Abstract

We investigate the plasmonic lattice solitons (PLSs) in nonlinear graphene sheet arrays (GSAs) composed of spatially separated graphene sheets embedded in dielectric. Both the nonlinearities of graphene and dielectric are considered. The self-focusing PLSs at the Brillouin zone edges can be yielded by balancing the normal diffraction of surface plasmon polaritons (SPPs) via either the nonlinear effect of graphene or self-focusing dielectric. The self-defocusing PLSs corresponding to anomalous diffraction of SPPs at the Brillouin zone center could be yielded by the nonlinearity of self-defocusing dielectric alone. The width and propagation distance of the PLSs are dependent on the period of the GSAs and the chemical potential of graphene. Thanks to the strong confinement of SPPs, the PLSs in GSAs can be squeezed into an effective width as small as λ/250. The study may find applications in optical circuits and switches on deep-subwavelength scale.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Surface vector plasmonic lattice solitons in semi-infinite graphene-pair arrays

Zhouqing Wang, Bing Wang, Hua Long, Kai Wang, and Peixiang Lu
Opt. Express 25(17) 20708-20717 (2017)

Vector plasmonic lattice solitons in nonlinear graphene-pair arrays

Zhouqing Wang, Bing Wang, Kai Wang, Hua Long, and Peixiang Lu
Opt. Lett. 41(15) 3619-3622 (2016)

Tunable subwavelength photonic lattices and solitons in periodically patterned graphene monolayer

Changming Huang, Fangwei Ye, Zhipei Sun, and Xianfeng Chen
Opt. Express 22(24) 30108-30117 (2014)

