photo-induced by incommensurate two-color optical fields,” Opt. Express 18(22), 23173–23182 (2010).

Tomadin, A.

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4, 1987 (2013).

Torrisi, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).

Tredicucci, A.

Tyurnina, A. V.

P. A. Obraztsov, M. G. Rybin, A. V. Tyurnina, S. V. Garnov, E. D. Obraztsova, A. N. Obraztsov, and Y. P. Svirko, “Broadband light-induced absorbance change in multilayer graphene,” Nano Lett. 11(4), 1540–1545 (2011).

Veksler, D.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

Vitiello, M. S.

Wang, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).

Wang, Q.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. S. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11(7), 2622–2627 (2011).

Wang, Y.

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. X. Shen, Q. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).

Wang, Z.

F. Zhang, S. Han, Y. Liu, Z. Wang, and X. Xu, “Dependence of the saturable absorption of graphene upon excitation photon energy,” Appl. Phys. Lett. 106(9), 091102 (2015).

Watanabe, S.

J. Itatani, J. Faure, M. Nantel, G. Mourou, and S. Watanabe, “Suppression of the amplified spontaneous emission in chirped-pulse-amplification lasers by clean high-energy seed-pulse injection,” Opt. Commun. 148(1–3), 70–74 (1998).

Wee, A. T. S.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. S. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11(7), 2622–2627 (2011).

Wen, S.

Wen, S. C.

Winzer, T.

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).

Wittmann, T.

G. Doumy, F. Quéré, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J. C. Gauthier, J.-P. Geindre, and T. Wittmann, “Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 026402 (2004).

Wolf, M.

T. Kampfrath, L. Perfetti, F. Schapper, C. Frischkorn, and M. Wolf, “Strongly coupled optical phonons in the ultrafast dynamics of the electronic energy and current relaxation in graphite,” Phys. Rev. Lett. 95(18), 187403 (2005).

Xie, G. Q.

W. D. Tan, C. Y. Su, R. J. Knize, G. Q. Xie, L. J. Li, and D. Y. Tang, “Mode locking of ceramic Nd:yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96(3), 031106 (2010).

Xing, G.

Xu, J.-H.

Xu, Q.

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. X. Shen, Q. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).

Xu, X.

F. Zhang, S. Han, Y. Liu, Z. Wang, and X. Xu, “Dependence of the saturable absorption of graphene upon excitation photon energy,” Appl. Phys. Lett. 106(9), 091102 (2015).

Yamashita, S.

M. Amos, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).

Yan, H. G.

H. G. Yan, D. H. Song, K. F. Mak, I. Chatzakis, J. Maultzsch, and T. F. Heinz, “Time-resolved Raman spectroscopy of optical phonons in graphite: phonon anharmonic coupling and anomalous stiffening,” Phys. Rev. B 80(12), 121403 (2009).

Yan, Y.

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).

Yang, H.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. S. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11(7), 2622–2627 (2011).

Zhang, F.

F. Zhang, S. Han, Y. Liu, Z. Wang, and X. Xu, “Dependence of the saturable absorption of graphene upon excitation photon energy,” Appl. Phys. Lett. 106(9), 091102 (2015).

Zhang, H.

S. B. Lu, L. L. Miao, Z. N. Guo, X. Qi, C. J. Zhao, H. Zhang, S. C. Wen, D. Y. Tang, and D. Y. Fan, “Broadband nonlinear optical response in multi-layer black phosphorus: an emerging infrared and mid-infrared optical material,” Opt. Express 23(9), 11183–11194 (2015).

Z. Zheng, C. Zhao, S. Lu, Y. Chen, Y. Li, H. Zhang, and S. Wen, “Microwave and optical saturable absorption in graphene,” Opt. Express 20(21), 23201–23214 (2012).

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. X. Shen, Q. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).

Zhang, X.

Zhao, C.

Zhao, C. J.

Zheng, Z.

ACS Nano (1)

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).

Adv. Funct. Mater. (1)

Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, and D. Y. Tang, “Atomic-layer graphene as a saturable absorber for ultrafast pulsed lasers,” Adv. Funct. Mater. 19(19), 3077–3083 (2009).

Appl. Phys. B (2)

C. C. Lee, J. M. Miller, and T. R. Schibli, “Doping-induced changes in the saturable absorption of monolayer graphene,” Appl. Phys. B 108(1), 129–135 (2012).

K.-H. Hong, B. Hou, J. A. Nees, E. Power, and G. A. Mourou, “Generation and measurement of >108 intensity contrast ratio in a relativistic kHz chirped-pulse amplified laser,” Appl. Phys. B 81(4), 447–457 (2005).

