Abstract

The ultrafast saturable absorption in graphene is experimentally and theoretically investigated in the femtosecond (fs) time regime. This phenomenon is well-modeled with valence band depletion, conduction band filling and ultrafast intraband carrier thermalization. The latter is dominated by intraband carrier-carrier scattering with a scattering time of 8 ( ± 3) fs, which is far beyond the time resolution of other ultrafast techniques with hundred fs laser pulses. Our results strongly suggest that graphene is an excellent atomic layer saturable absorber.

© 2010 OSA

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    [CrossRef]
  2. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
    [CrossRef]
  3. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
    [CrossRef] [PubMed]
  4. P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nat. Nanotechnol. 2(10), 605–615 (2007).
    [CrossRef]
  5. T. Ando, Y. S. Zheng, and H. Suzuura, “Dynamical Conductivity and Zero-Mode Anomaly in Honeycomb Lattices,” J. Phys. Soc. Jpn. 71(5), 1318–1324 (2002).
    [CrossRef]
  6. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Unusual microwave response of dirac quasiparticles in graphene,” Phys. Rev. Lett. 96(25), 256802 (2006).
    [CrossRef] [PubMed]
  7. T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008).
    [CrossRef]
  8. A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
    [CrossRef] [PubMed]
  9. F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
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  10. 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).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2009

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

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

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband Nonlinear Optical Response of Graphene Dispersions,” Adv. Mater. 21(23), 2430–2435 (2009).
[CrossRef]

Z. Liu, Y. Wang, X. Zhang, Y. Xu, Y. Chen, and J. Tian, “Nonlinear optical properties of graphene oxide in nanosecond and picosecond regimes,” Appl. Phys. Lett. 94(2), 021902 (2009).
[CrossRef]

R. W. Newson, J. Dean, B. Schmidt, and H. M. van Driel, “Ultrafast carrier kinetics in exfoliated graphene and thin graphite films,” Opt. Express 17(4), 2326–2333 (2009).
[CrossRef] [PubMed]

2008

J. Hass, F. Varchon, J. E. Millán-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, “Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene,” Phys. Rev. Lett. 100(12), 125504 (2008).
[CrossRef] [PubMed]

Z. H. Ni, W. Chen, X. F. Fan, J. L. Kuo, T. Yu, A. T. S. Wee, and Z. X. Shen, “Raman spectroscopy of epitaxial graphene on a SiC substrate,” Phys. Rev. B 77(11), 115416 (2008).
[CrossRef]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008).
[CrossRef]

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[CrossRef] [PubMed]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[CrossRef] [PubMed]

J. M. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Measurement of ultrafast carrier dynamics in epitaxial graphene,” Appl. Phys. Lett. 92(4), 042116 (2008).
[CrossRef]

D. Sun, Z. K. Wu, C. Divin, X. Li, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy,” Phys. Rev. Lett. 101(15), 157402 (2008).
[CrossRef] [PubMed]

2007

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nat. Nanotechnol. 2(10), 605–615 (2007).
[CrossRef]

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett. 7(2), 238–242 (2007).
[CrossRef] [PubMed]

2006

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Unusual microwave response of dirac quasiparticles in graphene,” Phys. Rev. Lett. 96(25), 256802 (2006).
[CrossRef] [PubMed]

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[CrossRef] [PubMed]

2002

T. Ando, Y. S. Zheng, and H. Suzuura, “Dynamical Conductivity and Zero-Mode Anomaly in Honeycomb Lattices,” J. Phys. Soc. Jpn. 71(5), 1318–1324 (2002).
[CrossRef]

1999

J. C. Burton, L. Sun, F. H. Long, Z. C. Feng, and I. T. Ferguson, “First- and second-order Raman scattering from semi-insulating 4H-SiC,” Phys. Rev. B 59(11), 7282–7284 (1999).
[CrossRef]

1990

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[CrossRef]

1947

P. R. Wallace, “The band theory of graphite,” Phys. Rev. 71(9), 622–634 (1947).
[CrossRef]

Ando, T.

T. Ando, Y. S. Zheng, and H. Suzuura, “Dynamical Conductivity and Zero-Mode Anomaly in Honeycomb Lattices,” J. Phys. Soc. Jpn. 71(5), 1318–1324 (2002).
[CrossRef]

Avouris, P.

P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nat. Nanotechnol. 2(10), 605–615 (2007).
[CrossRef]

Berger, C.