References

  • View by:
  • |
  • |
  • |

  1. V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34(1), 62–69 (1972).
  2. H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
    [Crossref]
  3. Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
    [Crossref] [PubMed]
  4. S. Blair and K. Wagner, “Spatial soliton angular deflection logic gates,” Appl. Opt. 38(32), 6749–6772 (1999).
    [Crossref] [PubMed]
  5. D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13(9), 794–796 (1988).
    [Crossref] [PubMed]
  6. Y. S. Kivshar, “Self-localization in arrays of defocusing waveguides,” Opt. Lett. 18(14), 1147–1149 (1993).
    [Crossref] [PubMed]
  7. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
    [Crossref] [PubMed]
  8. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (2003).
    [Crossref] [PubMed]
  9. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
    [Crossref] [PubMed]
  10. E. Feigenbaum and M. Orenstein, “Plasmon-soliton,” Opt. Lett. 32(6), 674–676 (2007).
    [Crossref] [PubMed]
  11. Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
    [Crossref] [PubMed]
  12. F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
    [Crossref] [PubMed]
  13. I. V. Irosh, P. A. Belov, A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear Tamm states in nanostructured plasmonic metamaterials,” Phys. Rev. A 86(2), 023819 (2012).
    [Crossref]
  14. Y. Kou, F. Ye, and X. Chen, “Multiband vector plasmonic lattice solitons,” Opt. Lett. 38(8), 1271–1273 (2013).
    [Crossref] [PubMed]
  15. 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]
  16. Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
    [Crossref] [PubMed]
  17. C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
    [Crossref] [PubMed]
  18. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
    [Crossref] [PubMed]
  19. A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81(1), 109–162 (2009).
    [Crossref]
  20. A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
    [Crossref] [PubMed]
  21. F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
    [Crossref]
  22. H. Huang, B. Wang, H. Long, K. Wang, and P. Lu, “Plasmon-negative refraction at the heterointerface of graphene sheet arrays,” Opt. Lett. 39(20), 5957–5960 (2014).
    [Crossref] [PubMed]
  23. Y. Fan, B. Wang, K. Wang, H. Long, and P. Lu, “Talbot effect in weakly coupled monolayer graphene sheet arrays,” Opt. Lett. 39(12), 3371–3373 (2014).
    [Crossref] [PubMed]
  24. Y. Fan, B. Wang, H. Huang, K. Wang, H. Long, and P. Lu, “Plasmonic Bloch oscillations in monolayer graphene sheet arrays,” Opt. Lett. 39(24), 6827–6830 (2014).
    [Crossref] [PubMed]
  25. 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]
  26. M. L. Nesterov, J. Bravo-Abad, A. Y. Nikitin, F. J. Garcia-Vidal, and L. Martin-Moreno, “Graphene supports the propagation of subwavelength optical solitons,” Laser Photonics Rev. 7(2), L7–L11 (2013).
    [Crossref]
  27. 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(2), 021014 (2013).
    [Crossref]
  28. D. A. Smirnova, I. V. Shadrivov, A. I. Smirnov, and Y. S. Kivshar, “Dissipative plasmon-solitons in multilayer graphene,” Laser Photonics Rev. 8(2), 291–296 (2014).
    [Crossref]
  29. Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. M. R. Peres, and M. I. Vasilevskiy, “Discrete solitons in graphene metamaterials,” Phys. Rev. B 91(4), 045424 (2015).
    [Crossref]
  30. R. W. Boyd and G. L. Fischer, Nonlinear Optical Materials (Elsevier Science Ltd, 2001).
  31. H. Hu, K. Wang, H. Long, W. Liu, B. Wang, and P. Lu, “Precise determination of the crystallographic orientations in single ZnS nanowires by second-harmonic generation microscopy,” Nano Lett. 15(5), 3351–3357 (2015).
    [Crossref] [PubMed]
  32. N. M. R. Peres, “Colloquium: The transport properties of graphene: an introduction,” Rev. Mod. Phys. 82(3), 2673–2700 (2010).
    [Crossref]
  33. P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
    [Crossref] [PubMed]
  34. B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
    [Crossref] [PubMed]
  35. L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
    [Crossref]
  36. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
    [Crossref] [PubMed]
  37. J. Schilling, “Uniaxial metallo-dielectric metamaterials with scalar positive permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046618 (2006).
    [Crossref] [PubMed]
  38. C. Qin, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Low-loss plasmonic supermodes in graphene multilayers,” Opt. Express 22(21), 25324–25332 (2014).
    [Crossref] [PubMed]
  39. B. Wang, X. Zhang, K. P. Loh, and J. Teng, “Tunable broadband transmission and phase modulation of light through graphene multilayers,” J. Appl. Phys. 115(21), 213102 (2014).
    [Crossref]
  40. S. H. Nam, A. J. Taylor, and A. Efimov, “Diabolical point and conical-like diffraction in periodic plasmonic nanostructures,” Opt. Express 18(10), 10120–10126 (2010).
    [Crossref] [PubMed]
  41. M. L. Brongersma and P. G. Kik, Surface Plasmon Nanophotonics (Springer, 2007).
  42. M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79(25), 4990–4993 (1997).
    [Crossref]
  43. O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91(11), 113901 (2003).
    [Crossref] [PubMed]
  44. R. D. Schaller, M. A. Petruska, and V. I. Klimov, “Tunable near-infrared optical gain and amplified spontaneous emission using PbSe nanocrystals,” J. Phys. Chem. B 107(50), 13765–13768 (2003).
    [Crossref]
  45. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
    [Crossref]

2015 (2)

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. M. R. Peres, and M. I. Vasilevskiy, “Discrete solitons in graphene metamaterials,” Phys. Rev. B 91(4), 045424 (2015).
[Crossref]

H. Hu, K. Wang, H. Long, W. Liu, B. Wang, and P. Lu, “Precise determination of the crystallographic orientations in single ZnS nanowires by second-harmonic generation microscopy,” Nano Lett. 15(5), 3351–3357 (2015).
[Crossref] [PubMed]

2014 (6)

2013 (3)

M. L. Nesterov, J. Bravo-Abad, A. Y. Nikitin, F. J. Garcia-Vidal, and L. Martin-Moreno, “Graphene supports the propagation of subwavelength optical solitons,” Laser Photonics Rev. 7(2), L7–L11 (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(2), 021014 (2013).
[Crossref]

