Abstract

Anderson localization has been observed in various types of waves, such as matter waves, optical waves and acoustic waves. Here we reveal that the effect of Anderson localization can be also induced in metallic nonlinear nanoparticle arrays excited by a random electrically driving field. We find that the dipole-induced nonlinearity results in ballistic expansion of dipole intensity during evolution; while the randomness of the external driving field can suppress such an expansion. Increasing the strength of randomness above the threshold value, a localized pattern of dipole intensity can be generated in the metallic nanoparticle arrays. By means of statistics, the mean intensity distribution of the dipoles reveals the formation of Anderson localization. We further show that the generated Anderson localization is highly confined, with its size down to the scale of incident wavelength. The reported results might facilitate the manipulations of electromagnetic fields in the scale of wavelength.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Local photochemical plasmon mode tuning in metal nanoparticle arrays

Susan Derenko, René Kullock, Zhi Wu, Andrew Sarangan, Christiane Schuster, Lukas M. Eng, and Thomas Härtling
Opt. Mater. Express 3(6) 794-805 (2013)

Tunable Anderson localization in disorder graphene sheet arrays

Yi Xu and Hai-dong Deng
Opt. Lett. 41(3) 567-570 (2016)

Plasmonic channel waveguides in random arrays of metallic nanoparticles

Eduardo Pisano, Victor Coello, Cesar E. Garcia-Ortiz, Yiting Chen, Jonas Beermann, and Sergey I. Bozhevolnyi
Opt. Express 24(15) 17080-17089 (2016)

References

  • View by:
  • |
  • |
  • |

  1. P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109, 1492–1505 (1958).
    [Crossref]
  2. J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
    [Crossref] [PubMed]
  3. G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose-Einstein condensate,” Nature,  453, 895–898 (2008).
    [Crossref] [PubMed]
  4. J. J. Ludlam, S. N. Taraskin, S. R. Elliott, and D. A. Drabold, “Universal features of localized eigenstates in disordered systems,” J.Phys. : Condens.Matter 17, 321–327 (2005).
  5. J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser, and J. C. Garreau, “Experimental Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves,” Phys. Rev. Lett. 101, 1–30 (2008).
    [Crossref]
  6. F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light,” Nature 398, 206–207 (1999).
    [Crossref]
  7. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
    [Crossref] [PubMed]
  8. S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37, 2304–2306 (2012).
    [Crossref] [PubMed]
  9. S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 163–180 (2013).
  10. H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. V. Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nature Phys. 4, 945–948 (2008).
    [Crossref]
  11. H. Deng, F. Ye, B. A. Malomed, X. Chen, and N. C. Panoiu, “Optically and electrically tunable dirac points and zitterbewegung in graphene-Based photonic superlattices,” Phys. Rev. B 91, 201402 (2015).
    [Crossref]
  12. H. Deng, X. Chen, B. A. Malomed, N. C. Panoiu, and F. Ye, “Transverse Anderson localization of light near Dirac points of photonic nanostructures,” Sci. Rep. 5, 15585 (2015).
    [Crossref] [PubMed]
  13. Y. Xu and H. D. Deng, “Tunable Anderson localization in disorder graphene sheet arrays,” Opt. Lett. 41, 567–570 (2016).
    [Crossref] [PubMed]
  14. S. Faez, A. Lagendijk, and A. Ossipov, “Critical scaling of polarization waves on a heterogeneous chain of resonators,” Phys. Rev. B,  83, 210–216 (2010).
  15. R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett. 108, 324–329 (2012).
    [Crossref]
  16. R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength plasmonic kinks in arrays of metallic nanoparticles,” Opt. Express,  20, 2733–2739 (2012).
    [Crossref] [PubMed]
  17. R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Oscillons, soltions, and domain walls in arrays of nonlinear plasmonic nanoparticles,” Sci. Rep. 2, 873 (2012).
    [Crossref]
  18. Z. Mai, S. Fu, Y. Li, X. Zhu, Y. Liu, and J. Li, “Control of the stability and soliton formation of dipole moments in a nonlinear plasmonic finite nanoparticle array,” Photonics Nanostruct.Fundam. Appl. 13, 42–49 (2015).
    [Crossref]
  19. M. Salerno, B. A. Malomed, and V. V. Konotop, “Shock wave dynamics in a discrete nonlinear Schrodinger equation with internal losses,” Phys. Rev. E,  62, 8651–8656 (2000).
    [Crossref]
  20. L. Yang, X. Xie, S. Wang, and J. Zhou, “Minimized spot of annular radially polarized focusing beam,” Opt. Lett. 38, 1331–1333 (2013).
    [Crossref] [PubMed]
  21. X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).
    [Crossref]
  22. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B,  6, 4370–4379 (1972).
    [Crossref]
  23. V. P. Drachev, A. K. Buin, H. Nakotte, and V. M. Shalaev, “Size dependent χ(3) for conduction electrons in Ag nanoparticles,” Nano Lett. 4, 1535–1539 (2004).
    [Crossref]