J. Hass, F. Varchon, J. E. Millán-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, “Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene,” Phys. Rev. Lett. 100(12), 125504 (2008).
[CrossRef] [PubMed]

D. Sun, Z. K. Wu, C. Divin, X. Li, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy,” Phys. Rev. Lett. 101(15), 157402 (2008).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Blau, W. J.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband Nonlinear Optical Response of Graphene Dispersions,” Adv. Mater. 21(23), 2430–2435 (2009).
[CrossRef]

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).
[CrossRef] [PubMed]

Breusing, M.

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

Burton, J. C.

J. C. Burton, L. Sun, F. H. Long, Z. C. Feng, and I. T. Ferguson, “First- and second-order Raman scattering from semi-insulating 4H-SiC,” Phys. Rev. B 59(11), 7282–7284 (1999).
[CrossRef]

Carbone, F.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[CrossRef] [PubMed]

Carbotte, J. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Unusual microwave response of dirac quasiparticles in graphene,” Phys. Rev. Lett. 96(25), 256802 (2006).
[CrossRef] [PubMed]

Casiraghi, C.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[CrossRef] [PubMed]

Castro Neto, A. H.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Chandrashekhar, M.

J. M. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Measurement of ultrafast carrier dynamics in epitaxial graphene,” Appl. Phys. Lett. 92(4), 042116 (2008).
[CrossRef]

Chen, W.

Z. H. Ni, W. Chen, X. F. Fan, J. L. Kuo, T. Yu, A. T. S. Wee, and Z. X. Shen, “Raman spectroscopy of epitaxial graphene on a SiC substrate,” Phys. Rev. B 77(11), 115416 (2008).
[CrossRef]

Chen, Y.

Z. Liu, Y. Wang, X. Zhang, Y. Xu, Y. Chen, and J. Tian, “Nonlinear optical properties of graphene oxide in nanosecond and picosecond regimes,” Appl. Phys. Lett. 94(2), 021902 (2009).
[CrossRef]

Chen, Z.

P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nat. Nanotechnol. 2(10), 605–615 (2007).
[CrossRef]

Coleman, J. N.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband Nonlinear Optical Response of Graphene Dispersions,” Adv. Mater. 21(23), 2430–2435 (2009).
[CrossRef]

Conrad, E. H.

J. Hass, F. Varchon, J. E. Millán-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, “Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene,” Phys. Rev. Lett. 100(12), 125504 (2008).
[CrossRef] [PubMed]

Crommie, M.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

Dawlaty, J. M.

J. M. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Measurement of ultrafast carrier dynamics in epitaxial graphene,” Appl. Phys. Lett. 92(4), 042116 (2008).
[CrossRef]

de Heer, W. A.

D. Sun, Z. K. Wu, C. Divin, X. Li, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy,” Phys. Rev. Lett. 101(15), 157402 (2008).
[CrossRef] [PubMed]

J. Hass, F. Varchon, J. E. Millán-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, “Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene,” Phys. Rev. Lett. 100(12), 125504 (2008).
[CrossRef] [PubMed]

Dean, J.

Divin, C.

D. Sun, Z. K. Wu, C. Divin, X. Li, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy,” Phys. Rev. Lett. 101(15), 157402 (2008).
[CrossRef] [PubMed]

Elsaesser, T.

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

Ensslin, K.

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett. 7(2), 238–242 (2007).
[CrossRef] [PubMed]

Fan, X. F.

Z. H. Ni, W. Chen, X. F. Fan, J. L. Kuo, T. Yu, A. T. S. Wee, and Z. X. Shen, “Raman spectroscopy of epitaxial graphene on a SiC substrate,” Phys. Rev. B 77(11), 115416 (2008).
[CrossRef]

Feng, Z. C.

J. C. Burton, L. Sun, F. H. Long, Z. C. Feng, and I. T. Ferguson, “First- and second-order Raman scattering from semi-insulating 4H-SiC,” Phys. Rev. B 59(11), 7282–7284 (1999).
[CrossRef]

Ferguson, I. T.

J. C. Burton, L. Sun, F. H. Long, Z. C. Feng, and I. T. Ferguson, “First- and second-order Raman scattering from semi-insulating 4H-SiC,” Phys. Rev. B 59(11), 7282–7284 (1999).
[CrossRef]

Ferrari, A. C.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[CrossRef] [PubMed]

First, P. N.

