Abstract

We studied nonlinear effects in plasmonic metal film waveguides and couplers stimulated by third-order optical response due to ponderomotive metal nonlinearities. We analyzed the structure and dispersion of nonlinear plasmonic guided modes and predicted the bifurcations and symmetry breaking of nonlinear modes for the critical powers, depending on the structure dimensions.

© 2011 Optical Society of America

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  1. S.I.Bozhevolnyi, ed., Plasmonic Nanoguides and Circuits (Pan Stanford, 2009).
  2. M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, Nano Lett. 7, 3145 (2007).
    [CrossRef] [PubMed]
  3. V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1980).
  4. G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
    [CrossRef]
  5. D. Mihalache, G. I. Stegeman, C. T. Seaton, E. M. Wright, R. Zanoni, A. D. Boardman, and T. Twardowski, Opt. Lett. 12, 187 (1987).
    [CrossRef] [PubMed]
  6. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 16, 21209 (2008).
    [CrossRef] [PubMed]
  7. J. R. Salgueiro and Y. S. Kivshar, Appl. Phys. Lett. 97, 081106 (2010).
    [CrossRef]
  8. A. Marini, A. V. Gorbach, and D. V. Skryabin, Opt. Lett. 35, 3532 (2010).
    [CrossRef] [PubMed]
  9. A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 17, 21732 (2009).
    [CrossRef] [PubMed]
  10. E. Feigenbaum and M. Orenstein, Opt. Lett. 32, 674 (2007).
    [CrossRef] [PubMed]
  11. A. Marini and D. V. Skryabin, Phys. Rev. A 81, 033850(2010).
    [CrossRef]
  12. A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, Phys. Rev. Lett. 105, 116804 (2010).
    [CrossRef] [PubMed]
  13. A. V. Krasavin, K. F. MacDonald, A. S. Schwanecke, and N. I. Zheludev, Appl. Phys. Lett. 89, 031118 (2006).
    [CrossRef]
  14. Y. Gefen, W. H. Shih, R. B. Laibowitz, and J. M. Viggiano, Phys. Rev. Lett. 57, 3097 (1986).
    [CrossRef] [PubMed]
  15. P. Ginzburg, A. Hayat, N. Berkovitch, and M. Orenstein, Opt. Lett. 35, 1551 (2010).
    [CrossRef] [PubMed]
  16. J. J. Burke, G. I. Stegeman, and T. Tamir, Phys. Rev. B 33, 5186 (1986).
    [CrossRef]
  17. A. R. Davoyan, I. V. Shadrivov, S. I. Bozhevolnyi, and Y. S. Kivshar, J. Nanophoton. 4, 043509 (2010).
    [CrossRef]
  18. M. A. Gilmore and B. L. Johnsona, J. Appl. Phys. 93, 4497 (2003).
    [CrossRef]

2010 (6)

J. R. Salgueiro and Y. S. Kivshar, Appl. Phys. Lett. 97, 081106 (2010).
[CrossRef]

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

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef] [PubMed]

A. R. Davoyan, I. V. Shadrivov, S. I. Bozhevolnyi, and Y. S. Kivshar, J. Nanophoton. 4, 043509 (2010).
[CrossRef]

P. Ginzburg, A. Hayat, N. Berkovitch, and M. Orenstein, Opt. Lett. 35, 1551 (2010).
[CrossRef] [PubMed]

A. Marini, A. V. Gorbach, and D. V. Skryabin, Opt. Lett. 35, 3532 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (1)

2007 (2)

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

M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, Nano Lett. 7, 3145 (2007).
[CrossRef] [PubMed]

2006 (1)

A. V. Krasavin, K. F. MacDonald, A. S. Schwanecke, and N. I. Zheludev, Appl. Phys. Lett. 89, 031118 (2006).
[CrossRef]

2003 (1)

M. A. Gilmore and B. L. Johnsona, J. Appl. Phys. 93, 4497 (2003).
[CrossRef]

1987 (1)

1986 (2)

Y. Gefen, W. H. Shih, R. B. Laibowitz, and J. M. Viggiano, Phys. Rev. Lett. 57, 3097 (1986).
[CrossRef] [PubMed]

J. J. Burke, G. I. Stegeman, and T. Tamir, Phys. Rev. B 33, 5186 (1986).
[CrossRef]

1985 (1)

G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
[CrossRef]

1980 (1)

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1980).

Agranovich, V. M.

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1980).

Ariyasu, J.