Appl. Phys. Lett. (6)

M. Amos, K. Fuse, and S. Yamashita, “Mechanical exfoliation of graphene for the passive mode-locking of fiber lasers,” Appl. Phys. Lett. 99(12), 121107 (2011).

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).

F. Zhang, S. Han, Y. Liu, Z. Wang, and X. Xu, “Dependence of the saturable absorption of graphene upon excitation photon energy,” Appl. Phys. Lett. 106(9), 091102 (2015).

M. Currie, J. D. Caldwell, F. J. Bezares, J. Robinson, T. Anderson, H. Chun, and M. Tadjer, “Quantifying pulsed laser induced damage to graphene,” Appl. Phys. Lett. 99(21), 211909 (2011).

W. D. Tan, C. Y. Su, R. J. Knize, G. Q. Xie, L. J. Li, and D. Y. Tang, “Mode locking of ceramic Nd:yttrium aluminum garnet with graphene as a saturable absorber,” Appl. Phys. Lett. 96(3), 031106 (2010).

C. Faugeras, A. Nerrière, M. Potemski, A. Mahmood, E. Dujardin, C. Berger, and W. A. de Heer, “Few-layer graphene on SiC, pyrolitic graphite, and graphene: a Raman scattering study,” Appl. Phys. Lett. 92(1), 011914 (2008).

J. Am. Chem. Soc. (1)

J. Bredenbeck, A. Ghosh, M. Smits, and M. Bonn, “Ultrafast two dimensional-infrared spectroscopy of a molecular monolayer,” J. Am. Chem. Soc. 130(7), 2152–2153 (2008).

J. Opt. (1)

B. Semnani, A. H. Majedi, and S. Safavi-Naeini, “Nonlinear quantum optical properties of graphene,” J. Opt. 18(3), 035402 (2016).

Mater. Sci. Forum (1)

C. L. Frewin, C. Coletti, C. Riedl, U. Starke, and S. E. Saddow, “A comprehensive study of hydrogen etching on the major SiC polytypes and crystal orientations,” Mater. Sci. Forum 615–617, 589–592 (2009).

Nano Lett. (4)

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. S. Wee, and W. Ji, “Giant two-photon absorption in bilayer graphene,” Nano Lett. 11(7), 2622–2627 (2011).

P. A. Obraztsov, M. G. Rybin, A. V. Tyurnina, S. V. Garnov, E. D. Obraztsova, A. N. Obraztsov, and Y. P. Svirko, “Broadband light-induced absorbance change in multilayer graphene,” Nano Lett. 11(4), 1540–1545 (2011).

L. G. Cançado, A. Jorio, E. H. Ferreira, F. Stavale, C. A. Achete, R. B. Capaz, M. V. O. Moutinho, A. Lombardo, T. S. Kulmala, and A. C. Ferrari, “Quantifying defects in graphene via Raman spectroscopy at different excitation energies,” Nano Lett. 11(8), 3190–3196 (2011).

P. A. George, J. Strait, J. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Ultrafast optical-pump terahertz-probe spectroscopy of the carrier relaxation and recombination dynamics in epitaxial graphene,” Nano Lett. 8(12), 4248–4251 (2008).

Nano Res. (1)

Q. Bao, H. Zhang, Z. Ni, Y. Wang, L. Polavarapu, Z. X. Shen, Q. Xu, D. Y. Tang, and K. P. Loh, “Monolayer graphene as a saturable absorber in a mode-locked laser,” Nano Res. 4(3), 297–307 (2011).

Nat. Commun. (1)

D. Brida, A. Tomadin, C. Manzoni, Y. J. Kim, A. Lombardo, S. Milana, R. R. Nair, K. S. Novoselov, A. C. Ferrari, G. Cerullo, and M. Polini, “Ultrafast collinear scattering and carrier multiplication in graphene,” Nat. Commun. 4, 1987 (2013).

Opt. Commun. (1)

J. Itatani, J. Faure, M. Nantel, G. Mourou, and S. Watanabe, “Suppression of the amplified spontaneous emission in chirped-pulse-amplification lasers by clean high-energy seed-pulse injection,” Opt. Commun. 148(1–3), 70–74 (1998).

Opt. Express (5)

Opt. Lett. (3)

Phys. Rev. B (3)

F. Meng, M. D. Thomson, and H. G. Roskos, “Relativistic Doppler frequency upconversion of terahertz pulses reflecting from a photoinduced plasma front in silicon,” Phys. Rev. B 90(15), 155207 (2014).

