Abstract

Mono-layer graphene integrated with optical waveguides is studied for the purpose of maximizing E-field interaction with the graphene layer, for the generation of ultra-large nonlinear parameters. It is shown that the common approach used to minimize the waveguide effective modal area does not accurately predict the configuration with the maximum nonlinear parameter. Both photonic and plasmonic waveguide configurations and graphene integration techniques realizable with today’s fabrication tools are studied. Importantly, nonlinear parameters exceeding 104 W−1/m, two orders of magnitude larger than that in silicon on insulator waveguides without graphene, are obtained for the quasi-TE mode in silicon waveguides incorporating mono-layer graphene in the evanescent part of the optical field. Dielectric loaded surface plasmon polariton waveguides incorporating mono-layer graphene are observed to generate nonlinear parameters as large as 105 W−1/m, three orders of magnitude larger than that in silicon on insulator waveguides without graphene. The ultra-large nonlinear parameters make such waveguides promising platforms for nonlinear integrated optics at ultra-low powers, and for previously unobserved nonlinear optical effects to be studied in a waveguide platform.

© 2014 Optical Society of America

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References

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2014 (1)

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. F. Krauss, and B. J. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat Commun. 5, 3160 (2014).
[Crossref] [PubMed]

2013 (8)

B. Y. Zhang, T. Liu, B. Meng, X. Li, G. Liang, X. Hu, and Q. J. Wang, “Broadband high photoresponse from pure monolayer graphene photodetector,” Nat Commun. 4, 1811 (2013).
[Crossref] [PubMed]

J. Gosciniak and D. T. H. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24(18), 185202 (2013).
[Crossref] [PubMed]

J. Gosciniak and D. T. H. Tan, “Theoretical investigation of graphene-based photonic modulators,” Sci Rep. 3, 1897 (2013).
[Crossref] [PubMed]

S. Hong, J. I. Dadap, N. Petrone, P. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).

M. L. Nesterov, J. Bravo-Abad, A. Y. Nikitin, F. J. García-Vidal, and L. Martin-Moreno, “Graphene supports the propagation of subwavelength optical soltions,” Laser Photon. Rev. 7(2), L7–L11 (2013).
[Crossref]

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nature Photon. 7(8), 597–607 (2013).
[Crossref]

A. V. Gorbach, A. Marini, and D. V. Skryabin, “Graphene-clad tapered fiber: effective nonlinearity and propagation losses,” Opt. Lett. 38(24), 5244–5247 (2013).
[Crossref] [PubMed]

T. Wang, N. Venkatram, J. Gosciniak, Y. Cui, G. Qian, W. Ji, and D. T. H. Tan, “Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths,” Opt. Express 21(26), 32192–32198 (2013).
[Crossref] [PubMed]

2012 (4)

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]

I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Effective mode area and its optimization in silicon-nanocrystal waveguides,” Opt. Lett. 37(12), 2295–2297 (2012).
[Crossref] [PubMed]

D. T. H. Tan, “Optical pulse compression on a silicon chip – Effect of group velocity dispersion and free carriers,” Appl. Phys. Lett. 101(21), 211112 (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]

2011 (3)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Y. Li, B. A. Malomed, J. Wu, W. Pang, S. Wang, and J. Zhou, “Quasi-compactons in inverted nonlinear photonic crystals,” Phys. Rev. A 84(4), 043839 (2011).
[Crossref]

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant Two-Photon Absorption in Bilayer Graphene,” Nano Lett. 11(7), 2622–2627 (2011).
[Crossref] [PubMed]

2010 (7)

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[Crossref]

T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4(5), 297–301 (2010).
[Crossref]

D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett. 96(6), 061101 (2010).
[Crossref]

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]

D. T. H. Tan, P. C. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat Commun. 1(8), 116 (2010).
[Crossref] [PubMed]

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4(12), 862–868 (2010).
[Crossref]

B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640Gb/s using slow-light,” Opt. Express 18(8), 7770–7781 (2010).
[Crossref] [PubMed]

2009 (2)

2008 (5)

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys. Condens. Matter 20(38), 384204 (2008).
[Crossref] [PubMed]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (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]

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321(5887), 385–388 (2008).
[Crossref] [PubMed]

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
[Crossref] [PubMed]

2007 (2)