Y. Kou, F. Ye, and X. Chen, “Multiband vector plasmonic lattice solitons,” Opt. Lett. 38(8), 1271–1273 (2013).
[Crossref] [PubMed]

2012 (3)

I. V. Irosh, P. A. Belov, A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear Tamm states in nanostructured plasmonic metamaterials,” Phys. Rev. A 86(2), 023819 (2012).
[Crossref]

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

2011 (1)

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

2010 (4)

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

N. M. R. Peres, “Colloquium: The transport properties of graphene: an introduction,” Rev. Mod. Phys. 82(3), 2673–2700 (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(10), 106802 (2010).
[Crossref] [PubMed]

S. H. Nam, A. J. Taylor, and A. Efimov, “Diabolical point and conical-like diffraction in periodic plasmonic nanostructures,” Opt. Express 18(10), 10120–10126 (2010).
[Crossref] [PubMed]

2009 (3)

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

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

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

2008 (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]

2007 (4)

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

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

E. Feigenbaum and M. Orenstein, “Plasmon-soliton,” Opt. Lett. 32(6), 674–676 (2007).
[Crossref] [PubMed]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

2006 (2)

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

J. Schilling, “Uniaxial metallo-dielectric metamaterials with scalar positive permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046618 (2006).
[Crossref] [PubMed]

2005 (1)

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

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]

2003 (4)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (2003).
[Crossref] [PubMed]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91(11), 113901 (2003).
[Crossref] [PubMed]

R. D. Schaller, M. A. Petruska, and V. I. Klimov, “Tunable near-infrared optical gain and amplified spontaneous emission using PbSe nanocrystals,” J. Phys. Chem. B 107(50), 13765–13768 (2003).
[Crossref]

2002 (1)

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref] [PubMed]

2000 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

1999 (1)

1998 (1)

H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

1997 (1)

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79(25), 4990–4993 (1997).
[Crossref]

1993 (1)

1988 (1)

1972 (1)

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34(1), 62–69 (1972).

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Alù, A.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Bartal, G.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

Belov, P. A.

I. V. Irosh, P. A. Belov, A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear Tamm states in nanostructured plasmonic metamaterials,” Phys. Rev. A 86(2), 023819 (2012).
[Crossref]

Berger, C.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Blair, S.

Bludov, Y. V.

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. M. R. Peres, and M. I. Vasilevskiy, “Discrete solitons in graphene metamaterials,” Phys. Rev. B 91(4), 045424 (2015).
[Crossref]

Bonaccorso, F.

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

Boyd, A. R.

H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref] [PubMed]

Bravo-Abad, J.

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

Brown, N.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (2003).
[Crossref] [PubMed]

Chen, P. Y.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Chen, X.

Chen, Z.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

Christodoulides, D. N.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (2003).
[Crossref] [PubMed]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91(11), 113901 (2003).
[Crossref] [PubMed]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79(25), 4990–4993 (1997).
[Crossref]

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13(9), 794–796 (1988).
[Crossref] [PubMed]

Cohen, O.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91(11), 113901 (2003).
[Crossref] [PubMed]

Conrad, E. H.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Coskun, T. H.

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79(25), 4990–4993 (1997).
[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(2), 021014 (2013).
[Crossref]

de Heer, W. A.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Dubonos, S. 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).
[Crossref] [PubMed]

Efimov, A.

Efremidis, N. K.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (2003).
[Crossref] [PubMed]

Eisenberg, H.

H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

Falkovsky, L. A.

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

Fan, Y.

Feigenbaum, E.

Ferrari, A. C.

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

Firsov, A. A.

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]

First, P. N.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Fleischer, J. W.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91(11), 113901 (2003).
[Crossref] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (2003).
[Crossref] [PubMed]

Garcia-Vidal, F. J.

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

García-Vidal, F. J.

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

Geim, A. K.

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

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

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

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]

Genov, D. A.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Guinea, F.

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

Hasan, T.

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

Hass, J.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Hone, J.