G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
[CrossRef]

Babichenko, V. S.

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1980).

Berkovitch, N.

Boardman, A. D.

Bozhevolnyi, S. I.

A. R. Davoyan, I. V. Shadrivov, S. I. Bozhevolnyi, and Y. S. Kivshar, J. Nanophoton. 4, 043509 (2010).
[CrossRef]

Burke, J. J.

J. J. Burke, G. I. Stegeman, and T. Tamir, Phys. Rev. B 33, 5186 (1986).
[CrossRef]

Chernyak, V. Y.

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1980).

Davoyan, A. R.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef] [PubMed]

A. R. Davoyan, I. V. Shadrivov, S. I. Bozhevolnyi, and Y. S. Kivshar, J. Nanophoton. 4, 043509 (2010).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 17, 21732 (2009).
[CrossRef] [PubMed]

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

Durach, M.

M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, Nano Lett. 7, 3145 (2007).
[CrossRef] [PubMed]

Feigenbaum, E.

Gefen, Y.

Y. Gefen, W. H. Shih, R. B. Laibowitz, and J. M. Viggiano, Phys. Rev. Lett. 57, 3097 (1986).
[CrossRef] [PubMed]

Gilmore, M. A.

M. A. Gilmore and B. L. Johnsona, J. Appl. Phys. 93, 4497 (2003).
[CrossRef]

Ginzburg, P.

Gorbach, A. V.

Gramotnev, D. K.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef] [PubMed]

Hayat, A.

Johnsona, B. L.

M. A. Gilmore and B. L. Johnsona, J. Appl. Phys. 93, 4497 (2003).
[CrossRef]

Kivshar, Y. S.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef] [PubMed]

J. R. Salgueiro and Y. S. Kivshar, Appl. Phys. Lett. 97, 081106 (2010).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, S. I. Bozhevolnyi, and Y. S. Kivshar, J. Nanophoton. 4, 043509 (2010).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 17, 21732 (2009).
[CrossRef] [PubMed]

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

Krasavin, A. V.

A. V. Krasavin, K. F. MacDonald, A. S. Schwanecke, and N. I. Zheludev, Appl. Phys. Lett. 89, 031118 (2006).
[CrossRef]

Laibowitz, R. B.

Y. Gefen, W. H. Shih, R. B. Laibowitz, and J. M. Viggiano, Phys. Rev. Lett. 57, 3097 (1986).
[CrossRef] [PubMed]

MacDonald, K. F.

A. V. Krasavin, K. F. MacDonald, A. S. Schwanecke, and N. I. Zheludev, Appl. Phys. Lett. 89, 031118 (2006).
[CrossRef]

Maradudin, A. A.

G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
[CrossRef]

Marini, A.

Mihalache, D.

Nelson, K.

M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, Nano Lett. 7, 3145 (2007).
[CrossRef] [PubMed]

Orenstein, M.

Rusina, A.

M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, Nano Lett. 7, 3145 (2007).
[CrossRef] [PubMed]

Salgueiro, J. R.

J. R. Salgueiro and Y. S. Kivshar, Appl. Phys. Lett. 97, 081106 (2010).
[CrossRef]

Schwanecke, A. S.

A. V. Krasavin, K. F. MacDonald, A. S. Schwanecke, and N. I. Zheludev, Appl. Phys. Lett. 89, 031118 (2006).
[CrossRef]

Seaton, C. T.

D. Mihalache, G. I. Stegeman, C. T. Seaton, E. M. Wright, R. Zanoni, A. D. Boardman, and T. Twardowski, Opt. Lett. 12, 187 (1987).
[CrossRef] [PubMed]

G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
[CrossRef]

Shadrivov, I. V.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef] [PubMed]

A. R. Davoyan, I. V. Shadrivov, S. I. Bozhevolnyi, and Y. S. Kivshar, J. Nanophoton. 4, 043509 (2010).
[CrossRef]

A. R. Davoyan, I. V. Shadrivov, and Y. S. Kivshar, Opt. Express 17, 21732 (2009).
[CrossRef] [PubMed]

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

Shih, W. H.

Y. Gefen, W. H. Shih, R. B. Laibowitz, and J. M. Viggiano, Phys. Rev. Lett. 57, 3097 (1986).
[CrossRef] [PubMed]

Skryabin, D. V.

Stegeman, G. I.

