Abstract

We study linear and nonlinear mode properties in a periodically patterned graphene sheet. We demonstrate that a subwavelength one-dimensional photonic lattice can be defined across the graphene monolayer, with its modulation depth and correspondingly the associated photonic band structures being controlled rapidly, by an external gate voltage. We find the existences of graphene lattice solitons at the deep-subwavelength scales in both dimensions, thanks to the combination of graphene intrinsic self-focusing nonlinearity and the graphene plasmonic confinement effects.

© 2014 Optical Society of America

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2014 (4)

T. J. Echtermeyer, P. Nene, M. Trushin, R. V. Gorbachev, A. Eiden, S. Milana, Z. Sun, J. Schliemann, E. Lidorikis, K. S. Novoselov, and A. C. Ferrari, “Photo-thermoelectric and photoelectric contributions to light detection in metal-graphene-metal photodetectors,” Nano Lett. 14, 3733–3742 (2014).
[Crossref] [PubMed]

D. A. Smirnova, I. V. Shadrivov, A. I. Smirnov, and Y. S. Kivshar, “Dissipative plasmon-solitons in multiplayer graphene,” Laser Photon. Rev. 8, 291–296 (2014).
[Crossref]

Y. Xue, F. Ye, D. Mihalache, N. C. Panoiu, and X. Chen, “Plasmonic lattice solitons beyond the coupled-mode theory,” Laser Photon. Rev. 8, L52–L57 (2014).
[Crossref]

C. Donnelly and D. T. H. Tan, “Ultra-large nonlinear parameter in graphene-silicon waveguide structures,” Opt. Express 22, 22820–22830 (2014).
[Crossref] [PubMed]

2013 (8)

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

P. Liu, X. Zhang, Z. Ma, W. Cai, L. Wang, and J. Xu, “Surface plasmon modes in graphene wedge and groove wavegudies,” Opt. Express 21, 32432–32440 (2013).
[Crossref]

M. G. Silveirinha, “Effective medium reponse of metallic nanowire arrays with a Kerr-type dielectric host,” Phys. Rev. B 87, 165127 (2013).
[Crossref]

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. Gullans, D. E. Chang, F. H. L. Koppens, F. J. G. Abajo, and M. D. Lukin, “Single-photon nonlinear optics with graphene plasmons,” Phys. Rev. Lett. 111, 247401 (2013).
[Crossref]

A. V. Gorbach, “Nonlinear graphene plasmonics: amplitude equation for surface plasmons,” Phys. Rev. A 87013830 (2013).
[Crossref]

M. L. Nesterov, J. B. Abad, A. Yu. Nikitin, F. J. G. Vidal, and L. M. Moreno, “Graphene supports the propagation of subwavelength optial solitons,” Laser Photon. Rev. 7, L7–L11 (2013).
[Crossref]

A. Martinez and Z. Sun, “Nanotube and graphene saturable absorbers for fibre lasers,” Nat. Photonics 7, 842 (2013).
[Crossref]

2012 (5)

Z. Sun, T. Hasan, and A. C. Ferrari, “Ultrafast lasers mode-locked by nanotubes and graphene,” Physica E 44, 1082 (2012).
[Crossref]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

J. Chen, M. Badioli, P. Alonso-Gonzlez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[Crossref]

T. Gu, N. Petrone, J. F. McMillan, A. V. 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, 554–559 (2012).
[Crossref]

2011 (5)

A. Roberts, D. Cormode, C. Reynolds, T. N. Lige, B. J. Leroy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99, 051912 (2011).
[Crossref]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref] [PubMed]

F. H. L. Koppens, D. E. Chang, and F. J. C. Abajo, “Graphene plasmonics: a platform for strong light-matter interactins,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

A. Yu. Nikitin, F. Guinea, F. J. G. Vidal, and L. M. Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microbbons,” Phys. Rev. B 84, 161407(R) (2011).
[Crossref]

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, 64–67 (2011).
[Crossref] [PubMed]

2010 (4)

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

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

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104, 106802 (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, 097401 (2010).
[Crossref] [PubMed]

2009 (3)

A. V. Gorbach and D. V. Skryabin, “Spatial solitons in periodic nanostructures,” Phys. Rev. A 79, 053812 (2009).
[Crossref]

O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides, and N. Moiseyev, “Nonlinear waves in subwavelength waveguide arrays: evanescent bands and the phoenix solitons,” Phys. Rev. Lett. 102, 163902 (2009).
[Crossref]

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

2008 (1)

2007 (3)

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
[Crossref] [PubMed]

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

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

2006 (1)

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, 666–669 (2004).
[Crossref] [PubMed]

Abad, J. B.

