Abstract

We present a coupled-mode theory describing light propagation in an array of nonlinear plasmonic waveguides. Our model predicts a two-band dependence of the propagation constant versus transverse quasi-momentum and existence of discrete and gap plasmon solitons.

© 2010 Optical Society of America

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  1. D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photon. 4, 83 (2010).
    [CrossRef]
  2. E. Feigenbaum and M. Orenstein, Opt. Lett. 32, 674 (2007).
    [CrossRef] [PubMed]
  3. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 17, 21732 (2009).
    [CrossRef] [PubMed]
  4. A. Marini and D. Skryabin, Phys. Rev. A 81, 033850 (2010).
    [CrossRef]
  5. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
    [CrossRef]
  6. X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
    [CrossRef] [PubMed]
  7. M. Y. Xu and J. S. Aitchison, Opt. Lett. 34, 350 (2009).
    [CrossRef] [PubMed]
  8. Z. Chen, T. Holmgaard, S. I. Bozhevolnyi, A. V. Krasavin, A. V. Zayats, L. Markey, and A. Dereux, Opt. Lett. 34, 310(2009).
    [CrossRef] [PubMed]
  9. S. Thongrattanasiri, J. Elser, and V. A. Podolskiy, J. Opt. Soc. Am. B 26, B102 (2009).
    [CrossRef]
  10. M. Guasoni, M. Conforti, and C. De Angelis, Opt. Commun. 283, 1161 (2010).
    [CrossRef]
  11. S. H. Nam, A. Taylor, and A. Efimov, Opt. Express 18, 10120 (2010).
    [CrossRef] [PubMed]
  12. Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
    [CrossRef] [PubMed]
  13. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 16, 21209 (2008).
    [CrossRef] [PubMed]
  14. F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
    [CrossRef] [PubMed]
  15. R. A. Vicencio and M. Johansson, Phys. Rev. A 79, 065801(2009).
    [CrossRef]
  16. N. K. Efremidis, P. Zhang, Z. G. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, Phys. Rev. A 81, 053817 (2010).
    [CrossRef]

2010 (6)

A. Marini and D. Skryabin, Phys. Rev. A 81, 033850 (2010).
[CrossRef]

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photon. 4, 83 (2010).
[CrossRef]

M. Guasoni, M. Conforti, and C. De Angelis, Opt. Commun. 283, 1161 (2010).
[CrossRef]

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef] [PubMed]

N. K. Efremidis, P. Zhang, Z. G. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, Phys. Rev. A 81, 053817 (2010).
[CrossRef]

S. H. Nam, A. Taylor, and A. Efimov, Opt. Express 18, 10120 (2010).
[CrossRef] [PubMed]

2009 (5)

2008 (2)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 16, 21209 (2008).
[CrossRef] [PubMed]

2007 (2)

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef] [PubMed]

E. Feigenbaum and M. Orenstein, Opt. Lett. 32, 674 (2007).
[CrossRef] [PubMed]

2006 (1)

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Aitchison, J. S.

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[CrossRef]

Bartal, G.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

Chan, C. T.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Chen, Z.

Chen, Z. G.

N. K. Efremidis, P. Zhang, Z. G. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, Phys. Rev. A 81, 053817 (2010).
[CrossRef]

Christodoulides, D. N.

N. K. Efremidis, P. Zhang, Z. G. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, Phys. Rev. A 81, 053817 (2010).
[CrossRef]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[CrossRef]

Conforti, M.

M. Guasoni, M. Conforti, and C. De Angelis, Opt. Commun. 283, 1161 (2010).
[CrossRef]

Davoyan, A. R.

De Angelis, C.

M. Guasoni, M. Conforti, and C. De Angelis, Opt. Commun. 283, 1161 (2010).
[CrossRef]

Dereux, A.

Efimov, A.

Efremidis, N. K.

N. K. Efremidis, P. Zhang, Z. G. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, Phys. Rev. A 81, 053817 (2010).
[CrossRef]

Elser, J.

Fan, X.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Feigenbaum, E.

Genov, D. A.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef] [PubMed]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photon. 4, 83 (2010).
[CrossRef]

Guasoni, M.

