Abstract

A negative value for the nonlinear refraction in graphene is experimentally observed and unambiguously verified by performing a theoretical analysis arising from the conductivity of the graphene monolayer. The nonlinear optical properties of multi-layer graphene are experimentally studied by employing the Z-scan technique. The measurements are carried out at 1150, 1550, 1900 and 2400 nm with a 100-femtosecond laser source. Under laser illumination the multi-layer graphene exhibits a transmittance increase due to saturable absorption, followed by optical limiting due to two-photon absorption. The saturation irradiance Isat and the two-photon absorption coefficient β are measured in the operating wavelength range. Furthermore, an irradiance-dependent nonlinear refraction is observed and discriminated from the conventional nonlinear refraction coefficient n2, which is not irradiance dependent. The values obtained for the irradiance-dependent nonlinear refraction are in the order of ∼10−9 cm2W−1, approximately 8 orders of magnitude larger than any bulk dielectrics.

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Corrections

7 June 2016: A correction was made to the body text.


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References

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2016 (1)

2015 (2)

W. Chen, Y. Wang, and W. Ji, “Two-Photon Absorption in Graphene Enhanced by the Excitonic Fano Resonance,” J. Phys. Chem. C 119(29), 16954–16961 (2015).
[Crossref]

R. Yingying, G. Brown, R. Mary, G. Demetriou, D. Popa, F. Torrisi, A. C. Ferrari, C. Feng, and A. K. Kar, “7.8-GHz Graphene-Based 2-μm Monolithic Waveguide Laser,” IEEE J. Sel. Top. Quantum Electron. 21(1), 395–400 (2015).
[Crossref]

2014 (3)

F. H. L. Koppens, T. Mueller, P. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nat. Nanotechnol. 9(10), 780–793 (2014).
[Crossref] [PubMed]

F. Xing, G.-X. Meng, Q. Zhang, L.-T. Pan, P. Wang, Z.-B. Liu, W.-S. Jiang, Y. Chen, and J.-G. Tian, “Ultrasensitive Flow Sensing of a Single Cell Using Graphene-Based Optical Sensors,” Nano Lett. 14(6), 3563–3569 (2014).
[Crossref] [PubMed]

K. J. A. Ooi, L. K. Ang, and D. T. H. Tan, “Waveguide engineering of graphene’s nonlinearity,” Appl. Phys. Lett. 105(11), 111110 (2014).
[Crossref]

2013 (4)

H. Harutyunyan, R. Beams, and L. Novotny, “Controllable optical negative refraction and phase conjugation in graphite thin films,” Nat. Phys. 9(7), 423–425 (2013).
[Crossref]

R. Mary, G. Brown, S. J. Beecher, F. Torrisi, S. Milana, D. Popa, T. Hasan, Z. Sun, E. Lidorikis, S. Ohara, A. C. Ferrari, and A. K. Kar, “1.5 GHz picosecond pulse generation from a monolithic waveguide laser with a graphene-film saturable output coupler,” Opt. Express 21(7), 7943–7950 (2013).
[Crossref] [PubMed]

M. N. Cizmeciyan, J. W. Kim, S. Bae, B. H. Hong, F. Rotermund, and A. Sennaroglu, “Graphene mode-locked femtosecond Cr:ZnSe laser at 2500 nm,” Opt. Lett. 38(3), 341–343 (2013).
[Crossref] [PubMed]

S. Husaini, J. E. Slagle, J. M. Murray, S. Guha, L. P. Gonzalez, and R. G. Bedford, “Broadband saturable absorption and optical limiting in graphene-polymer composites,” Appl. Phys. Lett. 102(19), 191112 (2013).
[Crossref]

2012 (5)

B. S. Kalanoor, P. B. Bisht, S. Akbar Ali, T. T. Baby, and S. Ramaprabhu, “Optical nonlinearity of silver-decorated graphene,” J. Opt. Soc. Am. B 29(4), 669–675 (2012).
[Crossref]

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

S. A. Mikhailov, “Theory of the nonlinear optical frequency mixing effect in graphene,” Physica E 44(6), 924–927 (2012).
[Crossref]

E. Pop, V. Varshney, and A. K. Roy, “Thermal properties of graphene: Fundamentals and applications,” MRS Bull. 37(12), 1273–1281 (2012).
[Crossref]

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
[Crossref] [PubMed]

2011 (3)

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).
[Crossref] [PubMed]