J. Hass, F. Varchon, J. E. Millán-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, “Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene,” Phys. Rev. Lett. 100(12), 125504 (2008).
[CrossRef] [PubMed]

D. Sun, Z. K. Wu, C. Divin, X. Li, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy,” Phys. Rev. Lett. 101(15), 157402 (2008).
[CrossRef] [PubMed]

Geim, A. K.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008).
[CrossRef]

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).
[CrossRef] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[CrossRef] [PubMed]

Girit, C.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

Graf, D.

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett. 7(2), 238–242 (2007).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Guinea, F.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Gusynin, V. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Unusual microwave response of dirac quasiparticles in graphene,” Phys. Rev. Lett. 96(25), 256802 (2006).
[CrossRef] [PubMed]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[CrossRef]

Hass, J.

J. Hass, F. Varchon, J. E. Millán-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, “Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene,” Phys. Rev. Lett. 100(12), 125504 (2008).
[CrossRef] [PubMed]

Heinz, T. F.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[CrossRef] [PubMed]

Hernandez, Y.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband Nonlinear Optical Response of Graphene Dispersions,” Adv. Mater. 21(23), 2430–2435 (2009).
[CrossRef]

Hierold, C.

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett. 7(2), 238–242 (2007).
[CrossRef] [PubMed]

Jiang, D.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[CrossRef] [PubMed]

Jungen, A.

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett. 7(2), 238–242 (2007).
[CrossRef] [PubMed]

Kuo, J. L.

Z. H. Ni, W. Chen, X. F. Fan, J. L. Kuo, T. Yu, A. T. S. Wee, and Z. X. Shen, “Raman spectroscopy of epitaxial graphene on a SiC substrate,” Phys. Rev. B 77(11), 115416 (2008).
[CrossRef]

Kuzmenko, A. B.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[CrossRef] [PubMed]

Lazzeri, M.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[CrossRef] [PubMed]

Li, X.

D. Sun, Z. K. Wu, C. Divin, X. Li, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy,” Phys. Rev. Lett. 101(15), 157402 (2008).
[CrossRef] [PubMed]

Liu, Z.

Z. Liu, Y. Wang, X. Zhang, Y. Xu, Y. Chen, and J. Tian, “Nonlinear optical properties of graphene oxide in nanosecond and picosecond regimes,” Appl. Phys. Lett. 94(2), 021902 (2009).
[CrossRef]

Long, F. H.

J. C. Burton, L. Sun, F. H. Long, Z. C. Feng, and I. T. Ferguson, “First- and second-order Raman scattering from semi-insulating 4H-SiC,” Phys. Rev. B 59(11), 7282–7284 (1999).
[CrossRef]

Lotya, M.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband Nonlinear Optical Response of Graphene Dispersions,” Adv. Mater. 21(23), 2430–2435 (2009).
[CrossRef]

Lui, C. H.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[CrossRef] [PubMed]

Magaud, L.

J. Hass, F. Varchon, J. E. Millán-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, “Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene,” Phys. Rev. Lett. 100(12), 125504 (2008).
[CrossRef] [PubMed]

Mak, K. F.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[CrossRef] [PubMed]

Mauri, F.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[CrossRef] [PubMed]

Meyer, J. C.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[CrossRef] [PubMed]

Millán-Otoya, J. E.

J. Hass, F. Varchon, J. E. Millán-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, “Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene,” Phys. Rev. Lett. 100(12), 125504 (2008).
[CrossRef] [PubMed]

Misewich, J. A.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[CrossRef] [PubMed]

Molitor, F.

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett. 7(2), 238–242 (2007).
[CrossRef] [PubMed]

Nair, R. 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).
[CrossRef] [PubMed]

Newson, R. W.

Ni, Z. H.

Z. H. Ni, W. Chen, X. F. Fan, J. L. Kuo, T. Yu, A. T. S. Wee, and Z. X. Shen, “Raman spectroscopy of epitaxial graphene on a SiC substrate,” Phys. Rev. B 77(11), 115416 (2008).
[CrossRef]

Norris, T. B.

D. Sun, Z. K. Wu, C. Divin, X. Li, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy,” Phys. Rev. Lett. 101(15), 157402 (2008).
[CrossRef] [PubMed]

Novoselov, K. S.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

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).
[CrossRef] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[CrossRef] [PubMed]

Perebeinos, V.

P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nat. Nanotechnol. 2(10), 605–615 (2007).
[CrossRef]

Peres, N. M. R.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

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).
[CrossRef] [PubMed]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008).
[CrossRef]

Piscanec, S.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[CrossRef] [PubMed]

Rana, F.