M. Guasoni, M. Conforti, and C. De Angelis, Opt. Commun. 283, 1161 (2010).
[CrossRef]

Holmgaard, T.

Hu, B.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef] [PubMed]

Johansson, M.

R. A. Vicencio and M. Johansson, Phys. Rev. A 79, 065801(2009).
[CrossRef]

Kip, D.

N. K. Efremidis, P. Zhang, Z. G. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, Phys. Rev. A 81, 053817 (2010).
[CrossRef]

Kivshar, Y. S.

Krasavin, A. V.

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[CrossRef]

Lee, J. C. W.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Liu, Y.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef] [PubMed]

Marini, A.

A. Marini and D. Skryabin, Phys. Rev. A 81, 033850 (2010).
[CrossRef]

Markey, L.

Mihalache, D.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef] [PubMed]

Nam, S. H.

Orenstein, M.

Panoiu, N. C.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef] [PubMed]

Podolskiy, V. A.

Ruter, C. E.

N. K. Efremidis, P. Zhang, Z. G. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, Phys. Rev. A 81, 053817 (2010).
[CrossRef]

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[CrossRef]

Shadrivov, I. V.

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[CrossRef]

Skryabin, D.

A. Marini and D. Skryabin, Phys. Rev. A 81, 033850 (2010).
[CrossRef]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[CrossRef]

Taylor, A.

Thongrattanasiri, S.

Vicencio, R. A.

R. A. Vicencio and M. Johansson, Phys. Rev. A 79, 065801(2009).
[CrossRef]

Wang, G. P.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Xu, M. Y.

Ye, F.

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef] [PubMed]

Zayats, A. V.

Zhang, P.

N. K. Efremidis, P. Zhang, Z. G. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, Phys. Rev. A 81, 053817 (2010).
[CrossRef]

Zhang, X.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (1)

Nat. Photon. (1)

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photon. 4, 83 (2010).
[CrossRef]

Opt. Commun. (1)

M. Guasoni, M. Conforti, and C. De Angelis, Opt. Commun. 283, 1161 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[CrossRef]

Phys. Rev. A (3)

R. A. Vicencio and M. Johansson, Phys. Rev. A 79, 065801(2009).
[CrossRef]

N. K. Efremidis, P. Zhang, Z. G. Chen, D. N. Christodoulides, C. E. Ruter, and D. Kip, Phys. Rev. A 81, 053817 (2010).
[CrossRef]

A. Marini and D. Skryabin, Phys. Rev. A 81, 033850 (2010).
[CrossRef]

Phys. Rev. Lett. (3)

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, Phys. Rev. Lett. 97, 073901 (2006).
[CrossRef] [PubMed]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, Phys. Rev. Lett. 99, 153901 (2007).
[CrossRef] [PubMed]

F. Ye, D. Mihalache, B. Hu, and N. C. Panoiu, Phys. Rev. Lett. 104, 106802 (2010).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Band structure of the periodic metal–dielectric stack. Dashed curves correspond to κ d = κ m .

Fig. 2
Fig. 2

Linear Bloch modes. Letters on the panels correspond to the respectively marked points in the band structure diagram in Fig. 1.

Fig. 3
Fig. 3

Normalized intensity I = n ( | R n | 2 + | L n | 2 ) versus δ for families of discrete and gap solitons. a, e, and g families have a metal stripe as their center of symmetry and should be considered as on-site solitons in our case ( κ m > κ d ), while b, d, and f are the off-site families centered on a dielectric stripe. c is the branch of asymmetric solitons.

Fig. 4
Fig. 4

Spatial profiles of the discrete and gap solitons. Letters on the panels correspond to the respectively marked soliton branches in Fig. 3. δ = 0.141 for solitons in (a)–(d), and δ = 0 in (e) and (f).

Equations (3)

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z x 2 E z z z 2 E x = D x ϵ 0 , x z 2 E x x x 2 E z = D z ϵ 0 ,
i z L n + i α L n = κ d R n 1 κ m R n f ϒ | L n | 2 L n , i z R n + i α R n = κ d L n + 1 κ m L n f ϒ | R n | 2 R n .
R n = r e i q n + i δ z α z , L n = l e i q n + i δ z α z ,

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