W. B. Cho, J. W. Kim, H. W. Lee, S. Bae, B. H. Hong, S. Y. Choi, I. H. Baek, K. Kim, D.-I. Yeom, and F. Rotermund, “High-quality, large-area monolayer graphene for efficient bulk laser mode-locking near 1.25 μm,” Opt. Lett. 36(20), 4089–4091 (2011).
[Crossref] [PubMed]

D. Popa, Z. Sun, T. Hasan, F. Torrisi, F. Wang, and A. C. Ferrari, “Graphene Q-switched, tunable fiber laser,” Appl. Phys. Lett. 98(7), 073106 (2011).
[Crossref]

2010 (10)

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. R. Kelleher, J. Travers, V. Nicolosi, and A. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3(9), 653–660 (2010).
[Crossref]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
[Crossref]

M. Dragoman, D. Neculoiu, G. Deligeorgis, G. Konstantinidis, D. Dragoman, A. Cismaru, A. A. Muller, and R. Plana, “Millimeter-wave generation via frequency multiplication in graphene,” Appl. Phys. Lett. 97(9), 093101 (2010).
[Crossref]

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).
[Crossref] [PubMed]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

D. Sun, C. Divin, J. Rioux, J. E. Sipe, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Coherent Control of Ballistic Photocurrents in Multilayer Epitaxial Graphene Using Quantum Interference,” Nano Lett. 10(4), 1293–1296 (2010).
[Crossref] [PubMed]

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent Nonlinear Optical Response of Graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[Crossref] [PubMed]

S. Ghosh, W. Bao, D. L. Nika, S. Subrina, E. P. Pokatilov, C. N. Lau, and A. A. Balandin, “Dimensional crossover of thermal transport in few-layer graphene,” Nat. Mater. 9(7), 555–558 (2010).
[Crossref] [PubMed]

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
[Crossref] [PubMed]

J. Wang, B. Gu, H.-T. Wang, and X.-W. Ni, “Z-scan analytical theory for material with saturable absorption and two-photon absorption,” Opt. Commun. 283(18), 3525–3528 (2010).
[Crossref]

2009 (6)

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube–Polymer Composites for Ultrafast Photonics,” Adv. Mater. 21(38), 3874–3899 (2009).
[Crossref]

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]

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).
[Crossref]

H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, “Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009).
[Crossref]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009).
[Crossref] [PubMed]

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

2008 (2)

L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
[Crossref]

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior Thermal Conductivity of Single-Layer Graphene,” Nano Lett. 8(3), 902–907 (2008).
[Crossref] [PubMed]

2006 (1)

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-Field Microscopy Through a SiC Superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

2005 (2)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Y. Gao, X. Zhang, Y. Li, H. Liu, Y. Wang, Q. Chang, W. Jiao, and Y. Song, “Saturable absorption and reverse saturable absorption in platinum nanoparticles,” Opt. Commun. 251(4-6), 429–433 (2005).
[Crossref]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

2000 (1)

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

1990 (1)

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]

Ahn, J.-H.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
[Crossref] [PubMed]

Akbar Ali, S.

An, J.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Ang, L. K.

K. J. A. Ooi, L. K. Ang, and D. T. H. Tan, “Waveguide engineering of graphene’s nonlinearity,” Appl. Phys. Lett. 105(11), 111110 (2014).
[Crossref]

Avouris, P.

F. H. L. Koppens, T. Mueller, P. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nat. Nanotechnol. 9(10), 780–793 (2014).
[Crossref] [PubMed]

Baby, T. T.

Bae, S.

Baek, I. H.

Balakrishnan, J.

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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).
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H. Harutyunyan, R. Beams, and L. Novotny, “Controllable optical negative refraction and phase conjugation in graphite thin films,” Nat. Phys. 9(7), 423–425 (2013).
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S. Husaini, J. E. Slagle, J. M. Murray, S. Guha, L. P. Gonzalez, and R. G. Bedford, “Broadband saturable absorption and optical limiting in graphene-polymer composites,” Appl. Phys. Lett. 102(19), 191112 (2013).
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Berger, C.

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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).
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F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
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R. Yingying, G. Brown, R. Mary, G. Demetriou, D. Popa, F. Torrisi, A. C. Ferrari, C. Feng, and A. K. Kar, “7.8-GHz Graphene-Based 2-μm Monolithic Waveguide Laser,” IEEE J. Sel. Top. Quantum Electron. 21(1), 395–400 (2015).
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X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
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Chang, Q.