M. L. Nesterov, J. B. Abad, A. Yu. Nikitin, F. J. G. Vidal, and L. M. Moreno, “Graphene supports the propagation of subwavelength optial solitons,” Laser Photon. Rev. 7, L7–L11 (2013).
[Crossref]

Abajo, F. J. C.

F. H. L. Koppens, D. E. Chang, and F. J. C. Abajo, “Graphene plasmonics: a platform for strong light-matter interactins,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

Abajo, F. J. G.

M. Gullans, D. E. Chang, F. H. L. Koppens, F. J. G. Abajo, and M. D. Lukin, “Single-photon nonlinear optics with graphene plasmons,” Phys. Rev. Lett. 111, 247401 (2013).
[Crossref]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[Crossref]

Agrawal, G.

Y. Kivshar and G. Agrawal, Optical Solitons (Academic, 2013).

Alonso-Gonzlez, P.

J. Chen, M. Badioli, P. Alonso-Gonzlez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Andreev, G. O.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Avouris, P.

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

Badioli, M.

J. Chen, M. Badioli, P. Alonso-Gonzlez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Bao, W.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Bartal, G.

O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides, and N. Moiseyev, “Nonlinear waves in subwavelength waveguide arrays: evanescent bands and the phoenix solitons,” Phys. Rev. Lett. 102, 163902 (2009).
[Crossref]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
[Crossref] [PubMed]

Basov, D. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Blomer, D.

Bonaccorso, F.

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

Buljan, H.

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

Cai, W.

Camara, N.

J. Chen, M. Badioli, P. Alonso-Gonzlez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Castro Neto, A. H.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Centeno, A.

J. Chen, M. Badioli, P. Alonso-Gonzlez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Chang, D. E.

M. Gullans, D. E. Chang, F. H. L. Koppens, F. J. G. Abajo, and M. D. Lukin, “Single-photon nonlinear optics with graphene plasmons,” Phys. Rev. Lett. 111, 247401 (2013).
[Crossref]

F. H. L. Koppens, D. E. Chang, and F. J. C. Abajo, “Graphene plasmonics: a platform for strong light-matter interactins,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

Chen, J.

J. Chen, M. Badioli, P. Alonso-Gonzlez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Chen, X.

Y. Xue, F. Ye, D. Mihalache, N. C. Panoiu, and X. Chen, “Plasmonic lattice solitons beyond the coupled-mode theory,” Laser Photon. Rev. 8, L52–L57 (2014).
[Crossref]

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[Crossref]

Christodoulides, D. N.

O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides, and N. Moiseyev, “Nonlinear waves in subwavelength waveguide arrays: evanescent bands and the phoenix solitons,” Phys. Rev. Lett. 102, 163902 (2009).
[Crossref]

Ciattoni, A.

A. Ciattoni and C. Rizza, “Highly nonlinear optical regime in graphene-assisted cavities: lasing threhold bares graphene nonlinearity,” arXiv:1403.0831 (2014).

Cormode, D.

A. Roberts, D. Cormode, C. Reynolds, T. N. Lige, B. J. Leroy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99, 051912 (2011).
[Crossref]

Dadap, J. I.

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).

de Abajo, F. J. G.

J. Chen, M. Badioli, P. Alonso-Gonzlez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Dominguez, G.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Donnelly, C.

Dreisow, F.

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Novoselov, K. S.

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[Crossref] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
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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, 666–669 (2004).
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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).

Osmond, J.

J. Chen, M. Badioli, P. Alonso-Gonzlez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

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Y. Xue, F. Ye, D. Mihalache, N. C. Panoiu, and X. Chen, “Plasmonic lattice solitons beyond the coupled-mode theory,” Laser Photon. Rev. 8, L52–L57 (2014).
[Crossref]

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O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides, and N. Moiseyev, “Nonlinear waves in subwavelength waveguide arrays: evanescent bands and the phoenix solitons,” Phys. Rev. Lett. 102, 163902 (2009).
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J. Chen, M. Badioli, P. Alonso-Gonzlez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
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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. V. 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, 554–559 (2012).
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A. Roberts, D. Cormode, C. Reynolds, T. N. Lige, B. J. Leroy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99, 051912 (2011).
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Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
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A. Roberts, D. Cormode, C. Reynolds, T. N. Lige, B. J. Leroy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99, 051912 (2011).
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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, 097401 (2010).
[Crossref] [PubMed]

Schliemann, J.