S. A. Mikhailov, “Non-linear electromagnetic response of graphene,” Europhys. Lett. 79(2), 27002 (2007).
[Crossref]

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99(1), 016803 (2007).
[Crossref] [PubMed]

2006 (2)

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[Crossref] [PubMed]

E. Dulkeith, Y. A. Vlasov, X. Chen, N. C. Panoiu, and R. M. Osgood., “Self-phase-modulation in submicron silicon-on-insulator photonic wires,” Opt. Express 14(12), 5524–5534 (2006).
[Crossref] [PubMed]

2005 (3)

H. Fukada, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J. Takahashi, and S. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13, 4629–4637 (2005).

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, “Nonlinear-optic silicon-nanowire waveguides,” Jpn. J. Appl. Phys. 44, 6541–6545 (2005).

2004 (1)

2003 (1)

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[Crossref]

2002 (1)

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

Agrawal, G. P.

Arakawa, Y.

H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, “Nonlinear-optic silicon-nanowire waveguides,” Jpn. J. Appl. Phys. 44, 6541–6545 (2005).

Asghari, M.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

Avouris, P.

T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4(5), 297–301 (2010).
[Crossref]

Balandin, A. A.

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]

Bao, Q.

Bao, W.

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]

Blanco-Redondo, A.

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. F. Krauss, and B. J. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat Commun. 5, 3160 (2014).
[Crossref] [PubMed]

Bravo-Abad, J.

M. L. Nesterov, J. Bravo-Abad, A. Y. Nikitin, F. J. García-Vidal, and L. Martin-Moreno, “Graphene supports the propagation of subwavelength optical soltions,” Laser Photon. Rev. 7(2), L7–L11 (2013).
[Crossref]

Calizo, I.

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]

Cardenas, J.

Chen, L.

Chen, W.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant Two-Photon Absorption in Bilayer Graphene,” Nano Lett. 11(7), 2622–2627 (2011).
[Crossref] [PubMed]

Chen, X.

Chu, S.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[Crossref]

Chu, T.

H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, “Nonlinear-optic silicon-nanowire waveguides,” Jpn. J. Appl. Phys. 44, 6541–6545 (2005).

Colman, P.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4(12), 862–868 (2010).
[Crossref]

Combrié, S.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4(12), 862–868 (2010).
[Crossref]

Corcoran, B.

Cui, Y.

Dadap, J. I.

Day, I. E.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

De Rossi, A.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4(12), 862–868 (2010).
[Crossref]

Dinu, M.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[Crossref]

Drake, J.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Duchesne, D.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[Crossref]

Dulkeith, E.

Eades, D.

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. F. Krauss, and B. J. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat Commun. 5, 3160 (2014).
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A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. F. Krauss, and B. J. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat Commun. 5, 3160 (2014).
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B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640Gb/s using slow-light,” Opt. Express 18(8), 7770–7781 (2010).
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D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett. 96(6), 061101 (2010).
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D. T. H. Tan, P. C. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat Commun. 1(8), 116 (2010).
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M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
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Fukada, H.

Gaeta, A. L.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nature Photon. 7(8), 597–607 (2013).
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A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
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M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
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M. A. Foster, K. D. Moll, and A. L. Gaeta, “Optimal waveguide dimensions for nonlinear interactions,” Opt. Express 12(13), 2880–2887 (2004).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
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M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
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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).
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J. Gosciniak and D. T. H. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24(18), 185202 (2013).
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Green, W. M. J.

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
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Gu, T.

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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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. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
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S. Hong, J. I. Dadap, N. Petrone, P. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).

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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C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321(5887), 385–388 (2008).
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S. Hong, J. I. Dadap, N. Petrone, P. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).

Hsieh, I.-W.

Hu, X.

B. Y. Zhang, T. Liu, B. Meng, X. Li, G. Liang, X. Hu, and Q. J. Wang, “Broadband high photoresponse from pure monolayer graphene photodetector,” Nat Commun. 4, 1811 (2013).
[Crossref] [PubMed]

Huang, H.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant Two-Photon Absorption in Bilayer Graphene,” Nano Lett. 11(7), 2622–2627 (2011).
[Crossref] [PubMed]

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A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. F. Krauss, and B. J. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat Commun. 5, 3160 (2014).
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P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4(12), 862–868 (2010).
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D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett. 96(6), 061101 (2010).
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Itabashi, S.

