Abstract

We demonstrate that optically driven two-dimensional lattices of nonlinear metal nanoparticles can support a variety of dissipative localized modes including Faraday ripples, trapped and walking solitons, oscillons, and switching waves connecting different polarization states.

© 2013 Optical Society of America

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References

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  1. M. Kauranen and A. V. Zayats, Nat. Photonics 6, 737 (2012).
    [CrossRef]
  2. T. Utikal, M. Hentschel, and H. Giessen, Appl. Phys. B 105, 51 (2011).
    [CrossRef]
  3. T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, Nat. Commun. 2, 333 (2011).
    [CrossRef]
  4. P. Ginzburg, A. V. Krasavin, and A. V. Zayats, New J. Phys. 15, 013031 (2013).
    [CrossRef]
  5. A. A. Zharov, R. E. Noskov, and M. V. Tsarev, J. Appl. Phys. 106, 073104 (2009).
    [CrossRef]
  6. R. E. Noskov, A. A. Zharov, and M. V. Tsarev, Phys. Rev. B 82, 073404 (2010).
    [CrossRef]
  7. H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
    [CrossRef]
  8. A. A. Govyadinov, G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, Phys. Rev. B 84, 155461 (2011).
    [CrossRef]
  9. R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Phys. Rev. Lett. 108, 093901 (2012).
    [CrossRef]
  10. R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Opt. Express 20, 2733 (2012).
    [CrossRef]
  11. R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Sci. Rep. 2, 873 (2012).
  12. J. Miles, J. Fluid Mech. 248, 671 (1993).
    [CrossRef]
  13. C. Torres-Torres, N. Peréa-López, J. A. Reyes-Esqueda, L. Rodríguez-Fernández, A. Crespo-Sosa, J. C. Cheang-Wong, and A. Oliver, Int. J. Nanomed. 5, 925 (2010).
    [CrossRef]

2013 (1)

P. Ginzburg, A. V. Krasavin, and A. V. Zayats, New J. Phys. 15, 013031 (2013).
[CrossRef]

2012 (4)

M. Kauranen and A. V. Zayats, Nat. Photonics 6, 737 (2012).
[CrossRef]

R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Phys. Rev. Lett. 108, 093901 (2012).
[CrossRef]

R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Opt. Express 20, 2733 (2012).
[CrossRef]

R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Sci. Rep. 2, 873 (2012).

2011 (3)

T. Utikal, M. Hentschel, and H. Giessen, Appl. Phys. B 105, 51 (2011).
[CrossRef]

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, Nat. Commun. 2, 333 (2011).
[CrossRef]

A. A. Govyadinov, G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, Phys. Rev. B 84, 155461 (2011).
[CrossRef]

2010 (2)

C. Torres-Torres, N. Peréa-López, J. A. Reyes-Esqueda, L. Rodríguez-Fernández, A. Crespo-Sosa, J. C. Cheang-Wong, and A. Oliver, Int. J. Nanomed. 5, 925 (2010).
[CrossRef]

R. E. Noskov, A. A. Zharov, and M. V. Tsarev, Phys. Rev. B 82, 073404 (2010).
[CrossRef]

2009 (1)

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, J. Appl. Phys. 106, 073104 (2009).
[CrossRef]

2008 (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

1993 (1)

J. Miles, J. Fluid Mech. 248, 671 (1993).
[CrossRef]

Belov, P. A.

R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Phys. Rev. Lett. 108, 093901 (2012).
[CrossRef]

R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Sci. Rep. 2, 873 (2012).

R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Opt. Express 20, 2733 (2012).
[CrossRef]

Cheang-Wong, J. C.

C. Torres-Torres, N. Peréa-López, J. A. Reyes-Esqueda, L. Rodríguez-Fernández, A. Crespo-Sosa, J. C. Cheang-Wong, and A. Oliver, Int. J. Nanomed. 5, 925 (2010).
[CrossRef]

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Crespo-Sosa, A.

C. Torres-Torres, N. Peréa-López, J. A. Reyes-Esqueda, L. Rodríguez-Fernández, A. Crespo-Sosa, J. C. Cheang-Wong, and A. Oliver, Int. J. Nanomed. 5, 925 (2010).
[CrossRef]

Giessen, H.

T. Utikal, M. Hentschel, and H. Giessen, Appl. Phys. B 105, 51 (2011).
[CrossRef]

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, Nat. Commun. 2, 333 (2011).
[CrossRef]

Ginzburg, P.