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(2), 021014 (2013).
[Crossref]

Hong, S.

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(2), 021014 (2013).
[Crossref]

Hu, B.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
[Crossref] [PubMed]

Hu, H.

H. Hu, K. Wang, H. Long, W. Liu, B. Wang, and P. Lu, “Precise determination of the crystallographic orientations in single ZnS nanowires by second-harmonic generation microscopy,” Nano Lett. 15(5), 3351–3357 (2015).
[Crossref] [PubMed]

Huang, H.

Irosh, I. V.

I. V. Irosh, P. A. Belov, A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear Tamm states in nanostructured plasmonic metamaterials,” Phys. Rev. A 86(2), 023819 (2012).
[Crossref]

Jablan, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

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]

Joseph, R. I.

Kim, P.

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Kivshar, Y. S.

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. M. R. Peres, and M. I. Vasilevskiy, “Discrete solitons in graphene metamaterials,” Phys. Rev. B 91(4), 045424 (2015).
[Crossref]

D. A. Smirnova, I. V. Shadrivov, A. I. Smirnov, and Y. S. Kivshar, “Dissipative plasmon-solitons in multilayer graphene,” Laser Photonics Rev. 8(2), 291–296 (2014).
[Crossref]

I. V. Irosh, P. A. Belov, A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear Tamm states in nanostructured plasmonic metamaterials,” Phys. Rev. A 86(2), 023819 (2012).
[Crossref]

Y. S. Kivshar, “Self-localization in arrays of defocusing waveguides,” Opt. Lett. 18(14), 1147–1149 (1993).
[Crossref] [PubMed]

Klimov, V. I.

R. D. Schaller, M. A. Petruska, and V. I. Klimov, “Tunable near-infrared optical gain and amplified spontaneous emission using PbSe nanocrystals,” J. Phys. Chem. B 107(50), 13765–13768 (2003).
[Crossref]

Kou, Y.

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref] [PubMed]

Li, T.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Li, X.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Liu, W.

H. Hu, K. Wang, H. Long, W. Liu, B. Wang, and P. Lu, “Precise determination of the crystallographic orientations in single ZnS nanowires by second-harmonic generation microscopy,” Nano Lett. 15(5), 3351–3357 (2015).
[Crossref] [PubMed]

Liu, Y.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

Loh, K. P.

B. Wang, X. Zhang, K. P. Loh, and J. Teng, “Tunable broadband transmission and phase modulation of light through graphene multilayers,” J. Appl. Phys. 115(21), 213102 (2014).
[Crossref]

Long, H.

Lu, P.

Marchenkov, A. N.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Martin-Moreno, L.

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

Mayou, D.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Mihalache, D.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
[Crossref] [PubMed]

Mikhailov, S. A.

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]

Mitchell, M.

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79(25), 4990–4993 (1997).
[Crossref]

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Morozov, S. 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).
[Crossref] [PubMed]

Nam, S. H.

Naud, C.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Nesterov, M. L.

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

Neto, A. H. C.

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

Nikitin, A. Y.

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

Novoselov, K. S.

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

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

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]

Orenstein, M.

Osgood, R. M.

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(2), 021014 (2013).
[Crossref]

Panoiu, N. C.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, “Subwavelength plasmonic lattice solitons in arrays of metallic nanowires,” Phys. Rev. Lett. 104(10), 106802 (2010).
[Crossref] [PubMed]

Peres, N. M. R.

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. M. R. Peres, and M. I. Vasilevskiy, “Discrete solitons in graphene metamaterials,” Phys. Rev. B 91(4), 045424 (2015).
[Crossref]

N. M. R. Peres, “Colloquium: The transport properties of graphene: an introduction,” Rev. Mod. Phys. 82(3), 2673–2700 (2010).
[Crossref]

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

Pershoguba, S. S.

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref] [PubMed]

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref] [PubMed]

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(2), 021014 (2013).
[Crossref]

Petruska, M. A.