2016 (1)

2015 (3)

H. Deng, F. Ye, B. A. Malomed, X. Chen, and N. C. Panoiu, “Optically and electrically tunable dirac points and zitterbewegung in graphene-Based photonic superlattices,” Phys. Rev. B 91, 201402 (2015).
[Crossref]

H. Deng, X. Chen, B. A. Malomed, N. C. Panoiu, and F. Ye, “Transverse Anderson localization of light near Dirac points of photonic nanostructures,” Sci. Rep. 5, 15585 (2015).
[Crossref] [PubMed]

Z. Mai, S. Fu, Y. Li, X. Zhu, Y. Liu, and J. Li, “Control of the stability and soliton formation of dipole moments in a nonlinear plasmonic finite nanoparticle array,” Photonics Nanostruct.Fundam. Appl. 13, 42–49 (2015).
[Crossref]

2014 (1)

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).
[Crossref]

2013 (2)

L. Yang, X. Xie, S. Wang, and J. Zhou, “Minimized spot of annular radially polarized focusing beam,” Opt. Lett. 38, 1331–1333 (2013).
[Crossref] [PubMed]

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 163–180 (2013).

2012 (4)

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett. 108, 324–329 (2012).
[Crossref]

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength plasmonic kinks in arrays of metallic nanoparticles,” Opt. Express,  20, 2733–2739 (2012).
[Crossref] [PubMed]

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Oscillons, soltions, and domain walls in arrays of nonlinear plasmonic nanoparticles,” Sci. Rep. 2, 873 (2012).
[Crossref]

S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37, 2304–2306 (2012).
[Crossref] [PubMed]

2010 (1)

S. Faez, A. Lagendijk, and A. Ossipov, “Critical scaling of polarization waves on a heterogeneous chain of resonators,” Phys. Rev. B,  83, 210–216 (2010).

2008 (4)

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. V. Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nature Phys. 4, 945–948 (2008).
[Crossref]

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose-Einstein condensate,” Nature,  453, 895–898 (2008).
[Crossref] [PubMed]

J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser, and J. C. Garreau, “Experimental Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves,” Phys. Rev. Lett. 101, 1–30 (2008).
[Crossref]

2007 (1)

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

2005 (1)

J. J. Ludlam, S. N. Taraskin, S. R. Elliott, and D. A. Drabold, “Universal features of localized eigenstates in disordered systems,” J.Phys. : Condens.Matter 17, 321–327 (2005).

2004 (1)

V. P. Drachev, A. K. Buin, H. Nakotte, and V. M. Shalaev, “Size dependent χ(3) for conduction electrons in Ag nanoparticles,” Nano Lett. 4, 1535–1539 (2004).
[Crossref]

2000 (1)

M. Salerno, B. A. Malomed, and V. V. Konotop, “Shock wave dynamics in a discrete nonlinear Schrodinger equation with internal losses,” Phys. Rev. E,  62, 8651–8656 (2000).
[Crossref]

1999 (1)

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light,” Nature 398, 206–207 (1999).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B,  6, 4370–4379 (1972).
[Crossref]

1958 (1)

P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109, 1492–1505 (1958).
[Crossref]

Anderson, P. W.

P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109, 1492–1505 (1958).
[Crossref]

Aspect, A.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Ballato, J.

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 163–180 (2013).

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

Belov, P. A.