Y. Gao, X. Zhang, Y. Li, H. Liu, Y. Wang, Q. Chang, W. Jiao, and Y. Song, “Saturable absorption and reverse saturable absorption in platinum nanoparticles,” Opt. Commun. 251(4-6), 429–433 (2005).
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W. Chen, Y. Wang, and W. Ji, “Two-Photon Absorption in Graphene Enhanced by the Excitonic Fano Resonance,” J. Phys. Chem. C 119(29), 16954–16961 (2015).
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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).
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F. Xing, G.-X. Meng, Q. Zhang, L.-T. Pan, P. Wang, Z.-B. Liu, W.-S. Jiang, Y. Chen, and J.-G. Tian, “Ultrasensitive Flow Sensing of a Single Cell Using Graphene-Based Optical Sensors,” Nano Lett. 14(6), 3563–3569 (2014).
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Choi, S. Y.

Cismaru, A.

M. Dragoman, D. Neculoiu, G. Deligeorgis, G. Konstantinidis, D. Dragoman, A. Cismaru, A. A. Muller, and R. Plana, “Millimeter-wave generation via frequency multiplication in graphene,” Appl. Phys. Lett. 97(9), 093101 (2010).
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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).
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X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
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D. Sun, C. Divin, J. Rioux, J. E. Sipe, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Coherent Control of Ballistic Photocurrents in Multilayer Epitaxial Graphene Using Quantum Interference,” Nano Lett. 10(4), 1293–1296 (2010).
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D. Sun, C. Divin, J. Rioux, J. E. Sipe, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Coherent Control of Ballistic Photocurrents in Multilayer Epitaxial Graphene Using Quantum Interference,” Nano Lett. 10(4), 1293–1296 (2010).
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M. Dragoman, D. Neculoiu, G. Deligeorgis, G. Konstantinidis, D. Dragoman, A. Cismaru, A. A. Muller, and R. Plana, “Millimeter-wave generation via frequency multiplication in graphene,” Appl. Phys. Lett. 97(9), 093101 (2010).
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M. Dragoman, D. Neculoiu, G. Deligeorgis, G. Konstantinidis, D. Dragoman, A. Cismaru, A. A. Muller, and R. Plana, “Millimeter-wave generation via frequency multiplication in graphene,” Appl. Phys. Lett. 97(9), 093101 (2010).
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R. Yingying, G. Brown, R. Mary, G. Demetriou, D. Popa, F. Torrisi, A. C. Ferrari, C. Feng, and A. K. Kar, “7.8-GHz Graphene-Based 2-μm Monolithic Waveguide Laser,” IEEE J. Sel. Top. Quantum Electron. 21(1), 395–400 (2015).
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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).
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Ferrari, A.

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. R. Kelleher, J. Travers, V. Nicolosi, and A. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3(9), 653–660 (2010).
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Ferrari, A. C.

R. Yingying, G. Brown, R. Mary, G. Demetriou, D. Popa, F. Torrisi, A. C. Ferrari, C. Feng, and A. K. Kar, “7.8-GHz Graphene-Based 2-μm Monolithic Waveguide Laser,” IEEE J. Sel. Top. Quantum Electron. 21(1), 395–400 (2015).
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F. H. L. Koppens, T. Mueller, P. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nat. Nanotechnol. 9(10), 780–793 (2014).
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R. Mary, G. Brown, S. J. Beecher, F. Torrisi, S. Milana, D. Popa, T. Hasan, Z. Sun, E. Lidorikis, S. Ohara, A. C. Ferrari, and A. K. Kar, “1.5 GHz picosecond pulse generation from a monolithic waveguide laser with a graphene-film saturable output coupler,” Opt. Express 21(7), 7943–7950 (2013).
[Crossref] [PubMed]

D. Popa, Z. Sun, T. Hasan, F. Torrisi, F. Wang, and A. C. Ferrari, “Graphene Q-switched, tunable fiber laser,” Appl. Phys. Lett. 98(7), 073106 (2011).
[Crossref]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
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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).
[Crossref] [PubMed]

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube–Polymer Composites for Ultrafast Photonics,” Adv. Mater. 21(38), 3874–3899 (2009).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,” Science 306(5696), 666–669 (2004).
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D. Sun, C. Divin, J. Rioux, J. E. Sipe, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Coherent Control of Ballistic Photocurrents in Multilayer Epitaxial Graphene Using Quantum Interference,” Nano Lett. 10(4), 1293–1296 (2010).
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Fuhrer, M. S.