Ji, W.

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Ju, L.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Katsnelson, M. I.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Kockaert, P.

Krauss, T. F.

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. F. Krauss, and B. J. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat Commun. 5, 3160 (2014).
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B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640Gb/s using slow-light,” Opt. Express 18(8), 7770–7781 (2010).
[Crossref] [PubMed]

Kwong, D. L.

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]

Kysar, J. W.

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321(5887), 385–388 (2008).
[Crossref] [PubMed]

Lau, C. N.

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]

Lee, C.

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321(5887), 385–388 (2008).
[Crossref] [PubMed]

Li, J.

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. F. Krauss, and B. J. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat Commun. 5, 3160 (2014).
[Crossref] [PubMed]

Li, X.

B. Y. Zhang, T. Liu, B. Meng, X. Li, G. Liang, X. Hu, and Q. J. Wang, “Broadband high photoresponse from pure monolayer graphene photodetector,” Nat Commun. 4, 1811 (2013).
[Crossref] [PubMed]

Li, Y.

Y. Li, B. A. Malomed, J. Wu, W. Pang, S. Wang, and J. Zhou, “Quasi-compactons in inverted nonlinear photonic crystals,” Phys. Rev. A 84(4), 043839 (2011).
[Crossref]

Liang, G.

B. Y. Zhang, T. Liu, B. Meng, X. Li, G. Liang, X. Hu, and Q. J. Wang, “Broadband high photoresponse from pure monolayer graphene photodetector,” Nat Commun. 4, 1811 (2013).
[Crossref] [PubMed]

Liang, T. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
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Lipson, M.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nature Photon. 7(8), 597–607 (2013).
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J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17(6), 4752–4757 (2009).
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A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
[Crossref] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[Crossref] [PubMed]

Liscidini, M.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[Crossref]

Little, B. E.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[Crossref]

Liu, M.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Liu, T.

B. Y. Zhang, T. Liu, B. Meng, X. Li, G. Liang, X. Hu, and Q. J. Wang, “Broadband high photoresponse from pure monolayer graphene photodetector,” Nat Commun. 4, 1811 (2013).
[Crossref] [PubMed]

Liu, X.

Lo, G. Q.

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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Malomed, B. A.

Y. Li, B. A. Malomed, J. Wu, W. Pang, S. Wang, and J. Zhou, “Quasi-compactons in inverted nonlinear photonic crystals,” Phys. Rev. A 84(4), 043839 (2011).
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Marini, A.

Martin-Moreno, L.

M. L. Nesterov, J. Bravo-Abad, A. Y. Nikitin, F. J. García-Vidal, and L. Martin-Moreno, “Graphene supports the propagation of subwavelength optical soltions,” Laser Photon. Rev. 7(2), L7–L11 (2013).
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Massar, S.

McMillan, J. F.

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]

Meng, B.

B. Y. Zhang, T. Liu, B. Meng, X. Li, G. Liang, X. Hu, and Q. J. Wang, “Broadband high photoresponse from pure monolayer graphene photodetector,” Nat Commun. 4, 1811 (2013).
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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]

Mikhailov, S. A.

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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S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys. Condens. Matter 20(38), 384204 (2008).
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S. A. Mikhailov, “Non-linear electromagnetic response of graphene,” Europhys. Lett. 79(2), 27002 (2007).
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S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99(1), 016803 (2007).
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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).
[Crossref] [PubMed]

Moll, K. D.

Monat, C.

Morandotti, R.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nature Photon. 7(8), 597–607 (2013).
[Crossref]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[Crossref]

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Moss, D. J.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nature Photon. 7(8), 597–607 (2013).
[Crossref]

B. Corcoran, C. Monat, M. Pelusi, C. Grillet, T. P. White, L. O’Faolain, T. F. Krauss, B. J. Eggleton, and D. J. Moss, “Optical signal processing on a silicon chip at 640Gb/s using slow-light,” Opt. Express 18(8), 7770–7781 (2010).
[Crossref] [PubMed]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[Crossref]

Mueller, T.