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Oscillons, soltions, and domain walls in arrays of nonlinear plasmonic nanoparticles,” Sci. Rep. 2, 873 (2012).
[Crossref]

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett. 108, 324–329 (2012).
[Crossref]

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength plasmonic kinks in arrays of metallic nanoparticles,” Opt. Express,  20, 2733–2739 (2012).
[Crossref] [PubMed]

Bernard, A.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Billy, J.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Bouyer, P.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Buin, A. K.

V. P. Drachev, A. K. Buin, H. Nakotte, and V. M. Shalaev, “Size dependent χ(3) for conduction electrons in Ag nanoparticles,” Nano Lett. 4, 1535–1539 (2004).
[Crossref]

Chabé, J.

J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser, and J. C. Garreau, “Experimental Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves,” Phys. Rev. Lett. 101, 1–30 (2008).
[Crossref]

Chen, X.

H. Deng, X. Chen, B. A. Malomed, N. C. Panoiu, and F. Ye, “Transverse Anderson localization of light near Dirac points of photonic nanostructures,” Sci. Rep. 5, 15585 (2015).
[Crossref] [PubMed]

H. Deng, F. Ye, B. A. Malomed, X. Chen, and N. C. Panoiu, “Optically and electrically tunable dirac points and zitterbewegung in graphene-Based photonic superlattices,” Phys. Rev. B 91, 201402 (2015).
[Crossref]

Chen, Y.

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B,  6, 4370–4379 (1972).
[Crossref]

Clément, D.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

D’Errico, C.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose-Einstein condensate,” Nature,  453, 895–898 (2008).
[Crossref] [PubMed]

Delande, D.

J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser, and J. C. Garreau, “Experimental Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves,” Phys. Rev. Lett. 101, 1–30 (2008).
[Crossref]

Deng, H.

H. Deng, F. Ye, B. A. Malomed, X. Chen, and N. C. Panoiu, “Optically and electrically tunable dirac points and zitterbewegung in graphene-Based photonic superlattices,” Phys. Rev. B 91, 201402 (2015).
[Crossref]

H. Deng, X. Chen, B. A. Malomed, N. C. Panoiu, and F. Ye, “Transverse Anderson localization of light near Dirac points of photonic nanostructures,” Sci. Rep. 5, 15585 (2015).
[Crossref] [PubMed]

Deng, H. D.

Drabold, D. A.

J. J. Ludlam, S. N. Taraskin, S. R. Elliott, and D. A. Drabold, “Universal features of localized eigenstates in disordered systems,” J.Phys. : Condens.Matter 17, 321–327 (2005).

Drachev, V. P.

V. P. Drachev, A. K. Buin, H. Nakotte, and V. M. Shalaev, “Size dependent χ(3) for conduction electrons in Ag nanoparticles,” Nano Lett. 4, 1535–1539 (2004).
[Crossref]

Elliott, S. R.

J. J. Ludlam, S. N. Taraskin, S. R. Elliott, and D. A. Drabold, “Universal features of localized eigenstates in disordered systems,” J.Phys. : Condens.Matter 17, 321–327 (2005).

Faez, S.

S. Faez, A. Lagendijk, and A. Ossipov, “Critical scaling of polarization waves on a heterogeneous chain of resonators,” Phys. Rev. B,  83, 210–216 (2010).

Fallani, L.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose-Einstein condensate,” Nature,  453, 895–898 (2008).
[Crossref] [PubMed]

Fattori, M.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose-Einstein condensate,” Nature,  453, 895–898 (2008).
[Crossref] [PubMed]

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

Fort, C.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose-Einstein condensate,” Nature,  453, 895–898 (2008).
[Crossref] [PubMed]

Frazier, R. J.

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 163–180 (2013).

S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37, 2304–2306 (2012).
[Crossref] [PubMed]

Fu, S.

Z. Mai, S. Fu, Y. Li, X. Zhu, Y. Liu, and J. Li, “Control of the stability and soliton formation of dipole moments in a nonlinear plasmonic finite nanoparticle array,” Photonics Nanostruct.Fundam. Appl. 13, 42–49 (2015).
[Crossref]

Garreau, J. C.

J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser, and J. C. Garreau, “Experimental Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves,” Phys. Rev. Lett. 101, 1–30 (2008).
[Crossref]

Grémaud, B.