R. D. Schaller, M. A. Petruska, and V. I. Klimov, “Tunable near-infrared optical gain and amplified spontaneous emission using PbSe nanocrystals,” J. Phys. Chem. B 107(50), 13765–13768 (2003).
[Crossref]

Qin, C.

Schaller, R. D.

R. D. Schaller, M. A. Petruska, and V. I. Klimov, “Tunable near-infrared optical gain and amplified spontaneous emission using PbSe nanocrystals,” J. Phys. Chem. B 107(50), 13765–13768 (2003).
[Crossref]

Schilling, J.

J. Schilling, “Uniaxial metallo-dielectric metamaterials with scalar positive permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046618 (2006).
[Crossref] [PubMed]

Schwartz, T.

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91(11), 113901 (2003).
[Crossref] [PubMed]

Segev, M.

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (2003).
[Crossref] [PubMed]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91(11), 113901 (2003).
[Crossref] [PubMed]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79(25), 4990–4993 (1997).
[Crossref]

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34(1), 62–69 (1972).

Shadrivov, I. V.

D. A. Smirnova, I. V. Shadrivov, A. I. Smirnov, and Y. S. Kivshar, “Dissipative plasmon-solitons in multilayer graphene,” Laser Photonics Rev. 8(2), 291–296 (2014).
[Crossref]

I. V. Irosh, P. A. Belov, A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear Tamm states in nanostructured plasmonic metamaterials,” Phys. Rev. A 86(2), 023819 (2012).
[Crossref]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Smirnov, A. I.

D. A. Smirnova, I. V. Shadrivov, A. I. Smirnov, and Y. S. Kivshar, “Dissipative plasmon-solitons in multilayer graphene,” Laser Photonics Rev. 8(2), 291–296 (2014).
[Crossref]

Smirnova, D. A.

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. M. R. Peres, and M. I. Vasilevskiy, “Discrete solitons in graphene metamaterials,” Phys. Rev. B 91(4), 045424 (2015).
[Crossref]

D. A. Smirnova, I. V. Shadrivov, A. I. Smirnov, and Y. S. Kivshar, “Dissipative plasmon-solitons in multilayer graphene,” Laser Photonics Rev. 8(2), 291–296 (2014).
[Crossref]

Soljacic, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Song, Z.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Stormer, H. L.

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Sun, Z.

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

Tan, Y. W.

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

Taylor, A. J.

Teng, J.

B. Wang, X. Zhang, K. P. Loh, and J. Teng, “Tunable broadband transmission and phase modulation of light through graphene multilayers,” J. Appl. Phys. 115(21), 213102 (2014).
[Crossref]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

Vasilevskiy, M. I.

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. M. R. Peres, and M. I. Vasilevskiy, “Discrete solitons in graphene metamaterials,” Phys. Rev. B 91(4), 045424 (2015).
[Crossref]

Wagner, K.

Wang, B.

H. Hu, K. Wang, H. Long, W. Liu, B. Wang, and P. Lu, “Precise determination of the crystallographic orientations in single ZnS nanowires by second-harmonic generation microscopy,” Nano Lett. 15(5), 3351–3357 (2015).
[Crossref] [PubMed]

B. Wang, X. Zhang, K. P. Loh, and J. Teng, “Tunable broadband transmission and phase modulation of light through graphene multilayers,” J. Appl. Phys. 115(21), 213102 (2014).
[Crossref]

C. Qin, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Low-loss plasmonic supermodes in graphene multilayers,” Opt. Express 22(21), 25324–25332 (2014).
[Crossref] [PubMed]

Y. Fan, B. Wang, K. Wang, H. Long, and P. Lu, “Talbot effect in weakly coupled monolayer graphene sheet arrays,” Opt. Lett. 39(12), 3371–3373 (2014).
[Crossref] [PubMed]

Y. Fan, B. Wang, H. Huang, K. Wang, H. Long, and P. Lu, “Plasmonic Bloch oscillations in monolayer graphene sheet arrays,” Opt. Lett. 39(24), 6827–6830 (2014).
[Crossref] [PubMed]

H. Huang, B. Wang, H. Long, K. Wang, and P. Lu, “Plasmon-negative refraction at the heterointerface of graphene sheet arrays,” Opt. Lett. 39(20), 5957–5960 (2014).
[Crossref] [PubMed]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

Wang, K.