P. Ginzburg, A. V. Krasavin, and A. V. Zayats, New J. Phys. 15, 013031 (2013).
[CrossRef]

Govyadinov, A. A.

A. A. Govyadinov, G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, Phys. Rev. B 84, 155461 (2011).
[CrossRef]

Hentschel, M.

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, Nat. Commun. 2, 333 (2011).
[CrossRef]

T. Utikal, M. Hentschel, and H. Giessen, Appl. Phys. B 105, 51 (2011).
[CrossRef]

Kauranen, M.

M. Kauranen and A. V. Zayats, Nat. Photonics 6, 737 (2012).
[CrossRef]

Kivshar, Yu. S.

R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Phys. Rev. Lett. 108, 093901 (2012).
[CrossRef]

R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Opt. Express 20, 2733 (2012).
[CrossRef]

R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Sci. Rep. 2, 873 (2012).

Krasavin, A. V.

P. Ginzburg, A. V. Krasavin, and A. V. Zayats, New J. Phys. 15, 013031 (2013).
[CrossRef]

Kratzer, K.

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, Nat. Commun. 2, 333 (2011).
[CrossRef]

Lippitz, M.

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, Nat. Commun. 2, 333 (2011).
[CrossRef]

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Markel, V. A.

A. A. Govyadinov, G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, Phys. Rev. B 84, 155461 (2011).
[CrossRef]

Miles, J.

J. Miles, J. Fluid Mech. 248, 671 (1993).
[CrossRef]

Molnar, D.

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, Nat. Commun. 2, 333 (2011).
[CrossRef]

Noskov, R. E.

R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Phys. Rev. Lett. 108, 093901 (2012).
[CrossRef]

R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Opt. Express 20, 2733 (2012).
[CrossRef]

R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Sci. Rep. 2, 873 (2012).

R. E. Noskov, A. A. Zharov, and M. V. Tsarev, Phys. Rev. B 82, 073404 (2010).
[CrossRef]

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, J. Appl. Phys. 106, 073104 (2009).
[CrossRef]

Oliver, A.

C. Torres-Torres, N. Peréa-López, J. A. Reyes-Esqueda, L. Rodríguez-Fernández, A. Crespo-Sosa, J. C. Cheang-Wong, and A. Oliver, Int. J. Nanomed. 5, 925 (2010).
[CrossRef]

Panasyuk, G. Y.

A. A. Govyadinov, G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, Phys. Rev. B 84, 155461 (2011).
[CrossRef]

Peréa-López, N.

C. Torres-Torres, N. Peréa-López, J. A. Reyes-Esqueda, L. Rodríguez-Fernández, A. Crespo-Sosa, J. C. Cheang-Wong, and A. Oliver, Int. J. Nanomed. 5, 925 (2010).
[CrossRef]

Reyes-Esqueda, J. A.

C. Torres-Torres, N. Peréa-López, J. A. Reyes-Esqueda, L. Rodríguez-Fernández, A. Crespo-Sosa, J. C. Cheang-Wong, and A. Oliver, Int. J. Nanomed. 5, 925 (2010).
[CrossRef]

Rodríguez-Fernández, L.

C. Torres-Torres, N. Peréa-López, J. A. Reyes-Esqueda, L. Rodríguez-Fernández, A. Crespo-Sosa, J. C. Cheang-Wong, and A. Oliver, Int. J. Nanomed. 5, 925 (2010).
[CrossRef]

Schotland, J. C.

A. A. Govyadinov, G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, Phys. Rev. B 84, 155461 (2011).
[CrossRef]

Schumacher, T.

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, Nat. Commun. 2, 333 (2011).
[CrossRef]

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Torres-Torres, C.

C. Torres-Torres, N. Peréa-López, J. A. Reyes-Esqueda, L. Rodríguez-Fernández, A. Crespo-Sosa, J. C. Cheang-Wong, and A. Oliver, Int. J. Nanomed. 5, 925 (2010).
[CrossRef]

Tsarev, M. V.

R. E. Noskov, A. A. Zharov, and M. V. Tsarev, Phys. Rev. B 82, 073404 (2010).
[CrossRef]

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, J. Appl. Phys. 106, 073104 (2009).
[CrossRef]

Utikal, T.

T. Utikal, M. Hentschel, and H. Giessen, Appl. Phys. B 105, 51 (2011).
[CrossRef]

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Zayats, A. V.