Gao, Y.

Y. Gao, X. Zhang, Y. Li, H. Liu, Y. Wang, Q. Chang, W. Jiao, and Y. Song, “Saturable absorption and reverse saturable absorption in platinum nanoparticles,” Opt. Commun. 251(4-6), 429–433 (2005).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,” Science 306(5696), 666–669 (2004).
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S. Ghosh, W. Bao, D. L. Nika, S. Subrina, E. P. Pokatilov, C. N. Lau, and A. A. Balandin, “Dimensional crossover of thermal transport in few-layer graphene,” Nat. Mater. 9(7), 555–558 (2010).
[Crossref] [PubMed]

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior Thermal Conductivity of Single-Layer Graphene,” Nano Lett. 8(3), 902–907 (2008).
[Crossref] [PubMed]

Godbout, N.

Gonzalez, L. P.

S. Husaini, J. E. Slagle, J. M. Murray, S. Guha, L. P. Gonzalez, and R. G. Bedford, “Broadband saturable absorption and optical limiting in graphene-polymer composites,” Appl. Phys. Lett. 102(19), 191112 (2013).
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Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,” Science 306(5696), 666–669 (2004).
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S. Husaini, J. E. Slagle, J. M. Murray, S. Guha, L. P. Gonzalez, and R. G. Bedford, “Broadband saturable absorption and optical limiting in graphene-polymer composites,” Appl. Phys. Lett. 102(19), 191112 (2013).
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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).
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E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent Nonlinear Optical Response of Graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
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H. Harutyunyan, R. Beams, and L. Novotny, “Controllable optical negative refraction and phase conjugation in graphite thin films,” Nat. Phys. 9(7), 423–425 (2013).
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Hasan, T.

R. Mary, G. Brown, S. J. Beecher, F. Torrisi, S. Milana, D. Popa, T. Hasan, Z. Sun, E. Lidorikis, S. Ohara, A. C. Ferrari, and A. K. Kar, “1.5 GHz picosecond pulse generation from a monolithic waveguide laser with a graphene-film saturable output coupler,” Opt. Express 21(7), 7943–7950 (2013).
[Crossref] [PubMed]

D. Popa, Z. Sun, T. Hasan, F. Torrisi, F. Wang, and A. C. Ferrari, “Graphene Q-switched, tunable fiber laser,” Appl. Phys. Lett. 98(7), 073106 (2011).
[Crossref]

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. R. Kelleher, J. Travers, V. Nicolosi, and A. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3(9), 653–660 (2010).
[Crossref]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
[Crossref]

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

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).
[Crossref] [PubMed]

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube–Polymer Composites for Ultrafast Photonics,” Adv. Mater. 21(38), 3874–3899 (2009).
[Crossref]

Hendry, E.

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent Nonlinear Optical Response of Graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
[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).
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T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
[Crossref]

Hong, B. H.

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).
[Crossref] [PubMed]

Husaini, S.

S. Husaini, J. E. Slagle, J. M. Murray, S. Guha, L. P. Gonzalez, and R. G. Bedford, “Broadband saturable absorption and optical limiting in graphene-polymer composites,” Appl. Phys. Lett. 102(19), 191112 (2013).
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S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
[Crossref] [PubMed]

Ji, W.

W. Chen, Y. Wang, and W. Ji, “Two-Photon Absorption in Graphene Enhanced by the Excitonic Fano Resonance,” J. Phys. Chem. C 119(29), 16954–16961 (2015).
[Crossref]

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).
[Crossref] [PubMed]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Jiang, W.-S.

F. Xing, G.-X. Meng, Q. Zhang, L.-T. Pan, P. Wang, Z.-B. Liu, W.-S. Jiang, Y. Chen, and J.-G. Tian, “Ultrasensitive Flow Sensing of a Single Cell Using Graphene-Based Optical Sensors,” Nano Lett. 14(6), 3563–3569 (2014).
[Crossref] [PubMed]

Jiao, W.

Y. Gao, X. Zhang, Y. Li, H. Liu, Y. Wang, Q. Chang, W. Jiao, and Y. Song, “Saturable absorption and reverse saturable absorption in platinum nanoparticles,” Opt. Commun. 251(4-6), 429–433 (2005).
[Crossref]

Jung, I.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Kalanoor, B. S.

Kar, A. K.