Wu, X.

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

Ye, F.

Y. Kou, F. Ye, and X. Chen, “Multiband vector plasmonic lattice solitons,” Opt. Lett. 38(8), 1271–1273 (2013).
[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(10), 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(2), 021014 (2013).
[Crossref]

Yuan, X.

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34(1), 62–69 (1972).

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref] [PubMed]

Zhang, X.

B. Wang, X. Zhang, K. P. Loh, and J. Teng, “Tunable broadband transmission and phase modulation of light through graphene multilayers,” J. Appl. Phys. 115(21), 213102 (2014).
[Crossref]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref] [PubMed]

Zhang, Y.

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

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]

Zharov, A. A.

I. V. Irosh, P. A. Belov, A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear Tamm states in nanostructured plasmonic metamaterials,” Phys. Rev. A 86(2), 023819 (2012).
[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]

ACS Nano (1)

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Appl. Opt. (1)

J. Appl. Phys. (1)

B. Wang, X. Zhang, K. P. Loh, and J. Teng, “Tunable broadband transmission and phase modulation of light through graphene multilayers,” J. Appl. Phys. 115(21), 213102 (2014).
[Crossref]

J. Phys. Chem. B (1)

R. D. Schaller, M. A. Petruska, and V. I. Klimov, “Tunable near-infrared optical gain and amplified spontaneous emission using PbSe nanocrystals,” J. Phys. Chem. B 107(50), 13765–13768 (2003).
[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]

Laser Photonics Rev. (2)

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

D. A. Smirnova, I. V. Shadrivov, A. I. Smirnov, and Y. S. Kivshar, “Dissipative plasmon-solitons in multilayer graphene,” Laser Photonics Rev. 8(2), 291–296 (2014).
[Crossref]

Nano Lett. (1)

H. Hu, K. Wang, H. Long, W. Liu, B. Wang, and P. Lu, “Precise determination of the crystallographic orientations in single ZnS nanowires by second-harmonic generation microscopy,” Nano Lett. 15(5), 3351–3357 (2015).
[Crossref] [PubMed]

Nat. Mater. (1)

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

Nat. Photonics (1)

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

Nature (2)

Y. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438(7065), 201–204 (2005).
[Crossref] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (7)

Phys. Rev. A (1)

I. V. Irosh, P. A. Belov, A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, “Nonlinear Tamm states in nanostructured plasmonic metamaterials,” Phys. Rev. A 86(2), 023819 (2012).
[Crossref]

Phys. Rev. B (3)

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009).
[Crossref]

Y. V. Bludov, D. A. Smirnova, Y. S. Kivshar, N. M. R. Peres, and M. I. Vasilevskiy, “Discrete solitons in graphene metamaterials,” Phys. Rev. B 91(4), 045424 (2015).
[Crossref]

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

J. Schilling, “Uniaxial metallo-dielectric metamaterials with scalar positive permeability,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(4), 046618 (2006).
[Crossref] [PubMed]

Phys. Rev. Lett. (9)

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of discrete solitons in optically induced real time waveguide arrays,” Phys. Rev. Lett. 90(2), 023902 (2003).
[Crossref] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref] [PubMed]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 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(10), 106802 (2010).
[Crossref] [PubMed]

H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79(25), 4990–4993 (1997).
[Crossref]

O. Cohen, T. Schwartz, J. W. Fleischer, M. Segev, and D. N. Christodoulides, “Multiband vector lattice solitons,” Phys. Rev. Lett. 91(11), 113901 (2003).
[Crossref] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref] [PubMed]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[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(2), 021014 (2013).
[Crossref]

Rep. Prog. Phys. (1)

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref] [PubMed]

Rev. Mod. Phys. (2)

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

N. M. R. Peres, “Colloquium: The transport properties of graphene: an introduction,” Rev. Mod. Phys. 82(3), 2673–2700 (2010).
[Crossref]

Science (3)

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312(5777), 1191–1196 (2006).
[Crossref] [PubMed]

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]

Sov. Phys. JETP (1)

V. E. Zakharov and A. B. Shabat, “Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,” Sov. Phys. JETP 34(1), 62–69 (1972).