T. J. Echtermeyer, P. Nene, M. Trushin, R. V. Gorbachev, A. Eiden, S. Milana, Z. Sun, J. Schliemann, E. Lidorikis, K. S. Novoselov, and A. C. Ferrari, “Photo-thermoelectric and photoelectric contributions to light detection in metal-graphene-metal photodetectors,” Nano Lett. 14, 3733–3742 (2014).
[Crossref] [PubMed]

Schreiber, T.

Segev, M.

O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides, and N. Moiseyev, “Nonlinear waves in subwavelength waveguide arrays: evanescent bands and the phoenix solitons,” Phys. Rev. Lett. 102, 163902 (2009).
[Crossref]

Shadrivov, I. V.

D. A. Smirnova, I. V. Shadrivov, A. I. Smirnov, and Y. S. Kivshar, “Dissipative plasmon-solitons in multiplayer graphene,” Laser Photon. Rev. 8, 291–296 (2014).
[Crossref]

Silveirinha, M. G.

M. G. Silveirinha, “Effective medium reponse of metallic nanowire arrays with a Kerr-type dielectric host,” Phys. Rev. B 87, 165127 (2013).
[Crossref]

Skryabin, D. V.

Smirnov, A. I.

D. A. Smirnova, I. V. Shadrivov, A. I. Smirnov, and Y. S. Kivshar, “Dissipative plasmon-solitons in multiplayer graphene,” Laser Photon. Rev. 8, 291–296 (2014).
[Crossref]

Smirnova, D. A.

D. A. Smirnova, I. V. Shadrivov, A. I. Smirnov, and Y. S. Kivshar, “Dissipative plasmon-solitons in multiplayer graphene,” Laser Photon. Rev. 8, 291–296 (2014).
[Crossref]

Soljacic, M.

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

Spasenovic, M.

J. Chen, M. Badioli, P. Alonso-Gonzlez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Sun, Z.

T. J. Echtermeyer, P. Nene, M. Trushin, R. V. Gorbachev, A. Eiden, S. Milana, Z. Sun, J. Schliemann, E. Lidorikis, K. S. Novoselov, and A. C. Ferrari, “Photo-thermoelectric and photoelectric contributions to light detection in metal-graphene-metal photodetectors,” Nano Lett. 14, 3733–3742 (2014).
[Crossref] [PubMed]

A. Martinez and Z. Sun, “Nanotube and graphene saturable absorbers for fibre lasers,” Nat. Photonics 7, 842 (2013).
[Crossref]

Z. Sun, T. Hasan, and A. C. Ferrari, “Ultrafast lasers mode-locked by nanotubes and graphene,” Physica E 44, 1082 (2012).
[Crossref]

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

Szameit, A.

Tan, D. T. H.

Thiemens, M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Thongrattanasiri, S.

J. Chen, M. Badioli, P. Alonso-Gonzlez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[Crossref]

Torner, L.

Trushin, M.

T. J. Echtermeyer, P. Nene, M. Trushin, R. V. Gorbachev, A. Eiden, S. Milana, Z. Sun, J. Schliemann, E. Lidorikis, K. S. Novoselov, and A. C. Ferrari, “Photo-thermoelectric and photoelectric contributions to light detection in metal-graphene-metal photodetectors,” Nano Lett. 14, 3733–3742 (2014).
[Crossref] [PubMed]

Tunnermann, A.

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, 64–67 (2011).
[Crossref] [PubMed]

Vakil, A.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref] [PubMed]

Vidal, F. J. G.

M. L. Nesterov, J. B. Abad, A. Yu. Nikitin, F. J. G. Vidal, and L. M. Moreno, “Graphene supports the propagation of subwavelength optial solitons,” Laser Photon. Rev. 7, L7–L11 (2013).
[Crossref]

A. Yu. Nikitin, F. Guinea, F. J. G. Vidal, and L. M. Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microbbons,” Phys. Rev. B 84, 161407(R) (2011).
[Crossref]

Vysloukh, V. A.

Wagner, M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

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, 64–67 (2011).
[Crossref] [PubMed]

Wang, L.

Wong, C. W.