D. Mihalache, G. I. Stegeman, C. T. Seaton, E. M. Wright, R. Zanoni, A. D. Boardman, and T. Twardowski, Opt. Lett. 12, 187 (1987).
[CrossRef] [PubMed]

J. J. Burke, G. I. Stegeman, and T. Tamir, Phys. Rev. B 33, 5186 (1986).
[CrossRef]

G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
[CrossRef]

Stockman, M. I.

M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, Nano Lett. 7, 3145 (2007).
[CrossRef] [PubMed]

Tamir, T.

J. J. Burke, G. I. Stegeman, and T. Tamir, Phys. Rev. B 33, 5186 (1986).
[CrossRef]

Twardowski, T.

Viggiano, J. M.

Y. Gefen, W. H. Shih, R. B. Laibowitz, and J. M. Viggiano, Phys. Rev. Lett. 57, 3097 (1986).
[CrossRef] [PubMed]

Wallis, R. F.

G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
[CrossRef]

Wright, E. M.

Zanoni, R.

Zharov, A. A.

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef] [PubMed]

Zheludev, N. I.

A. V. Krasavin, K. F. MacDonald, A. S. Schwanecke, and N. I. Zheludev, Appl. Phys. Lett. 89, 031118 (2006).
[CrossRef]

Appl. Phys. Lett. (2)

J. R. Salgueiro and Y. S. Kivshar, Appl. Phys. Lett. 97, 081106 (2010).
[CrossRef]

A. V. Krasavin, K. F. MacDonald, A. S. Schwanecke, and N. I. Zheludev, Appl. Phys. Lett. 89, 031118 (2006).
[CrossRef]

J. Appl. Phys. (2)

G. I. Stegeman, C. T. Seaton, J. Ariyasu, R. F. Wallis, and A. A. Maradudin, J. Appl. Phys. 58, 2453 (1985).
[CrossRef]

M. A. Gilmore and B. L. Johnsona, J. Appl. Phys. 93, 4497 (2003).
[CrossRef]

J. Nanophoton. (1)

A. R. Davoyan, I. V. Shadrivov, S. I. Bozhevolnyi, and Y. S. Kivshar, J. Nanophoton. 4, 043509 (2010).
[CrossRef]

Nano Lett. (1)

M. Durach, A. Rusina, M. I. Stockman, and K. Nelson, Nano Lett. 7, 3145 (2007).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (1)

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

Phys. Rev. B (1)

J. J. Burke, G. I. Stegeman, and T. Tamir, Phys. Rev. B 33, 5186 (1986).
[CrossRef]

Phys. Rev. Lett. (2)

A. R. Davoyan, I. V. Shadrivov, A. A. Zharov, D. K. Gramotnev, and Y. S. Kivshar, Phys. Rev. Lett. 105, 116804 (2010).
[CrossRef] [PubMed]

Y. Gefen, W. H. Shih, R. B. Laibowitz, and J. M. Viggiano, Phys. Rev. Lett. 57, 3097 (1986).
[CrossRef] [PubMed]

Sov. Phys. JETP Lett. (1)

V. M. Agranovich, V. S. Babichenko, and V. Y. Chernyak, Sov. Phys. JETP Lett. 32, 512 (1980).

Other (1)

S.I.Bozhevolnyi, ed., Plasmonic Nanoguides and Circuits (Pan Stanford, 2009).

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Figures (3)

Fig. 1
Fig. 1

(a) Dispersion of nonlinear guided modes shown as the total power flow, S, versus effective guide index, β. The green and red curves correspond to the symmetric and antisymmetric modes, respectively, and the blue curve is the asymmetric branch. (b)–(d) Characteristic mode profiles corresponding to points 1–4, at β = 16.7 . Arrows define magnetic field amplitude structure schematically.

Fig. 2
Fig. 2

(a) Wavenumber dispersion of linear modes in the coupler with the variation of distance between films, d. Film thicknesses are fixed at w = 50 nm . Dashed lines define the symmetric and antisymmetric modes of the single metal film. (b) Diagram of bifurcation power levels with coupler width variation. The dashed line defines the bifurcation power level for the single film. The inset shows the legend schematically describing mode structure.

Fig. 3
Fig. 3

Dispersion of nonlinear fundamental modes in the coupler for the distance between films of 46 nm . A symmetric modes appear at the bifurcation points 1–4, and are shown schematically in the inset.

Equations (1)

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ε m n ln = ε m ( ω ) + 3 2 ( ω p 3 π 2 ε 0 m e ) 2 / 3 h 2 e 4 ω 4 | E | 2 ,

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