P. Ginzburg, A. V. Krasavin, and A. V. Zayats, New J. Phys. 15, 013031 (2013).
[CrossRef]

M. Kauranen and A. V. Zayats, Nat. Photonics 6, 737 (2012).
[CrossRef]

Zharov, A. A.

R. E. Noskov, A. A. Zharov, and M. V. Tsarev, Phys. Rev. B 82, 073404 (2010).
[CrossRef]

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, J. Appl. Phys. 106, 073104 (2009).
[CrossRef]

Appl. Phys. B (1)

T. Utikal, M. Hentschel, and H. Giessen, Appl. Phys. B 105, 51 (2011).
[CrossRef]

Int. J. Nanomed. (1)

C. Torres-Torres, N. Peréa-López, J. A. Reyes-Esqueda, L. Rodríguez-Fernández, A. Crespo-Sosa, J. C. Cheang-Wong, and A. Oliver, Int. J. Nanomed. 5, 925 (2010).
[CrossRef]

J. Appl. Phys. (1)

A. A. Zharov, R. E. Noskov, and M. V. Tsarev, J. Appl. Phys. 106, 073104 (2009).
[CrossRef]

J. Fluid Mech. (1)

J. Miles, J. Fluid Mech. 248, 671 (1993).
[CrossRef]

Nat. Commun. (1)

T. Schumacher, K. Kratzer, D. Molnar, M. Hentschel, H. Giessen, and M. Lippitz, Nat. Commun. 2, 333 (2011).
[CrossRef]

Nat. Photonics (2)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

M. Kauranen and A. V. Zayats, Nat. Photonics 6, 737 (2012).
[CrossRef]

New J. Phys. (1)

P. Ginzburg, A. V. Krasavin, and A. V. Zayats, New J. Phys. 15, 013031 (2013).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (2)

A. A. Govyadinov, G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, Phys. Rev. B 84, 155461 (2011).
[CrossRef]

R. E. Noskov, A. A. Zharov, and M. V. Tsarev, Phys. Rev. B 82, 073404 (2010).
[CrossRef]

Phys. Rev. Lett. (1)

R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Phys. Rev. Lett. 108, 093901 (2012).
[CrossRef]

Sci. Rep. (1)

R. E. Noskov, P. A. Belov, and Yu. S. Kivshar, Sci. Rep. 2, 873 (2012).

Supplementary Material (3)

» Media 1: MOV (11369 KB)     
» Media 2: MOV (473 KB)     
» Media 3: MOV (1451 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Artistic view of a square lattice of metal nanoparticles illuminated by a laser beam. Reddish particles indicate a discrete plasmon soliton.

Fig. 2.
Fig. 2.

Bifurcation diagram showing the regimes of bistability and MI with the existence domains for standing and walking solitons. Green stars mark external field parameters used for snapshots in Figs. 3(a), 3(c), 3(d), and 4(a). Inset demonstrates the dependence of polarization |P0|2 on the intensity for homogeneous excitation. Red and green dots indicate regions of MI with respect to slow and fast eigenmodes of the lattice, respectively.

Fig. 3.
Fig. 3.

Snapshots of the particles’ polarizations |Pn,m|2 corresponding to (a) (Media 1) Faraday ripples (Ω=0.01, |E0|2=1.5×104) and (c) (Media 2) standing (Ω=0.1, |E0|2=1.7×104) and (d) (Media 3) walking plasmon solitons (Ω=0.01, |E0|2=104). The panel (b) shows the contour map of the instability growth rate in the plane of wave vectors corresponding to (a), and the black circle denotes the light cone, K=k0. In the panel (c) “A,” “B,” “C,” and “D” mark one-particle, asymmetric and symmetric two-particle, and asymmetric three-particle discrete solitons, respectively. All simulations are carried out for a 101×101 nanoparticle array. See also Media 1, Media 2, and Media 3 for the associated time animations.

Fig. 4.
Fig. 4.

(a) Profile of the polarizations |Pn,m|2 for the stationary kink obtained at Ω=0.01 and |E0|2=0.83×104. Small amplitude modulations are caused by the edge effects. (b) Normalized kink’s velocity versus intensity of the applied field at Ω=0.01. Shaded areas show existence domains of (blue) solitons and (red) MI.

Equations (2)

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

idPn,mdτ+(Ωiγ+|Pn,m|2)Pn,m+nnmmGnn,mmPn,m=En,m,
Gnn,mm=η2[(k0d)2ik0dΔr1Δr2]exp(ik0dΔr)Δr

Metrics