J. M. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Measurement of ultrafast carrier dynamics in epitaxial graphene,” Appl. Phys. Lett. 92(4), 042116 (2008).
[CrossRef]

Ropers, C.

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

Roth, S.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[CrossRef] [PubMed]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[CrossRef]

Scardaci, V.

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[CrossRef] [PubMed]

Schmidt, B.

Sfeir, M. Y.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[CrossRef] [PubMed]

Sharapov, S. G.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Unusual microwave response of dirac quasiparticles in graphene,” Phys. Rev. Lett. 96(25), 256802 (2006).
[CrossRef] [PubMed]

Sharma, N.

J. Hass, F. Varchon, J. E. Millán-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, “Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene,” Phys. Rev. Lett. 100(12), 125504 (2008).
[CrossRef] [PubMed]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[CrossRef]

Shen, Y. R.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

Shen, Z. X.

Z. H. Ni, W. Chen, X. F. Fan, J. L. Kuo, T. Yu, A. T. S. Wee, and Z. X. Shen, “Raman spectroscopy of epitaxial graphene on a SiC substrate,” Phys. Rev. B 77(11), 115416 (2008).
[CrossRef]

Shivaraman, S.

J. M. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Measurement of ultrafast carrier dynamics in epitaxial graphene,” Appl. Phys. Lett. 92(4), 042116 (2008).
[CrossRef]

Spencer, M. G.

J. M. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Measurement of ultrafast carrier dynamics in epitaxial graphene,” Appl. Phys. Lett. 92(4), 042116 (2008).
[CrossRef]

Sprinkle, M.

J. Hass, F. Varchon, J. E. Millán-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, “Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene,” Phys. Rev. Lett. 100(12), 125504 (2008).
[CrossRef] [PubMed]

Stampfer, C.

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett. 7(2), 238–242 (2007).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008).
[CrossRef]

Sun, D.

D. Sun, Z. K. Wu, C. Divin, X. Li, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy,” Phys. Rev. Lett. 101(15), 157402 (2008).
[CrossRef] [PubMed]

Sun, L.

J. C. Burton, L. Sun, F. H. Long, Z. C. Feng, and I. T. Ferguson, “First- and second-order Raman scattering from semi-insulating 4H-SiC,” Phys. Rev. B 59(11), 7282–7284 (1999).
[CrossRef]

Suzuura, H.

T. Ando, Y. S. Zheng, and H. Suzuura, “Dynamical Conductivity and Zero-Mode Anomaly in Honeycomb Lattices,” J. Phys. Soc. Jpn. 71(5), 1318–1324 (2002).
[CrossRef]

Tian, C.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

Tian, J.

Z. Liu, Y. Wang, X. Zhang, Y. Xu, Y. Chen, and J. Tian, “Nonlinear optical properties of graphene oxide in nanosecond and picosecond regimes,” Appl. Phys. Lett. 94(2), 021902 (2009).
[CrossRef]

van der Marel, D.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[CrossRef] [PubMed]

van Driel, H. M.

van Heumen, E.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[CrossRef] [PubMed]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[CrossRef]

Varchon, F.

J. Hass, F. Varchon, J. E. Millán-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, “Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene,” Phys. Rev. Lett. 100(12), 125504 (2008).
[CrossRef] [PubMed]

Wallace, P. R.

P. R. Wallace, “The band theory of graphite,” Phys. Rev. 71(9), 622–634 (1947).
[CrossRef]

Wang, F.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

Wang, J.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband Nonlinear Optical Response of Graphene Dispersions,” Adv. Mater. 21(23), 2430–2435 (2009).
[CrossRef]

Wang, Y.

Z. Liu, Y. Wang, X. Zhang, Y. Xu, Y. Chen, and J. Tian, “Nonlinear optical properties of graphene oxide in nanosecond and picosecond regimes,” Appl. Phys. Lett. 94(2), 021902 (2009).
[CrossRef]

Wee, A. T. S.

Z. H. Ni, W. Chen, X. F. Fan, J. L. Kuo, T. Yu, A. T. S. Wee, and Z. X. Shen, “Raman spectroscopy of epitaxial graphene on a SiC substrate,” Phys. Rev. B 77(11), 115416 (2008).
[CrossRef]

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[CrossRef]

Wirtz, L.

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett. 7(2), 238–242 (2007).
[CrossRef] [PubMed]

Wu, Y.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[CrossRef] [PubMed]

Wu, Z. K.