H. G. Yan, D. H. Song, K. F. Mak, I. Chatzakis, J. Maultzsch, and T. F. Heinz, “Time-resolved Raman spectroscopy of optical phonons in graphite: phonon anharmonic coupling and anomalous stiffening,” Phys. Rev. B 80(12), 121403 (2009).

M. Breusing, S. Kuehn, T. Winzer, E. Malić, F. Milde, N. Severin, J. P. Rabe, C. Ropers, A. Knorr, and T. Elsaesser, “Ultrafast nonequilibrium carrier dynamics in a single graphene layer,” Phys. Rev. B 83(15), 153410 (2011).

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

G. Doumy, F. Quéré, O. Gobert, M. Perdrix, P. Martin, P. Audebert, J. C. Gauthier, J.-P. Geindre, and T. Wittmann, “Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(2), 026402 (2004).

Phys. Rev. Lett. (2)

M. Breusing, C. Ropers, and T. Elsaesser, “Ultrafast carrier dynamics in graphite,” Phys. Rev. Lett. 102(8), 086809 (2009).

T. Kampfrath, L. Perfetti, F. Schapper, C. Frischkorn, and M. Wolf, “Strongly coupled optical phonons in the ultrafast dynamics of the electronic energy and current relaxation in graphite,” Phys. Rev. Lett. 95(18), 187403 (2005).

Rev. Sci. Instrum. (1)

S. Backus, C. G. Durfee, M. M. Murnane, and H. C. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69(3), 1207–1223 (1998).

Science (1)

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).

Other (1)

A. Zhidkov, A. Sasaki, T. Utsumi, I. Fukumoto, T. Tajima, F. Saito, Y. Hironaka, K. G. Nakamura, K. Kondo, and M. Yoshida, “Prepulse effects on the interaction of intense femtosecond laser pulses with high-Z solids,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(5 5 Pt B), 7232–7240 (2000).

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Figures (6)

Fig. 1
Fig. 1 Representative Raman spectrum of multilayer graphene on SiC measured at a wavelength of 532 nm. The red solid line is the single Lorentzian fit. The inset shows the transmittance spectrum of the graphene sheet measured by FTIR spectroscopy in the near-infrared.
Fig. 2
Fig. 2 Experimental setup for measuring the saturable absorption of graphene. HWP: half-wave plate, PBS: thin-film polarizing beamsplitter, BS: beamsplitter, M: mirror, MG: multilayer graphene, ND: neutral density filter.
Fig. 3
Fig. 3 Experimental (points) and simulated (curves) saturable absorption for the multilayer graphene sample, for both 150-fs (CPA, circles) and 20-fs (HCF, triangles) pulses. Transmittance as function of (a) peak intensity and (b) corresponding fluence. The simulation is based on a sample with 280 layers and an effective scattering time of τ = 4 fs for the carriers at the initial excitation energy.
Fig. 4
Fig. 4 Schematic depiction of the optical excitation (a) and carrier relaxation (b, c) in graphene, with (b) carrier redistribution due to carrier-carrier scattering during a short time scale after the excitation, and (c) carrier relaxation due to carrier-phonon scattering with carrier accumulation in the bottom (top) of the conduction (valance) band on a longer time scale. Note that, for our situation, we find step (b) to occur effectively already during excitation.
Fig. 5
Fig. 5 (a) Normalized differential transmittance spectra for the 20-fs HCF pulses for different incident intensities, as indicated in the legend; the dash-dotted lines are the calculated normalized differential transmittance spectra for excitation intensities of 18, 15, 9 and 4 GW/cm2. (b) Calculated Fermi-Dirac distributions following elastic carrier redistribution in the 1st, 50th, 100th and 200th graphene layer, for an excitation intensity of 15 GW/cm2. (c) Magnified spectral region about the incident HCF intensity spectrum.
Fig. 6
Fig. 6 Time-dependent saturable absorption and pulse shaping effects predicted by simulations for a 100-layer graphene structure and 20-fs optical pulse duration (τ = 4 fs). (a) Temporal transmittance, and (b) corresponding normalized intensity profiles.

Equations (3)

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f ω /2 (t) t = f ω /2 I(ω,t)πα / (ω) D( ω /2 )Δ(ω) + f ω /2 I(ω,t)πα / (ω) D( ω /2 )Δ(ω) f ω /2 τ ,
f ω /2 (t) t = f ω /2 I(ω,t)πα / (ω) D( ω /2 )Δ(ω) + f ω /2 I(ω,t)πα / (ω) D( ω /2 )Δ(ω) + 1 f ω /2 τ ,
T( ω )= n { 1πα[ f n ve ( ω /2 ) f n ce ( ω /2 ) ] }

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