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The Physics of ultrafast saturable absorption in graphene
Guichuan Xing, Hongchen Guo, Xinhai Zhang, Tze Chien Sum, and Cheng Hon Alfred Huan »View Author Affiliations
1Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University,21 Nanyang Link, 637371, Singapore
2Institute of Materials Research and Engineering, A* STAR (Agency for Science, Technology and Research), 3 Research Link, 117602, Singapore
*Corresponding author: tzechien@ntu.edu.sg
Optics Express, Vol. 18, Issue 5, pp. 4564-4573 (2010)
http://dx.doi.org/10.1364/OE.18.004564
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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
OCIS Codes
(190.4400) Nonlinear optics : Nonlinear optics, materials
(320.7110) Ultrafast optics : Ultrafast nonlinear optics
(160.4236) Materials : Nanomaterials
ToC Category:
Materials
History
Original Manuscript: January 4, 2010
Revised Manuscript: February 9, 2010
Manuscript Accepted: February 9, 2010
Published: February 19, 2010
Virtual Issues
February 24, 2010 Spotlight on Optics
Citation
Guichuan Xing, Hongchen Guo, Xinhai Zhang, Tze Chien Sum, and Cheng Hon Alfred Huan, "The Physics of ultrafast saturable absorption in graphene," Opt. Express 18, 4564-4573 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-4564
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References
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- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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. 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]
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- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- P. Avouris, Z. Chen, and V. Perebeinos, “Carbon-based electronics,” Nat. Nanotechnol. 2(10), 605–615 (2007). [CrossRef]
- 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. 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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. 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]
- 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]
- 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. 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]
- 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]
- 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. 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]
- 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]
- 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]
- 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]
- 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]
- 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. 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. 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]
- P. R. Wallace, “The band theory of graphite,” Phys. Rev. 71(9), 622–634 (1947). [CrossRef]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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
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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.
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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.
2009, Castro Neto, 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]
- 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]
- 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]
- 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. 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- P. R. Wallace, “The band theory of graphite,” Phys. Rev. 71(9), 622–634 (1947). [CrossRef]
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