R. Yingying, G. Brown, R. Mary, G. Demetriou, D. Popa, F. Torrisi, A. C. Ferrari, C. Feng, and A. K. Kar, “7.8-GHz Graphene-Based 2-μm Monolithic Waveguide Laser,” IEEE J. Sel. Top. Quantum Electron. 21(1), 395–400 (2015).
[Crossref]

R. Mary, G. Brown, S. J. Beecher, F. Torrisi, S. Milana, D. Popa, T. Hasan, Z. Sun, E. Lidorikis, S. Ohara, A. C. Ferrari, and A. K. Kar, “1.5 GHz picosecond pulse generation from a monolithic waveguide laser with a graphene-film saturable output coupler,” Opt. Express 21(7), 7943–7950 (2013).
[Crossref] [PubMed]

Kelleher, E. R.

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. R. Kelleher, J. Travers, V. Nicolosi, and A. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3(9), 653–660 (2010).
[Crossref]

Kim, H.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
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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).
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S. Husaini, J. E. Slagle, J. M. Murray, S. Guha, L. P. Gonzalez, and R. G. Bedford, “Broadband saturable absorption and optical limiting in graphene-polymer composites,” Appl. Phys. Lett. 102(19), 191112 (2013).
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Y. Gao, X. Zhang, Y. Li, H. Liu, Y. Wang, Q. Chang, W. Jiao, and Y. Song, “Saturable absorption and reverse saturable absorption in platinum nanoparticles,” Opt. Commun. 251(4-6), 429–433 (2005).
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S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
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N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science 308(5721), 534–537 (2005).
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D. Sun, C. Divin, J. Rioux, J. E. Sipe, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Coherent Control of Ballistic Photocurrents in Multilayer Epitaxial Graphene Using Quantum Interference,” Nano Lett. 10(4), 1293–1296 (2010).
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[Crossref] [PubMed]

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[Crossref]

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. R. Kelleher, J. Travers, V. Nicolosi, and A. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3(9), 653–660 (2010).
[Crossref]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
[Crossref]

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).
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F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube–Polymer Composites for Ultrafast Photonics,” Adv. Mater. 21(38), 3874–3899 (2009).
[Crossref]

Tan, D. T. H.

K. J. A. Ooi, L. K. Ang, and D. T. H. Tan, “Waveguide engineering of graphene’s nonlinearity,” Appl. Phys. Lett. 105(11), 111110 (2014).
[Crossref]

Tan, P. H.

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube–Polymer Composites for Ultrafast Photonics,” Adv. Mater. 21(38), 3874–3899 (2009).
[Crossref]

Tang, D.

H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, “Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009).
[Crossref]

Tang, D. 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).
[Crossref]

H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009).
[Crossref] [PubMed]

Taubner, T.

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-Field Microscopy Through a SiC Superlens,” Science 313(5793), 1595 (2006).
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A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior Thermal Conductivity of Single-Layer Graphene,” Nano Lett. 8(3), 902–907 (2008).
[Crossref] [PubMed]

Tian, J.-G.

F. Xing, G.-X. Meng, Q. Zhang, L.-T. Pan, P. Wang, Z.-B. Liu, W.-S. Jiang, Y. Chen, and J.-G. Tian, “Ultrasensitive Flow Sensing of a Single Cell Using Graphene-Based Optical Sensors,” Nano Lett. 14(6), 3563–3569 (2014).
[Crossref] [PubMed]

Torrisi, F.

R. Yingying, G. Brown, R. Mary, G. Demetriou, D. Popa, F. Torrisi, A. C. Ferrari, C. Feng, and A. K. Kar, “7.8-GHz Graphene-Based 2-μm Monolithic Waveguide Laser,” IEEE J. Sel. Top. Quantum Electron. 21(1), 395–400 (2015).
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R. Mary, G. Brown, S. J. Beecher, F. Torrisi, S. Milana, D. Popa, T. Hasan, Z. Sun, E. Lidorikis, S. Ohara, A. C. Ferrari, and A. K. Kar, “1.5 GHz picosecond pulse generation from a monolithic waveguide laser with a graphene-film saturable output coupler,” Opt. Express 21(7), 7943–7950 (2013).
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D. Popa, Z. Sun, T. Hasan, F. Torrisi, F. Wang, and A. C. Ferrari, “Graphene Q-switched, tunable fiber laser,” Appl. Phys. Lett. 98(7), 073106 (2011).
[Crossref]

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. R. Kelleher, J. Travers, V. Nicolosi, and A. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3(9), 653–660 (2010).
[Crossref]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
[Crossref]

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).
[Crossref] [PubMed]

Travers, J.