D. Sun, Z. K. Wu, C. Divin, X. Li, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy,” Phys. Rev. Lett. 101(15), 157402 (2008).
[CrossRef] [PubMed]

Xu, Y.

Z. Liu, Y. Wang, X. Zhang, Y. Xu, Y. Chen, and J. Tian, “Nonlinear optical properties of graphene oxide in nanosecond and picosecond regimes,” Appl. Phys. Lett. 94(2), 021902 (2009).
[CrossRef]

Yu, T.

Z. H. Ni, W. Chen, X. F. Fan, J. L. Kuo, T. Yu, A. T. S. Wee, and Z. X. Shen, “Raman spectroscopy of epitaxial graphene on a SiC substrate,” Phys. Rev. B 77(11), 115416 (2008).
[CrossRef]

Zettl, A.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

Zhang, X.

Z. Liu, Y. Wang, X. Zhang, Y. Xu, Y. Chen, and J. Tian, “Nonlinear optical properties of graphene oxide in nanosecond and picosecond regimes,” Appl. Phys. Lett. 94(2), 021902 (2009).
[CrossRef]

Zhang, Y.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

Zheng, Y. S.

T. Ando, Y. S. Zheng, and H. Suzuura, “Dynamical Conductivity and Zero-Mode Anomaly in Honeycomb Lattices,” J. Phys. Soc. Jpn. 71(5), 1318–1324 (2002).
[CrossRef]

Adv. Mater.

J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, and W. J. Blau, “Broadband Nonlinear Optical Response of Graphene Dispersions,” Adv. Mater. 21(23), 2430–2435 (2009).
[CrossRef]

Appl. Phys. Lett.

Z. Liu, Y. Wang, X. Zhang, Y. Xu, Y. Chen, and J. Tian, “Nonlinear optical properties of graphene oxide in nanosecond and picosecond regimes,” Appl. Phys. Lett. 94(2), 021902 (2009).
[CrossRef]

J. M. Dawlaty, S. Shivaraman, M. Chandrashekhar, F. Rana, and M. G. Spencer, “Measurement of ultrafast carrier dynamics in epitaxial graphene,” Appl. Phys. Lett. 92(4), 042116 (2008).
[CrossRef]

IEEE J. Quantum Electron.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26(4), 760–769 (1990).
[CrossRef]

J. Phys. Soc. Jpn.

T. Ando, Y. S. Zheng, and H. Suzuura, “Dynamical Conductivity and Zero-Mode Anomaly in Honeycomb Lattices,” J. Phys. Soc. Jpn. 71(5), 1318–1324 (2002).
[CrossRef]

Nano Lett.

D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, “Spatially resolved Raman spectroscopy of single- and few-layer graphene,” Nano Lett. 7(2), 238–242 (2007).
[CrossRef] [PubMed]

Nat. Mater.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[CrossRef] [PubMed]

Nat. Nanotechnol.

P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nat. Nanotechnol. 2(10), 605–615 (2007).
[CrossRef]

Opt. Express

Phys. Rev.

P. R. Wallace, “The band theory of graphite,” Phys. Rev. 71(9), 622–634 (1947).
[CrossRef]

Phys. Rev. B

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008).
[CrossRef]

Z. H. Ni, W. Chen, X. F. Fan, J. L. Kuo, T. Yu, A. T. S. Wee, and Z. X. Shen, “Raman spectroscopy of epitaxial graphene on a SiC substrate,” Phys. Rev. B 77(11), 115416 (2008).
[CrossRef]

J. C. Burton, L. Sun, F. H. Long, Z. C. Feng, and I. T. Ferguson, “First- and second-order Raman scattering from semi-insulating 4H-SiC,” Phys. Rev. B 59(11), 7282–7284 (1999).
[CrossRef]

Phys. Rev. Lett.

