Abstract

We address Anderson localization of light in disordered optical lattices where the disorder strength varies across the transverse direction. Such variation changes the preferred domains where formation of localized eigenmodes is most probable, hence drastically impacting light localization properties. Thus, step-like disorder results in formation of modes with different decay rates at both sides of the interface, while a smoothly varying disorder yields appearance of modes that are extended within weakly disordered domains and rapidly fade away in strongly disordered domains.

© 2012 Optical Society of America

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  1. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
    [CrossRef]
  2. H. de Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
    [CrossRef]
  3. A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
    [CrossRef]
  4. T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
    [CrossRef]
  5. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
    [CrossRef]
  6. Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
    [CrossRef]
  7. A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner, Opt. Lett. 35, 1172 (2010).
    [CrossRef]
  8. L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, Opt. Express 19, 13636 (2011).
    [CrossRef]
  9. D. M. Jovic, Y. S. Kivshar, C. Denz, and M. R. Belic, Phys. Rev. A 83, 033813 (2011).
    [CrossRef]
  10. V. Folli and C. Conti, Opt. Lett. 36, 2830 (2011).
    [CrossRef]
  11. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
    [CrossRef]
  12. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
    [CrossRef]
  13. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 36, 466 (2011).
    [CrossRef]
  14. S. Ghosh, G. P. Agrawal, B. P. Pal, and R. K. Varshney, Opt. Commun. 284, 201 (2011).
    [CrossRef]
  15. Y. V. Bludov and V. V. Konotop, Phys. Rev. E 76, 046604 (2007).
    [CrossRef]

2011 (5)

2010 (1)

2009 (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
[CrossRef]

2008 (2)

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

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

2007 (2)

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef]

Y. V. Bludov and V. V. Konotop, Phys. Rev. E 76, 046604 (2007).
[CrossRef]

2004 (1)

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef]

2000 (1)

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef]

1989 (1)

H. de Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
[CrossRef]

1958 (1)

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

Abouraddy, A. F.

Agrawal, G. P.

S. Ghosh, G. P. Agrawal, B. P. Pal, and R. K. Varshney, Opt. Commun. 284, 201 (2011).
[CrossRef]

Anderson, P. W.

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

Assanto, G.

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

Avidan, A.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Bartal, G.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef]

Bartelt, H.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef]

Belic, M. R.

D. M. Jovic, Y. S. Kivshar, C. Denz, and M. R. Belic, Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Bludov, Y. V.

Y. V. Bludov and V. V. Konotop, Phys. Rev. E 76, 046604 (2007).
[CrossRef]

Chabanov, A. A.

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef]

Christodoulides, D. N.

L. Martin, G. Di Giuseppe, A. Perez-Leija, R. Keil, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, A. F. Abouraddy, D. N. Christodoulides, and B. E. A. Saleh, Opt. Express 19, 13636 (2011).
[CrossRef]

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

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Conti, C.

de Raedt, H.

H. de Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
[CrossRef]

de Vries, P.

H. de Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
[CrossRef]

Denz, C.

D. M. Jovic, Y. S. Kivshar, C. Denz, and M. R. Belic, Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Di Giuseppe, G.

Dreisow, F.

Fishman, S.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef]

Folli, V.

Genack, A. Z.

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef]

Ghosh, S.

S. Ghosh, G. P. Agrawal, B. P. Pal, and R. K. Varshney, Opt. Commun. 284, 201 (2011).
[CrossRef]

Heinrich, M.

Jovic, D. M.

D. M. Jovic, Y. S. Kivshar, C. Denz, and M. R. Belic, Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Kartashov, Y. V.

Keil, R.

Kivshar, Y. S.

D. M. Jovic, Y. S. Kivshar, C. Denz, and M. R. Belic, Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Kobelke, J.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef]

Konotop, V. V.

Y. V. Bludov and V. V. Konotop, Phys. Rev. E 76, 046604 (2007).
[CrossRef]

Lagendijk, A.