J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser, and J. C. Garreau, “Experimental Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves,” Phys. Rev. Lett. 101, 1–30 (2008).
[Crossref]

Hambrecht, B.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Hawkins, T.

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 163–180 (2013).

Hu, H.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. V. Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nature Phys. 4, 945–948 (2008).
[Crossref]

Inguscio, M.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose-Einstein condensate,” Nature,  453, 895–898 (2008).
[Crossref] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B,  6, 4370–4379 (1972).
[Crossref]

Josse, V.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Karbasi, S.

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 163–180 (2013).

S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37, 2304–2306 (2012).
[Crossref] [PubMed]

Kivshar, Y. S.

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength plasmonic kinks in arrays of metallic nanoparticles,” Opt. Express,  20, 2733–2739 (2012).
[Crossref] [PubMed]

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett. 108, 324–329 (2012).
[Crossref]

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Oscillons, soltions, and domain walls in arrays of nonlinear plasmonic nanoparticles,” Sci. Rep. 2, 873 (2012).
[Crossref]

Koch, K. W.

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 163–180 (2013).

S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37, 2304–2306 (2012).
[Crossref] [PubMed]

Konotop, V. V.

M. Salerno, B. A. Malomed, and V. V. Konotop, “Shock wave dynamics in a discrete nonlinear Schrodinger equation with internal losses,” Phys. Rev. E,  62, 8651–8656 (2000).
[Crossref]

Lagendijk, A.

S. Faez, A. Lagendijk, and A. Ossipov, “Critical scaling of polarization waves on a heterogeneous chain of resonators,” Phys. Rev. B,  83, 210–216 (2010).

Lemarié, G.

J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser, and J. C. Garreau, “Experimental Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves,” Phys. Rev. Lett. 101, 1–30 (2008).
[Crossref]

Lenke, R.

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light,” Nature 398, 206–207 (1999).
[Crossref]

Li, J.

Z. Mai, S. Fu, Y. Li, X. Zhu, Y. Liu, and J. Li, “Control of the stability and soliton formation of dipole moments in a nonlinear plasmonic finite nanoparticle array,” Photonics Nanostruct.Fundam. Appl. 13, 42–49 (2015).
[Crossref]

Li, Y.

Z. Mai, S. Fu, Y. Li, X. Zhu, Y. Liu, and J. Li, “Control of the stability and soliton formation of dipole moments in a nonlinear plasmonic finite nanoparticle array,” Photonics Nanostruct.Fundam. Appl. 13, 42–49 (2015).
[Crossref]

Liu, Y.

Z. Mai, S. Fu, Y. Li, X. Zhu, Y. Liu, and J. Li, “Control of the stability and soliton formation of dipole moments in a nonlinear plasmonic finite nanoparticle array,” Photonics Nanostruct.Fundam. Appl. 13, 42–49 (2015).
[Crossref]

Ludlam, J. J.

J. J. Ludlam, S. N. Taraskin, S. R. Elliott, and D. A. Drabold, “Universal features of localized eigenstates in disordered systems,” J.Phys. : Condens.Matter 17, 321–327 (2005).

Lugan, P.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Mafi, A.

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 163–180 (2013).

S. Karbasi, C. R. Mirr, P. G. Yarandi, R. J. Frazier, K. W. Koch, and A. Mafi, “Observation of transverse Anderson localization in an optical fiber,” Opt. Lett. 37, 2304–2306 (2012).
[Crossref] [PubMed]

Mai, Z.

Z. Mai, S. Fu, Y. Li, X. Zhu, Y. Liu, and J. Li, “Control of the stability and soliton formation of dipole moments in a nonlinear plasmonic finite nanoparticle array,” Photonics Nanostruct.Fundam. Appl. 13, 42–49 (2015).
[Crossref]

Malomed, B. A.