T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4(5), 297–301 (2010).
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M. L. Nesterov, J. Bravo-Abad, A. Y. Nikitin, F. J. García-Vidal, and L. Martin-Moreno, “Graphene supports the propagation of subwavelength optical soltions,” Laser Photon. Rev. 7(2), L7–L11 (2013).
[Crossref]

Nikitin, A. Y.

M. L. Nesterov, J. Bravo-Abad, A. Y. Nikitin, F. J. García-Vidal, and L. Martin-Moreno, “Graphene supports the propagation of subwavelength optical soltions,” Laser Photon. Rev. 7(2), L7–L11 (2013).
[Crossref]

Novoselov, K. S.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

O’Faolain, L.

Osgood, R. M.

Pang, W.

Y. Li, B. A. Malomed, J. Wu, W. Pang, S. Wang, and J. Zhou, “Quasi-compactons in inverted nonlinear photonic crystals,” Phys. Rev. A 84(4), 043839 (2011).
[Crossref]

Panoiu, N. C.

Pelusi, M.

Petrone, N.

S. Hong, J. I. Dadap, N. Petrone, P. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).

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]

Ping, L. K.

Poitras, C. B.

Premaratne, M.

Preston, K.

Qian, G.

Quochi, F.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[Crossref]

Razzari, L.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[Crossref]

Roberts, S. W.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

Robinson, J. T.

Rukhlenko, I. D.

Sagnes, I.

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4(12), 862–868 (2010).
[Crossref]

Savchenko, A. K.

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]

Schmidt, B. S.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[Crossref] [PubMed]

Sharping, J. E.

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[Crossref] [PubMed]

Shirane, M.

H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, “Nonlinear-optic silicon-nanowire waveguides,” Jpn. J. Appl. Phys. 44, 6541–6545 (2005).

Shoji, T.

Sipe, J. E.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[Crossref]

Skryabin, D. V.

Sun, P. C.

D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett. 96(6), 061101 (2010).
[Crossref]

D. T. H. Tan, P. C. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat Commun. 1(8), 116 (2010).
[Crossref] [PubMed]

Takahashi, J.

Takahashi, M.

Tan, D. T. H.

J. Gosciniak and D. T. H. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24(18), 185202 (2013).
[Crossref] [PubMed]

T. Wang, N. Venkatram, J. Gosciniak, Y. Cui, G. Qian, W. Ji, and D. T. H. Tan, “Multi-photon absorption and third-order nonlinearity in silicon at mid-infrared wavelengths,” Opt. Express 21(26), 32192–32198 (2013).
[Crossref] [PubMed]

J. Gosciniak and D. T. H. Tan, “Theoretical investigation of graphene-based photonic modulators,” Sci Rep. 3, 1897 (2013).
[Crossref] [PubMed]

D. T. H. Tan, “Optical pulse compression on a silicon chip – Effect of group velocity dispersion and free carriers,” Appl. Phys. Lett. 101(21), 211112 (2012).
[Crossref]

D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett. 96(6), 061101 (2010).
[Crossref]

D. T. H. Tan, P. C. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat Commun. 1(8), 116 (2010).
[Crossref] [PubMed]

Teweldebrhan, D.

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]

Tsang, H. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

Tsuchizawa, T.

Turner, A. C.

A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express 16(7), 4881–4887 (2008).
[Crossref] [PubMed]

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[Crossref] [PubMed]

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Van Der Zande, A.

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]

Venkatram, N.

Virally, S.

Vlasov, Y. A.

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Wang, Q.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant Two-Photon Absorption in Bilayer Graphene,” Nano Lett. 11(7), 2622–2627 (2011).
[Crossref] [PubMed]

Wang, Q. J.

B. Y. Zhang, T. Liu, B. Meng, X. Li, G. Liang, X. Hu, and Q. J. Wang, “Broadband high photoresponse from pure monolayer graphene photodetector,” Nat Commun. 4, 1811 (2013).
[Crossref] [PubMed]

Wang, S.

Y. Li, B. A. Malomed, J. Wu, W. Pang, S. Wang, and J. Zhou, “Quasi-compactons in inverted nonlinear photonic crystals,” Phys. Rev. A 84(4), 043839 (2011).
[Crossref]

Wang, T.

Watanabe, T.

Wee, A. T.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant Two-Photon Absorption in Bilayer Graphene,” Nano Lett. 11(7), 2622–2627 (2011).
[Crossref] [PubMed]

Wei, X.