T. Gu, N. Petrone, J. F. McMillan, A. V. 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, 554–559 (2012).
[Crossref]

Xia, F.

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

Xu, J.

Xue, Y.

Y. Xue, F. Ye, D. Mihalache, N. C. Panoiu, and X. Chen, “Plasmonic lattice solitons beyond the coupled-mode theory,” Laser Photon. Rev. 8, L52–L57 (2014).
[Crossref]

Ye, F.

Y. Xue, F. Ye, D. Mihalache, N. C. Panoiu, and X. Chen, “Plasmonic lattice solitons beyond the coupled-mode theory,” Laser Photon. Rev. 8, L52–L57 (2014).
[Crossref]

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104, 106802 (2010).
[Crossref] [PubMed]

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, 64–67 (2011).
[Crossref] [PubMed]

Yu, M.

T. Gu, N. Petrone, J. F. McMillan, A. V. 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, 554–559 (2012).
[Crossref]

Zande, A. V.

T. Gu, N. Petrone, J. F. McMillan, A. V. 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, 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, 64–67 (2011).
[Crossref] [PubMed]

Zhang, L. M.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

Zhang, X.

P. Liu, X. Zhang, Z. Ma, W. Cai, L. Wang, and J. Xu, “Surface plasmon modes in graphene wedge and groove wavegudies,” Opt. Express 21, 32432–32440 (2013).
[Crossref]

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, 64–67 (2011).
[Crossref] [PubMed]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
[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, 666–669 (2004).
[Crossref] [PubMed]

Zhao, Z.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

ACS Nano (1)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6, 431–440 (2012).
[Crossref]

Appl. Phys. Lett. (1)

A. Roberts, D. Cormode, C. Reynolds, T. N. Lige, B. J. Leroy, and A. S. Sandhu, “Response of graphene to femtosecond high-intensity laser irradiation,” Appl. Phys. Lett. 99, 051912 (2011).
[Crossref]

Europhys. Lett. (1)

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

Laser Photon. Rev. (3)

Y. Xue, F. Ye, D. Mihalache, N. C. Panoiu, and X. Chen, “Plasmonic lattice solitons beyond the coupled-mode theory,” Laser Photon. Rev. 8, L52–L57 (2014).
[Crossref]

M. L. Nesterov, J. B. Abad, A. Yu. Nikitin, F. J. G. Vidal, and L. M. Moreno, “Graphene supports the propagation of subwavelength optial solitons,” Laser Photon. Rev. 7, L7–L11 (2013).
[Crossref]

D. A. Smirnova, I. V. Shadrivov, A. I. Smirnov, and Y. S. Kivshar, “Dissipative plasmon-solitons in multiplayer graphene,” Laser Photon. Rev. 8, 291–296 (2014).
[Crossref]

Nano Lett. (2)

F. H. L. Koppens, D. E. Chang, and F. J. C. Abajo, “Graphene plasmonics: a platform for strong light-matter interactins,” Nano Lett. 11, 3370–3377 (2011).
[Crossref] [PubMed]

T. J. Echtermeyer, P. Nene, M. Trushin, R. V. Gorbachev, A. Eiden, S. Milana, Z. Sun, J. Schliemann, E. Lidorikis, K. S. Novoselov, and A. C. Ferrari, “Photo-thermoelectric and photoelectric contributions to light detection in metal-graphene-metal photodetectors,” Nano Lett. 14, 3733–3742 (2014).
[Crossref] [PubMed]

Nat. Mater. (1)

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

Nat. Photonics (4)

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

A. Martinez and Z. Sun, “Nanotube and graphene saturable absorbers for fibre lasers,” Nat. Photonics 7, 842 (2013).
[Crossref]

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

T. Gu, N. Petrone, J. F. McMillan, A. V. 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, 554–559 (2012).
[Crossref]

Nature (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, 64–67 (2011).
[Crossref] [PubMed]

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487, 82–85 (2012).
[PubMed]

J. Chen, M. Badioli, P. Alonso-Gonzlez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. G. de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
[PubMed]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. A (2)

A. V. Gorbach and D. V. Skryabin, “Spatial solitons in periodic nanostructures,” Phys. Rev. A 79, 053812 (2009).
[Crossref]

A. V. Gorbach, “Nonlinear graphene plasmonics: amplitude equation for surface plasmons,” Phys. Rev. A 87013830 (2013).
[Crossref]

Phys. Rev. B (3)