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. R. Kelleher, J. Travers, V. Nicolosi, and A. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3(9), 653–660 (2010).
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X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
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T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-Field Microscopy Through a SiC Superlens,” Science 313(5793), 1595 (2006).
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T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
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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).
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E. Pop, V. Varshney, and A. K. Roy, “Thermal properties of graphene: Fundamentals and applications,” MRS Bull. 37(12), 1273–1281 (2012).
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X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
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Virally, S.

Vitiello, M. S.

F. H. L. Koppens, T. Mueller, P. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nat. Nanotechnol. 9(10), 780–793 (2014).
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Wang, F.

D. Popa, Z. Sun, T. Hasan, F. Torrisi, F. Wang, and A. C. Ferrari, “Graphene Q-switched, tunable fiber laser,” Appl. Phys. Lett. 98(7), 073106 (2011).
[Crossref]

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. R. Kelleher, J. Travers, V. Nicolosi, and A. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3(9), 653–660 (2010).
[Crossref]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
[Crossref]

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).
[Crossref] [PubMed]

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube–Polymer Composites for Ultrafast Photonics,” Adv. Mater. 21(38), 3874–3899 (2009).
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J. Wang, B. Gu, H.-T. Wang, and X.-W. Ni, “Z-scan analytical theory for material with saturable absorption and two-photon absorption,” Opt. Commun. 283(18), 3525–3528 (2010).
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J. Wang, B. Gu, H.-T. Wang, and X.-W. Ni, “Z-scan analytical theory for material with saturable absorption and two-photon absorption,” Opt. Commun. 283(18), 3525–3528 (2010).
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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).
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Wang, P.

F. Xing, G.-X. Meng, Q. Zhang, L.-T. Pan, P. Wang, Z.-B. Liu, W.-S. Jiang, Y. Chen, and J.-G. Tian, “Ultrasensitive Flow Sensing of a Single Cell Using Graphene-Based Optical Sensors,” Nano Lett. 14(6), 3563–3569 (2014).
[Crossref] [PubMed]

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).
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Wang, Y.

W. Chen, Y. Wang, and W. Ji, “Two-Photon Absorption in Graphene Enhanced by the Excitonic Fano Resonance,” J. Phys. Chem. C 119(29), 16954–16961 (2015).
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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).
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Y. Gao, X. Zhang, Y. Li, H. Liu, Y. Wang, Q. Chang, W. Jiao, and Y. Song, “Saturable absorption and reverse saturable absorption in platinum nanoparticles,” Opt. Commun. 251(4-6), 429–433 (2005).
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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).
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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).
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T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
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Xia, C. Q.

Xing, F.

F. Xing, G.-X. Meng, Q. Zhang, L.-T. Pan, P. Wang, Z.-B. Liu, W.-S. Jiang, Y. Chen, and J.-G. Tian, “Ultrasensitive Flow Sensing of a Single Cell Using Graphene-Based Optical Sensors,” Nano Lett. 14(6), 3563–3569 (2014).
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S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
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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).
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Yang, D.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Yeom, D.-I.

Yingying, R.

R. Yingying, G. Brown, R. Mary, G. Demetriou, D. Popa, F. Torrisi, A. C. Ferrari, C. Feng, and A. K. Kar, “7.8-GHz Graphene-Based 2-μm Monolithic Waveguide Laser,” IEEE J. Sel. Top. Quantum Electron. 21(1), 395–400 (2015).
[Crossref]

Yu, M.

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
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Zhang, H.

H. Zhang, S. Virally, Q. Bao, L. K. Ping, S. Massar, N. Godbout, and P. Kockaert, “Z-scan measurement of the nonlinear refractive index of graphene,” Opt. Lett. 37(11), 1856–1858 (2012).
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H. Zhang, D. Y. Tang, L. M. Zhao, Q. L. Bao, and K. P. Loh, “Large energy mode locking of an erbium-doped fiber laser with atomic layer graphene,” Opt. Express 17(20), 17630–17635 (2009).
[Crossref] [PubMed]

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).
[Crossref]

H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, “Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009).
[Crossref]

Zhang, Q.

F. Xing, G.-X. Meng, Q. Zhang, L.-T. Pan, P. Wang, Z.-B. Liu, W.-S. Jiang, Y. Chen, and J.-G. Tian, “Ultrasensitive Flow Sensing of a Single Cell Using Graphene-Based Optical Sensors,” Nano Lett. 14(6), 3563–3569 (2014).
[Crossref] [PubMed]

Zhang, X.