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321(5887), 385–388 (2008).
[Crossref] [PubMed]

White, T. P.

Wong, C. S.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

Wong, C. W.

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]

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4(12), 862–868 (2010).
[Crossref]

Wu, J.

Y. Li, B. A. Malomed, J. Wu, W. Pang, S. Wang, and J. Zhou, “Quasi-compactons in inverted nonlinear photonic crystals,” Phys. Rev. A 84(4), 043839 (2011).
[Crossref]

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T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4(5), 297–301 (2010).
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H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, “Nonlinear-optic silicon-nanowire waveguides,” Jpn. J. Appl. Phys. 44, 6541–6545 (2005).

Yamada, K.

Yang, H.

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant Two-Photon Absorption in Bilayer Graphene,” Nano Lett. 11(7), 2622–2627 (2011).
[Crossref] [PubMed]

Yang, Z.

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[Crossref]

Yeh, P.

S. Hong, J. I. Dadap, N. Petrone, P. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Yokoyama, H.

H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, “Nonlinear-optic silicon-nanowire waveguides,” Jpn. J. Appl. Phys. 44, 6541–6545 (2005).

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).
[Crossref]

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Zhang, B. Y.

B. Y. Zhang, T. Liu, B. Meng, X. Li, G. Liang, X. Hu, and Q. J. Wang, “Broadband high photoresponse from pure monolayer graphene photodetector,” Nat Commun. 4, 1811 (2013).
[Crossref] [PubMed]

Zhang, H.

Zhang, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Zhang, Y.

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. F. Krauss, and B. J. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat Commun. 5, 3160 (2014).
[Crossref] [PubMed]

Zhou, J.

Y. Li, B. A. Malomed, J. Wu, W. Pang, S. Wang, and J. Zhou, “Quasi-compactons in inverted nonlinear photonic crystals,” Phys. Rev. A 84(4), 043839 (2011).
[Crossref]

Ziegler, K.

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys. Condens. Matter 20(38), 384204 (2008).
[Crossref] [PubMed]

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99(1), 016803 (2007).
[Crossref] [PubMed]

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (4)

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003).
[Crossref]

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari, “Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 μm wavelength,” Appl. Phys. Lett. 80(3), 416–418 (2002).
[Crossref]

D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, “Group velocity dispersion and self phase modulation in silicon nitride waveguides,” Appl. Phys. Lett. 96(6), 061101 (2010).
[Crossref]

D. T. H. Tan, “Optical pulse compression on a silicon chip – Effect of group velocity dispersion and free carriers,” Appl. Phys. Lett. 101(21), 211112 (2012).
[Crossref]

Europhys. Lett. (1)

S. A. Mikhailov, “Non-linear electromagnetic response of graphene,” Europhys. Lett. 79(2), 27002 (2007).
[Crossref]

J. Phys. Condens. Matter (1)

S. A. Mikhailov and K. Ziegler, “Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects,” J. Phys. Condens. Matter 20(38), 384204 (2008).
[Crossref] [PubMed]

Jpn. J. Appl. Phys. (1)

H. Yamada, M. Shirane, T. Chu, H. Yokoyama, S. Ishida, and Y. Arakawa, “Nonlinear-optic silicon-nanowire waveguides,” Jpn. J. Appl. Phys. 44, 6541–6545 (2005).

Laser Photon. Rev. (1)

M. L. Nesterov, J. Bravo-Abad, A. Y. Nikitin, F. J. García-Vidal, and L. Martin-Moreno, “Graphene supports the propagation of subwavelength optical soltions,” Laser Photon. Rev. 7(2), L7–L11 (2013).
[Crossref]

Nano Lett. (2)

H. Yang, X. Feng, Q. Wang, H. Huang, W. Chen, A. T. Wee, and W. Ji, “Giant Two-Photon Absorption in Bilayer Graphene,” Nano Lett. 11(7), 2622–2627 (2011).
[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]

Nanotechnology (1)

J. Gosciniak and D. T. H. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24(18), 185202 (2013).
[Crossref] [PubMed]

Nat Commun. (3)

B. Y. Zhang, T. Liu, B. Meng, X. Li, G. Liang, X. Hu, and Q. J. Wang, “Broadband high photoresponse from pure monolayer graphene photodetector,” Nat Commun. 4, 1811 (2013).
[Crossref] [PubMed]