H. de Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
[CrossRef]

Lahini, Y.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Lederer, F.

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

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef]

Martin, L.

Morandotti, R.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Nolte, S.

Pal, B. P.

S. Ghosh, G. P. Agrawal, B. P. Pal, and R. K. Varshney, Opt. Commun. 284, 201 (2011).
[CrossRef]

Perez-Leija, A.

Pertsch, T.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef]

Peschel, U.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef]

Pozzi, F.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

Saleh, B. E. A.

Schuster, K.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef]

Schwartz, T.

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef]

Segev, M.

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

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef]

Silberberg, Y.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

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

Sorel, M.

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[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]

Stoytchev, M.

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef]

Szameit, A.

Torner, L.

Tünnermann, A.

A. Szameit, Y. V. Kartashov, P. Zeil, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, V. A. Vysloukh, and L. Torner, Opt. Lett. 35, 1172 (2010).
[CrossRef]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef]

Varshney, R. K.

S. Ghosh, G. P. Agrawal, B. P. Pal, and R. K. Varshney, Opt. Commun. 284, 201 (2011).
[CrossRef]

Vysloukh, V. A.

Zeil, P.

Nature (2)

A. A. Chabanov, M. Stoytchev, and A. Z. Genack, Nature 404, 850 (2000).
[CrossRef]

T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
[CrossRef]

Opt. Commun. (1)

S. Ghosh, G. P. Agrawal, B. P. Pal, and R. K. Varshney, Opt. Commun. 284, 201 (2011).
[CrossRef]

Opt. Express (1)

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. (1)

P. W. Anderson, Phys. Rev. 109, 1492 (1958).
[CrossRef]

Phys. Rev. A (1)

D. M. Jovic, Y. S. Kivshar, C. Denz, and M. R. Belic, Phys. Rev. A 83, 033813 (2011).
[CrossRef]

Phys. Rev. E (1)

Y. V. Bludov and V. V. Konotop, Phys. Rev. E 76, 046604 (2007).
[CrossRef]

Phys. Rev. Lett. (3)

Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
[CrossRef]

H. de Raedt, A. Lagendijk, and P. de Vries, Phys. Rev. Lett. 62, 47 (1989).
[CrossRef]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef]

Prog. Opt. (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Dynamics of propagation up to ξ=600 averaged over 103 disorder realizations at Sl=0.0 (left) and Sl=0.2 (right). In both cases Sr=0.6 and pl=pr=11.

Fig. 2.
Fig. 2.

Average output intensity distributions at (a) Sl=0.0, (b) Sl=0.2, and (c) Sl=0.6 obtained at ξ=600 for 103 disorder realizations. In all cases Sr=0.6 and pl=pr=11.

Fig. 3.
Fig. 3.

(a) Decay rates αl, αr versus Sl at pl=pr=11 and Sr=0.6. (b) nl/nr versus Sl at pl=pr=11 and Sr=0.6. (c) Decay rate αr versus pl at Sl=0.0, Sr=0.4, pr=11. (d) Decay rates αrnl, αr versus A2 at Sl=0.0, Sr=0.4, pl=pr=11.

Fig. 4.
Fig. 4.

Histograms showing the ratio of the number of events nm when the maximum of the lowest-order eigenmode is localized on m-th waveguide to ntot for step-like disorder with (a) Sl=0.3, Sr=0.6 and (b) Sl=0.4, Sr=0.6 and (c) disorder growing to the periphery (blue) and to the center (red) of array with max(Sl,r)=0.5. In all cases pl=pr=11.

Fig. 5.
Fig. 5.

Average output intensity distributions obtained at ξ=600 for ntot=103 in the case when (a) disorder strength decreases from 0.5 in the center of array to 0 at its periphery, (b) when disorder strength grows from 0 at the periphery of the array to 0.5 in its center, and (c) when disorder strength increases linearly from 0.2 to 0.6 within 10 waveguides. In all cases pl=pr=11.

Equations (1)

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iqξ=122qη2R(η)qq|q|2.

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