Y. Gao, X. Zhang, Y. Li, H. Liu, Y. Wang, Q. Chang, W. Jiao, and Y. Song, “Saturable absorption and reverse saturable absorption in platinum nanoparticles,” Opt. Commun. 251(4-6), 429–433 (2005).
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N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,” Science 306(5696), 666–669 (2004).
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Zhao, L.

H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, “Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009).
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Zhao, L. M.

Zheng, C.

Zheng, Y.

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

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).
[Crossref]

Adv. Mater. (2)

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]

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube–Polymer Composites for Ultrafast Photonics,” Adv. Mater. 21(38), 3874–3899 (2009).
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Appl. Phys. Lett. (6)

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H. Zhang, Q. Bao, D. Tang, L. Zhao, and K. Loh, “Large energy soliton erbium-doped fiber laser with a graphene-polymer composite mode locker,” Appl. Phys. Lett. 95(14), 141103 (2009).
[Crossref]

D. Popa, Z. Sun, T. Hasan, F. Torrisi, F. Wang, and A. C. Ferrari, “Graphene Q-switched, tunable fiber laser,” Appl. Phys. Lett. 98(7), 073106 (2011).
[Crossref]

D. Popa, Z. Sun, F. Torrisi, T. Hasan, F. Wang, and A. C. Ferrari, “Sub 200 fs pulse generation from a graphene mode-locked fiber laser,” Appl. Phys. Lett. 97(20), 203106 (2010).
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K. J. A. Ooi, L. K. Ang, and D. T. H. Tan, “Waveguide engineering of graphene’s nonlinearity,” Appl. Phys. Lett. 105(11), 111110 (2014).
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IEEE J. Quantum Electron. (1)

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]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Yingying, G. Brown, R. Mary, G. Demetriou, D. Popa, F. Torrisi, A. C. Ferrari, C. Feng, and A. K. Kar, “7.8-GHz Graphene-Based 2-μm Monolithic Waveguide Laser,” IEEE J. Sel. Top. Quantum Electron. 21(1), 395–400 (2015).
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J. Opt. Soc. Am. B (1)

J. Phys. Chem. C (1)

W. Chen, Y. Wang, and W. Ji, “Two-Photon Absorption in Graphene Enhanced by the Excitonic Fano Resonance,” J. Phys. Chem. C 119(29), 16954–16961 (2015).
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J. Phys. Conf. Ser. (1)

L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).
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MRS Bull. (1)

E. Pop, V. Varshney, and A. K. Roy, “Thermal properties of graphene: Fundamentals and applications,” MRS Bull. 37(12), 1273–1281 (2012).
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Nano Lett. (4)

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, “Superior Thermal Conductivity of Single-Layer Graphene,” Nano Lett. 8(3), 902–907 (2008).
[Crossref] [PubMed]

F. Xing, G.-X. Meng, Q. Zhang, L.-T. Pan, P. Wang, Z.-B. Liu, W.-S. Jiang, Y. Chen, and J.-G. Tian, “Ultrasensitive Flow Sensing of a Single Cell Using Graphene-Based Optical Sensors,” Nano Lett. 14(6), 3563–3569 (2014).
[Crossref] [PubMed]

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).
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D. Sun, C. Divin, J. Rioux, J. E. Sipe, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Coherent Control of Ballistic Photocurrents in Multilayer Epitaxial Graphene Using Quantum Interference,” Nano Lett. 10(4), 1293–1296 (2010).
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Nano Res. (1)

Z. Sun, D. Popa, T. Hasan, F. Torrisi, F. Wang, E. R. Kelleher, J. Travers, V. Nicolosi, and A. Ferrari, “A stable, wideband tunable, near transform-limited, graphene-mode-locked, ultrafast laser,” Nano Res. 3(9), 653–660 (2010).
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Nat. Mater. (1)

S. Ghosh, W. Bao, D. L. Nika, S. Subrina, E. P. Pokatilov, C. N. Lau, and A. A. Balandin, “Dimensional crossover of thermal transport in few-layer graphene,” Nat. Mater. 9(7), 555–558 (2010).
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Nat. Nanotechnol. (2)