J. Hass, F. Varchon, J. E. Millán-Otoya, M. Sprinkle, N. Sharma, W. A. de Heer, C. Berger, P. N. First, L. Magaud, and E. H. Conrad, “Why multilayer graphene on 4H-SiC(0001[over ]) behaves like a single sheet of graphene,” Phys. Rev. Lett. 100(12), 125504 (2008).
[CrossRef] [PubMed]

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[CrossRef] [PubMed]

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[CrossRef] [PubMed]

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

A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, “Raman spectrum of graphene and graphene layers,” Phys. Rev. Lett. 97(18), 187401 (2006).
[CrossRef] [PubMed]

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, “Unusual microwave response of dirac quasiparticles in graphene,” Phys. Rev. Lett. 96(25), 256802 (2006).
[CrossRef] [PubMed]

D. Sun, Z. K. Wu, C. Divin, X. Li, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Ultrafast relaxation of excited Dirac fermions in epitaxial graphene using optical differential transmission spectroscopy,” Phys. Rev. Lett. 101(15), 157402 (2008).
[CrossRef] [PubMed]

Rev. Mod. Phys.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
[CrossRef]

Science

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

Other

Y. R. Shen, “The Principles of Nonlinear Optics,” John Wiley, New York and Chichester, 1984, pp. 334–336, 437–446.

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Figures (6)

Fig. 1
Fig. 1

Representative Raman spectrum of two-layer epitaxial graphene (EG) on SiC. The inset is Raman image of the intensity of the G-band. Scale bar = 1 um.

Fig. 2
Fig. 2

(a) The momentum conserved photon absorption process in graphene (b) Instantaneous photon absorption generate nonequilibrium distributions of electrons (blue) and holes (red), which subsequently thermalize through ultrafast intraband carrier-carrier and carrier-optical phonon scattering to form Fermi-Dirac distributions (c) Typical nonlinear transmittance of graphene layers at different Z position (circle dots) and the theoretical predictions with Eq. (11) using different τ 1. The inset shows a schematic of the Gaussian laser pulse transmission through the graphene layers.

Fig. 3
Fig. 3

Thermalized electron temperature (T e) and the corresponding chemical potential (μ e) as a function of electron density, excited at 1.55 eV.

Fig. 4
Fig. 4

Input laser pulse (a) temporal (c) spatial profile, Gaussian laser pulse (b) temporal transmittances with τ 1 = 7 fs (solid lines) and τ 1 = 100 fs (dashed lines), (d) spatial transmittances with τ 1 = 7 fs at peak pump intensity of 1 GW/cm2 (red), 5 GW/cm2 (green) and 80 GW/cm2 (blue).

Fig. 5
Fig. 5

Transmittance vs. incident pump intensity for different layers of graphene.

Fig. 6
Fig. 6

(a) Typical experimental dates (circle data) fitted with empirical Eq. (14), (b) The obtained I s vs. pump intensity.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

W t a = 2 π | M t | 2 D ( ω 2 ) [ f t ( ω 2 ) f t ( ω 2 ) ] ω
| M t | 2 = | n | v F σ e i ω E t | m | 2 = 1 8 e 2 v F 2 I t ω 2
T [ t ] = 1 W t a W t i = 1 π e 2 c = 1 π α
f ( ε ) t = f ( ε ) π α D ( ε ) I 0 w exp [ t 2 τ 2 ] + f ( ε ) π α D ( ε ) I 0 w exp [ t 2 τ 2 ] + 1 f ( ε ) τ 1
f ( ε ) t = f ( ε ) π α D ( ε ) I 0 w exp [ t 2 τ 2 ] + f ( ε ) π α D ( ε ) I 0 w exp [ t 2 τ 2 ] f ( ε ) τ 1
f ( ω / 2 ) = 1 ; f ( ω / 2 ) = 0
f t ( ω / 2 ) f t ( ω / 2 ) = 1 2 π α I 0 D ( ω / 2 ) ω G ( t )
G ( t ) =   t exp [ x 2 τ 2 + x t τ 1 + π α I 0 D ( ω / 2 ) ω π τ ( E r f [ x τ ] E r f [ t τ ] ) ] d x
A b s [ I 0 ] =   ( f t ( ω / 2 ) f t ( ω / 2 ) ) π α I 0 exp [ t 2 τ 2 ] d t
I 0 = I 00 exp [ 2 r 2 w 2 ] ( 1 + z 2 z 0 2 ) 1
W a =   0   A b s [ I 00 exp [ 2 r 2 w 2 ] ( 1 + z 2 z 0 2 ) 1 ] 2 π r d r
n =   0   D ( ε ) f F D ( ε ) d ε   and   1 2 n ω =   0   ε D ( ε ) f F D ( ε ) d ε
T ( t ) = 1 π α + 2 I 0 D ( ω / 2 ) ω G ( t ) ( π α ) 2
T ( r ) = 1 A b s [ I 00 exp ( 2 r 2 / w 0 2 ) ] I 00 τ π exp ( 2 r 2 / w 0 2 )
I T I i n = α 0 1 + I i n / I s I i n

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