H. Deng, F. Ye, B. A. Malomed, X. Chen, and N. C. Panoiu, “Optically and electrically tunable dirac points and zitterbewegung in graphene-Based photonic superlattices,” Phys. Rev. B 91, 201402 (2015).
[Crossref]

H. Deng, X. Chen, B. A. Malomed, N. C. Panoiu, and F. Ye, “Transverse Anderson localization of light near Dirac points of photonic nanostructures,” Sci. Rep. 5, 15585 (2015).
[Crossref] [PubMed]

M. Salerno, B. A. Malomed, and V. V. Konotop, “Shock wave dynamics in a discrete nonlinear Schrodinger equation with internal losses,” Phys. Rev. E,  62, 8651–8656 (2000).
[Crossref]

Maret, G.

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light,” Nature 398, 206–207 (1999).
[Crossref]

Mirr, C. R.

Modugno, G.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose-Einstein condensate,” Nature,  453, 895–898 (2008).
[Crossref] [PubMed]

Modugno, M.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose-Einstein condensate,” Nature,  453, 895–898 (2008).
[Crossref] [PubMed]

Nakotte, H.

V. P. Drachev, A. K. Buin, H. Nakotte, and V. M. Shalaev, “Size dependent χ(3) for conduction electrons in Ag nanoparticles,” Nano Lett. 4, 1535–1539 (2004).
[Crossref]

Noskov, R. E.

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett. 108, 324–329 (2012).
[Crossref]

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength plasmonic kinks in arrays of metallic nanoparticles,” Opt. Express,  20, 2733–2739 (2012).
[Crossref] [PubMed]

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Oscillons, soltions, and domain walls in arrays of nonlinear plasmonic nanoparticles,” Sci. Rep. 2, 873 (2012).
[Crossref]

Ossipov, A.

S. Faez, A. Lagendijk, and A. Ossipov, “Critical scaling of polarization waves on a heterogeneous chain of resonators,” Phys. Rev. B,  83, 210–216 (2010).

Page, J. H.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. V. Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nature Phys. 4, 945–948 (2008).
[Crossref]

Panoiu, N. C.

H. Deng, F. Ye, B. A. Malomed, X. Chen, and N. C. Panoiu, “Optically and electrically tunable dirac points and zitterbewegung in graphene-Based photonic superlattices,” Phys. Rev. B 91, 201402 (2015).
[Crossref]

H. Deng, X. Chen, B. A. Malomed, N. C. Panoiu, and F. Ye, “Transverse Anderson localization of light near Dirac points of photonic nanostructures,” Sci. Rep. 5, 15585 (2015).
[Crossref] [PubMed]

Roati, G.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose-Einstein condensate,” Nature,  453, 895–898 (2008).
[Crossref] [PubMed]

Salerno, M.

M. Salerno, B. A. Malomed, and V. V. Konotop, “Shock wave dynamics in a discrete nonlinear Schrodinger equation with internal losses,” Phys. Rev. E,  62, 8651–8656 (2000).
[Crossref]

Sanchez-Palencia, L.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

Scheffold, F.

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light,” Nature 398, 206–207 (1999).
[Crossref]

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

Segev, M.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

Shalaev, V. M.

V. P. Drachev, A. K. Buin, H. Nakotte, and V. M. Shalaev, “Size dependent χ(3) for conduction electrons in Ag nanoparticles,” Nano Lett. 4, 1535–1539 (2004).
[Crossref]

Skipetrov, S. E.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. V. Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nature Phys. 4, 945–948 (2008).
[Crossref]

Strybulevych, A.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. V. Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nature Phys. 4, 945–948 (2008).
[Crossref]

Szriftgiser, P.

J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser, and J. C. Garreau, “Experimental Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves,” Phys. Rev. Lett. 101, 1–30 (2008).
[Crossref]

Taraskin, S. N.

J. J. Ludlam, S. N. Taraskin, S. R. Elliott, and D. A. Drabold, “Universal features of localized eigenstates in disordered systems,” J.Phys. : Condens.Matter 17, 321–327 (2005).

Tiggelen, B. A. V.

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. V. Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nature Phys. 4, 945–948 (2008).
[Crossref]

Tweer, R.

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light,” Nature 398, 206–207 (1999).
[Crossref]

Wang, S.

Xie, X.

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).
[Crossref]

L. Yang, X. Xie, S. Wang, and J. Zhou, “Minimized spot of annular radially polarized focusing beam,” Opt. Lett. 38, 1331–1333 (2013).
[Crossref] [PubMed]

Xu, Y.

Yang, K.

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).
[Crossref]

Yang, L.