S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T. Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Ozyilmaz, J.-H. Ahn, B. H. Hong, and S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent electrodes,” Nat. Nanotechnol. 5(8), 574–578 (2010).
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F. H. L. Koppens, T. Mueller, P. Avouris, A. C. Ferrari, M. S. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nat. Nanotechnol. 9(10), 780–793 (2014).
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Nat. Photonics (2)

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

T. Gu, N. Petrone, J. F. McMillan, A. van der Zande, M. Yu, G. Q. Lo, D. L. Kwong, J. Hone, and C. W. Wong, “Regenerative oscillation and four-wave mixing in graphene optoelectronics,” Nat. Photonics 6(8), 554–559 (2012).
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Nat. Phys. (1)

H. Harutyunyan, R. Beams, and L. Novotny, “Controllable optical negative refraction and phase conjugation in graphite thin films,” Nat. Phys. 9(7), 423–425 (2013).
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Opt. Commun. (2)

J. Wang, B. Gu, H.-T. Wang, and X.-W. Ni, “Z-scan analytical theory for material with saturable absorption and two-photon absorption,” Opt. Commun. 283(18), 3525–3528 (2010).
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Y. Gao, X. Zhang, Y. Li, H. Liu, Y. Wang, Q. Chang, W. Jiao, and Y. Song, “Saturable absorption and reverse saturable absorption in platinum nanoparticles,” Opt. Commun. 251(4-6), 429–433 (2005).
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Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. Lett. (2)

E. Hendry, P. J. Hale, J. Moger, A. K. Savchenko, and S. A. Mikhailov, “Coherent Nonlinear Optical Response of Graphene,” Phys. Rev. Lett. 105(9), 097401 (2010).
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J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
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S. A. Mikhailov, “Theory of the nonlinear optical frequency mixing effect in graphene,” Physica E 44(6), 924–927 (2012).
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Science (4)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,” Science 306(5696), 666–669 (2004).
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N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science 308(5721), 534–537 (2005).
[Crossref] [PubMed]

T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-Field Microscopy Through a SiC Superlens,” Science 313(5793), 1595 (2006).
[Crossref] [PubMed]

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Other (2)

H. Wang, A. Hsu, K. Kang, J. Kong, and T. Palacios, “Gigahertz ambipolar frequency multiplier based on CVD graphene,” in Electron Devices Meeting (IEDM),2010IEEE International, 2010), 23.26.21–23.26.24.
[Crossref]

E. Malic and A. Knorr, Graphene and Carbon Nanotubes: Ultrafast Optics and Relaxation Dynamics (Wiley, Berlin, 2013).

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Figures (4)

Fig. 1
Fig. 1 Open aperture Z-scan traces at 5 consecutive pulse energies at 1550 nm showing the competitive saturable absorption and two-photon absorption processes.
Fig. 2
Fig. 2 Change in transmittance (at z = 0) with input irradiance at 1150, 1550, 1900 and 2400nm (dots) with the corresponding theoretical fits (solid lines).
Fig. 3
Fig. 3 Closed aperture Z-scan traces at 1150, 1550, 1900 and 2400 nm at an irradiance of 22 GWcm−2 with the corresponding theoretical fits.
Fig. 4
Fig. 4 (a) Total saturation irradiance Isat versus wavelength, in conditions of room temperature along with the experimental values from Table 1 (black dots); (b) Real (blue line) and imaginary (red line) parts of the nonlinear refractive index versus wavelength at 22 GWcm−2 along with the experimental values from Table 1 (black dots).

Tables (1)

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Table 1 Nonlinear Coefficients

Equations (7)

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a ( I ) = a 0 1 + I I s a t + β I .
σ ( ω ) = i e 2 ( 2 k B T ) π 2 ( ω + i γ 1 ) [ E F 2 k B T + log ( 2 e E F k B T + 1 ) ] + e 2 4 { 1 2 + 1 π arc tan [ ( ω + i γ 2 ) 2 E F 2 k B T ] } i 2 π log { [ ( ω + i γ 2 ) 2 E F ] 2 [ ( ω + i γ 2 ) 2 E F ] 2 + ( 2 k B T ) 2 } .
σ ( ω ) = σ 0 = e 2 4 .
χ ( ω ) = i N σ ( ω ) ε 0 ω d e f f = χ + i χ .
I s a t = N c ε 0 γ 1 γ 2 ( ω 0 e v F ) 2 .
χ ( ω ) = i N σ ( ω ) ε 0 ω d e f f 1 ( 1 + I I s a t ) .
n ( I ) + i k ( I ) = 1 + χ ( ω ) .

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