A. Yu. Nikitin, F. Guinea, F. J. G. Vidal, and L. M. Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microbbons,” Phys. Rev. B 84, 161407(R) (2011).
[Crossref]

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

M. G. Silveirinha, “Effective medium reponse of metallic nanowire arrays with a Kerr-type dielectric host,” Phys. Rev. B 87, 165127 (2013).
[Crossref]

Phys. Rev. Lett. (5)

O. Peleg, M. Segev, G. Bartal, D. N. Christodoulides, and N. Moiseyev, “Nonlinear waves in subwavelength waveguide arrays: evanescent bands and the phoenix solitons,” Phys. Rev. Lett. 102, 163902 (2009).
[Crossref]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99, 153901 (2007).
[Crossref] [PubMed]

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104, 106802 (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, 097401 (2010).
[Crossref] [PubMed]

M. Gullans, D. E. Chang, F. H. L. Koppens, F. J. G. Abajo, and M. D. Lukin, “Single-photon nonlinear optics with graphene plasmons,” Phys. Rev. Lett. 111, 247401 (2013).
[Crossref]

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).

Physica E (1)

Z. Sun, T. Hasan, and A. C. Ferrari, “Ultrafast lasers mode-locked by nanotubes and graphene,” Physica E 44, 1082 (2012).
[Crossref]

Science (2)

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, 666–669 (2004).
[Crossref] [PubMed]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref] [PubMed]

Other (3)

A. Ciattoni and C. Rizza, “Highly nonlinear optical regime in graphene-assisted cavities: lasing threhold bares graphene nonlinearity,” arXiv:1403.0831 (2014).

Y. Kivshar and G. Agrawal, Optical Solitons (Academic, 2013).

http://www.comsol.com .

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Figures (4)

Fig. 1
Fig. 1 (a) Surface corrugated ground plane for achieving a conductivity modulation. (b, c) The band structure of the patterned graphene at chemical potential μ c 0 = 0.3 ev (b) and 0.5 ev (c). (d) Evolution of the bandeges versus chemical potential. Solid lines stand for βr, and dashed for βi. (e, f) The Bloch mode profiles at the first (e) and second bands (f), corresponding to the points labelled in (b). D = 400 nm, λ = 10μm.
Fig. 2
Fig. 2 Profiles of a typical soliton at the semi-infinite gap. (a) and (b) show the transverse distributions of the amplitude (a) and imaginary part of Ez (b) of the electric component of soliton, respectively. (c) and (d) show the 1D profile of soliton along x axis (at y = 0) (c) and y axis (at x = 0), respectively. D = 400 nm, λ = 10μm, δεg = 4.
Fig. 3
Fig. 3 Propagation constants (a,d), effective width (b, e) and power (c, f) for soltions in semi-infinite gap (left column) and the first- finite gap (right column). D = 400 nm, λ = 10μm.
Fig. 4
Fig. 4 Profiles of a typical soliton in the first-finite gap. (a) and (b) show the transverse distributions of the amplitude (a) and imaginary part of Ez (b) of the electric component of soliton, respectively. (c) and (d) show the 1D profile of soliton along x axis(at y = 0) (c) and y axis (at x = 0). D = 400 nm, λ = 10μm, δεg = 6.

Equations (4)

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

μ c ( y ) = h ¯ V F π n ( y ) = h ¯ V F π ε 0 V bias ed = h ¯ V F π ε 0 V bias ed 0 [ 1 + a d 0 cos ( 2 π y / D ) ] μ c 0 [ 1 a 2 d 0 cos ( 2 π y / D ) ] = μ c 0 μ c 0 a 2 d 0 cos ( 2 π y / D ) ,
ε 1 = 1 η 0 k 0 Δ e 2 μ c 0 π h ¯ 2 ( ω + i τ 1 ) [ 1 a 2 d 0 cos ( 2 π y / D ) ] = 1 η 0 k 0 Δ e 2 μ c 0 π h ¯ 2 ( ω + i τ 1 ) + η 0 k 0 Δ e 2 μ c 0 π h ¯ 2 ( ω + i τ 1 ) a 2 d 0 cos ( 2 π y / D )
σ 3 = i 3 32 e 4 V F 2 π μ c h ¯ 2 ω 3 ,
ε g = 1 + i σ g η 0 k 0 Δ = 1 + i η 0 k 0 Δ ( σ 1 + σ 3 | E | 2 ) = ε 1 + χ g ( 3 ) | E | 2 ,

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