A. Blanco-Redondo, C. Husko, D. Eades, Y. Zhang, J. Li, T. F. Krauss, and B. J. Eggleton, “Observation of soliton compression in silicon photonic crystals,” Nat Commun. 5, 3160 (2014).
[Crossref] [PubMed]

D. T. H. Tan, P. C. Sun, and Y. Fainman, “Monolithic nonlinear pulse compressor on a silicon chip,” Nat Commun. 1(8), 116 (2010).
[Crossref] [PubMed]

Nat. Photonics (5)

P. Colman, C. Husko, S. Combrié, I. Sagnes, C. W. Wong, and A. De Rossi, “Temporal solitons and pulse compression in photonic crystal waveguides,” Nat. Photonics 4(12), 862–868 (2010).
[Crossref]

M. Ferrera, L. Razzari, D. Duchesne, R. Morandotti, Z. Yang, M. Liscidini, J. E. Sipe, S. Chu, B. E. Little, and D. J. Moss, “Low-power continuous-wave nonlinear optics in doped silica glass integrated waveguide structures,” Nat. Photonics 2(12), 737–740 (2008).
[Crossref]

T. Mueller, F. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4(5), 297–301 (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).
[Crossref]

X. Liu, R. M. Osgood, Y. A. Vlasov, and W. M. J. Green, “Mid-infrared optical parametric amplifier using silicon nanophotonic waveguides,” Nat. Photonics 4(8), 557–560 (2010).
[Crossref]

Nature (3)

M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441(7096), 960–963 (2006).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref] [PubMed]

Nature Photon. (1)

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nature Photon. 7(8), 597–607 (2013).
[Crossref]

Opt. Express (7)

Opt. Lett. (3)

Phys. Rev. A (1)

Y. Li, B. A. Malomed, J. Wu, W. Pang, S. Wang, and J. Zhou, “Quasi-compactons in inverted nonlinear photonic crystals,” Phys. Rev. A 84(4), 043839 (2011).
[Crossref]

Phys. Rev. Lett. (2)

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99(1), 016803 (2007).
[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]

Phys. Rev. X (1)

S. Hong, J. I. Dadap, N. Petrone, P. Yeh, J. Hone, and R. M. Osgood, “Optical third-harmonic generation in graphene,” Phys. Rev. X 3, 021014 (2013).

Sci Rep. (1)

J. Gosciniak and D. T. H. Tan, “Theoretical investigation of graphene-based photonic modulators,” Sci Rep. 3, 1897 (2013).
[Crossref] [PubMed]

Science (1)

C. Lee, X. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic properties and intrinsic strength of monolayer graphene,” Science 321(5887), 385–388 (2008).
[Crossref] [PubMed]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

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Figures (4)

Fig. 1
Fig. 1

Schematic of (a) SU8 channel waveguide with graphene monolayer in the center (quasi-TE mode of a typical waveguide is shown), (b) silicon channel waveguide with graphene monolayer (quasi-TE mode of a typical waveguide is shown) and (c) DLSPP waveguide consisting of a silicon core, graphene monolayer and 50nm gold layer (TM mode of a typical waveguide is shown).

Fig. 2
Fig. 2

Nonlinear parameter as a function of waveguide width and height for the SU-8 channel waveguide incorporating graphene for the (a) quasi-TE mode and (b) quasi-TM mode. Color bar shows the value of the nonlinear parameter (W−1/m).

Fig. 3
Fig. 3

Nonlinear parameter as a function of waveguide width and height for the graphene-Si channel waveguide incorporating graphene. (a) quasi-TE mode and (b) quasi-TM mode. Color bars show the magnitude of the nonlinear parameter (W−1/m).

Fig. 4
Fig. 4

Nonlinear parameter and (W−1/m) as a function of waveguide width and height for silicon based dielectric loaded surface plasmon polariton waveguide incorporating graphene.

Equations (4)

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

ϕ ( z ) = β ( ω ) z + β N L ( I ) z = ω z ( n o + n 2 I ) c
I = P A e f f
A e f f = ( D S z d x d y ) 2 D S z 2 d x d y
γ = 2 π λ D S z 2 n 2 ( x , y ) d x d y ( D S z d x d y ) 2

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