Other (2)

M. L. Brongersma and P. G. Kik, Surface Plasmon Nanophotonics (Springer, 2007).

R. W. Boyd and G. L. Fischer, Nonlinear Optical Materials (Elsevier Science Ltd, 2001).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1 (a) Schematic of the GSA. (b) Diffraction relation of SPPs in linear GSA with d = 30 nm and μc = 0.15 eV. (c) Diffraction relation when μc = 0.15 eV and the period of GSA varies. (d) Diffraction relation as the chemical potential is varying when d = 30 nm.
Fig. 2
Fig. 2 PLSs yielded by graphene nonlinearity as kx = π/d. (a) Normalized transverse electric field (Ex ) of the PLSs at kx = π/d. (b) Normalized intensity distribution of the PLSs.
Fig. 3
Fig. 3 PLSs yielded by graphene nonlinearity as kx = π/d. (a) Propagation of PLSs in the GSAs without loss. (b) Diffraction of SPPs in linear GSAs. (c) Propagation of PLSs in the GSAs as the loss is considered.
Fig. 4
Fig. 4 (a), (b) Normalized transverse electric field Ex and intensity |(E)|2 profiles of the PLSs at kx = π/d. Here the self-focusing dielectrics between graphene are utilized. (c), (d) normalized transverse electric field and intensity profiles of the PLSs at kx = 0. Here self-defocusing dielectrics are utilized.
Fig. 5
Fig. 5 (a), (b) Distributions of electric field (Ex ) and intensity of the PLSs at kx = π/d. The PLSs result from the nonlinearity of graphene and self-focusing dielectrics between graphene. (c), (d) Distributions of electric field and intensity of the PLSs at kx = 0. The PLSs result from the nonlinearity of graphene and self-defocusing dielectrics.
Fig. 6
Fig. 6 (a) Electric field intensity of PLSs at kx = π/d propagating in the nonlinear GSA. The PLSs result from the nonlinearity of graphene and self-focusing dielectrics between graphene. (b) Electric field intensity of PLSs at kx = 0. The PLSs result from the nonlinearity of graphene and self-defocusing dielectrics.
Fig. 7
Fig. 7 (a), (b) Intensity distribution of the self-focusing PLSs and the propagation constants kz vary as the period d increases when μc = 0.15 eV. (c), (d) Intensity distribution and propagation constant of the self-focusing PLSs vary with the chemical potential of graphene μc when d = 30 nm. Here both the nonlinearities of graphene and dielectric are considered.
Fig. 8
Fig. 8 (a) Effective width of the self-focusing PLSs as a function of the injected field intensity. (b) Propagation constant of the self-focusing PLSs versus the injected intensity.

Equations (7)

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

cos ( φ ) = cos h ( κ d ) κ ξ 2 sin h ( κ d ) ,
( 0 k 0 ε r ( x ) η 0 η 0 k 0 x 1 ε r ( x ) x + k 0 η 0 0 ) ( H y E x ) = k z ( H y E x ) ,
σ N L = i 3 8 e 2 π 2 ( e V F μ c ω ) 2 μ c ω ,
M ^ ( h y e x ) = z ( h y e x ) ,
M ^ = ( 0 i k 0 ε r ( x ) η 0 i ( η 0 k 0 x 1 ε r ( x ) x + k 0 η 0 ) 0 ) .
( h y e x ) N + 1 = ( h y e x ) N e i M ^ Δ z = ( h y e x ) N e i M ^ L Δ z e i M ^ N L Δ z ,
e i M ^ N L Δ z = n = 0 N ( i M ^ N L Δ z ) n n ! ,

Metrics