Yarandi, P. G.

Ye, F.

H. Deng, F. Ye, B. A. Malomed, X. Chen, and N. C. Panoiu, “Optically and electrically tunable dirac points and zitterbewegung in graphene-Based photonic superlattices,” Phys. Rev. B 91, 201402 (2015).
[Crossref]

H. Deng, X. Chen, B. A. Malomed, N. C. Panoiu, and F. Ye, “Transverse Anderson localization of light near Dirac points of photonic nanostructures,” Sci. Rep. 5, 15585 (2015).
[Crossref] [PubMed]

Zaccanti, M.

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose-Einstein condensate,” Nature,  453, 895–898 (2008).
[Crossref] [PubMed]

Zhou, J.

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).
[Crossref]

L. Yang, X. Xie, S. Wang, and J. Zhou, “Minimized spot of annular radially polarized focusing beam,” Opt. Lett. 38, 1331–1333 (2013).
[Crossref] [PubMed]

Zhu, X.

Z. Mai, S. Fu, Y. Li, X. Zhu, Y. Liu, and J. Li, “Control of the stability and soliton formation of dipole moments in a nonlinear plasmonic finite nanoparticle array,” Photonics Nanostruct.Fundam. Appl. 13, 42–49 (2015).
[Crossref]

Zuo, Z.

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

J.Phys. : Condens.Matter (1)

J. J. Ludlam, S. N. Taraskin, S. R. Elliott, and D. A. Drabold, “Universal features of localized eigenstates in disordered systems,” J.Phys. : Condens.Matter 17, 321–327 (2005).

Nano Lett. (1)

V. P. Drachev, A. K. Buin, H. Nakotte, and V. M. Shalaev, “Size dependent χ(3) for conduction electrons in Ag nanoparticles,” Nano Lett. 4, 1535–1539 (2004).
[Crossref]

Nat. Commun. (1)

S. Karbasi, R. J. Frazier, K. W. Koch, T. Hawkins, J. Ballato, and A. Mafi, “Image transport through a disordered optical fibre mediated by transverse Anderson localization,” Nat. Commun. 5, 163–180 (2013).

Nature (4)

J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, “Direct observation of Anderson localization of matter waves in a controlled disorder,” Nature 453, 891–894 (2008).
[Crossref] [PubMed]

G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, “Anderson localization of a non-interacting Bose-Einstein condensate,” Nature,  453, 895–898 (2008).
[Crossref] [PubMed]

F. Scheffold, R. Lenke, R. Tweer, and G. Maret, “Localization or classical diffusion of light,” Nature 398, 206–207 (1999).
[Crossref]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446, 52–55 (2007).
[Crossref] [PubMed]

Nature Phys. (1)

H. Hu, A. Strybulevych, J. H. Page, S. E. Skipetrov, and B. A. V. Tiggelen, “Localization of ultrasound in a three-dimensional elastic network,” Nature Phys. 4, 945–948 (2008).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Photonics Nanostruct.Fundam. Appl. (1)

Z. Mai, S. Fu, Y. Li, X. Zhu, Y. Liu, and J. Li, “Control of the stability and soliton formation of dipole moments in a nonlinear plasmonic finite nanoparticle array,” Photonics Nanostruct.Fundam. Appl. 13, 42–49 (2015).
[Crossref]

Phys. Rev. (1)

P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109, 1492–1505 (1958).
[Crossref]

Phys. Rev. B (3)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B,  6, 4370–4379 (1972).
[Crossref]

S. Faez, A. Lagendijk, and A. Ossipov, “Critical scaling of polarization waves on a heterogeneous chain of resonators,” Phys. Rev. B,  83, 210–216 (2010).

H. Deng, F. Ye, B. A. Malomed, X. Chen, and N. C. Panoiu, “Optically and electrically tunable dirac points and zitterbewegung in graphene-Based photonic superlattices,” Phys. Rev. B 91, 201402 (2015).
[Crossref]

Phys. Rev. E (1)

M. Salerno, B. A. Malomed, and V. V. Konotop, “Shock wave dynamics in a discrete nonlinear Schrodinger equation with internal losses,” Phys. Rev. E,  62, 8651–8656 (2000).
[Crossref]

Phys. Rev. Lett. (3)

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett. 108, 324–329 (2012).
[Crossref]

J. Chabé, G. Lemarié, B. Grémaud, D. Delande, P. Szriftgiser, and J. C. Garreau, “Experimental Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves,” Phys. Rev. Lett. 101, 1–30 (2008).
[Crossref]

X. Xie, Y. Chen, K. Yang, and J. Zhou, “Harnessing the point-spread function for high-resolution far-field optical microscopy,” Phys. Rev. Lett. 113, 263901 (2014).
[Crossref]

Sci. Rep. (2)

H. Deng, X. Chen, B. A. Malomed, N. C. Panoiu, and F. Ye, “Transverse Anderson localization of light near Dirac points of photonic nanostructures,” Sci. Rep. 5, 15585 (2015).
[Crossref] [PubMed]

R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Oscillons, soltions, and domain walls in arrays of nonlinear plasmonic nanoparticles,” Sci. Rep. 2, 873 (2012).
[Crossref]

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 (7)

Fig. 1
Fig. 1 Schematic illustration of an array of spherical silver nanoparticles embedded in a SiO2 host; the radius of the sphere is a, and the center-to-center distance of two adjacent particles is d. The dipoles are induced by an electrical driving field.
Fig. 2
Fig. 2 Bright plasmonic dipole mode in a 100-particle system excited by a homogeneous electric field of |E0|2 = 0.90 × 10−4 under Ω = −0.1 (the incident wavelength is approximately 440 nm): (a) initial dipole intensity at τ = 0, (b) dipole intensity at τ = 2000, (c) the evolution of the dipole intensity under and excitation of |E0|2 = 0.90 × 10−4, and (d) the evolution of the dipole intensity under and excitation of |E0|2 = 0.6 × 10−4, which is below the threshold value |Ec|2.
Fig. 3
Fig. 3 Localized plasmonic dipole mode in a 100-particle system excited by the random electrical driving field under Ω = −0.1: (a) initial dipole intensity distribution at τ = 0, (b) the dipole intensity distribution at τ = 2000, and (c) the evolution of dipole intensity.
Fig. 4
Fig. 4 The statistical results of 200 real-time evolutions of dipole intensity excited by the random electrical driving field under Ω = −0.1. The varying range intensity of the random driving field for each simulation is kept the same, i.e., set as |E0|2 = 0.45 × 10−4 ∼ 1.35 × 10−4: (a) Mean distribution of dipole intensity at τ = 2000. The blue circles denote the calculated mean value; while the red curve represents the fitting result of 0.14exp[±(x − 51)/2.5] + 0.007. (b) The evolution dynamics of the mean dipole intensity.
Fig. 5
Fig. 5 (a)∼(c) The evolution of dipole intensity in a 100-particle system excited by the random electrical driving field under Ω = −0.1, |E0|2 = 0.9 × 10−4: (a) κ = 0.2, (b) κ = 0.4, and (c) κ = 0.6. (d)∼(f) The corresponding statistical results for (a)∼(c) after 200 real-time evolutions: (d) κ = 0.2, (e) κ = 0.4, and (f) κ = 0.6.
Fig. 6
Fig. 6 The statistical results of 200 real-time simulations with different values of κ. The detuning is set as Ω = −0.1. (a) The distribution of mean value of the dipole intensity at τ = 2000; (b) the width evolution of localized dipole modes for different values of κ.
Fig. 7
Fig. 7 The relation between κc and the middle value of random external field (|E0|2) with the same settings as discussed above.

Equations (6)

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

i d P n d τ + ( i γ + Ω + | P n | 2 ) P n + m n G n , m P m = E n ,
i d P n d τ + ( i γ + Ω + | P n | 2 ) P n + m n G n , m P m = E n ,
G n , m = η 2 [ ( k 0 d ) 2 i k 0 d | n m | 1 | n m | 2 ] e i k 0 d | n m | | n m | ,
G n , m = η ( i k 0 d | n m | + 1 | n m | 2 ) e i k 0 d | n m | | n m | ,
| E | 2 = | E 0 | 2 ± κ | E 0 | 2 ,
W = ( n = 1 N | P n | 2 ) 2 n = 1 N | P n | 4 ,

Metrics