Abstract

We investigate the interplay of Bloch oscillations and Anderson localization in optics. Gradual washing out of Bloch oscillations and the formation of nearly stationary averaged intensity distributions, which are symmetric for narrow and strongly asymmetric for broad input excitations, are observed experimentally in laser-written waveguide arrays. At large disorder levels Bloch oscillations are completely destroyed and both narrow and wide excitations lead to symmetric stationary averaged intensity distributions with exponentially decaying tails.

© 2013 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
    [CrossRef]
  2. G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
    [CrossRef]
  3. T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
    [CrossRef]
  4. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
    [CrossRef]
  5. D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
    [CrossRef]
  6. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
    [CrossRef]
  7. Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
    [CrossRef]
  8. G. H. Wannier, Phys. Rev. 117, 432 (1960).
    [CrossRef]
  9. F. Bentosela, V. Grecchi, and F. Zironi, Phys. Rev. B 31, 6909 (1985).
    [CrossRef]
  10. F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, and R. Weder, Commun. Math. Phys. 88, 387 (1983).
    [CrossRef]
  11. E. Diez, F. Domínguez-Adame, and A. Sánchez, Microelectron. Eng. 43–44117 (1998).
    [CrossRef]
  12. S. Longhi, Phys. Rev. B 81, 195118 (2010).
    [CrossRef]
  13. W. Zhang and S. E. Ulloa, Phys. Rev. B 74, 115304 (2006).
    [CrossRef]
  14. R. El-Ganainy, M.-A. Miri, and D. Christodoulides, Europhys. Lett. 99, 64004 (2012).
    [CrossRef]
  15. A. R. Kolovsky, Phys. Rev. Lett. 101, 190602 (2008).
    [CrossRef]
  16. T. Schulte, S. Drenkelforth, G. Kleine Büning, W. Ertmer, J. Arlt, M. Lewenstein, and L. Santos, Phys. Rev. A 77, 023610 (2008).
    [CrossRef]
  17. S. Drenkelforth, G. Kleine Büning, J. Will, T. Schulte, N. Murray, W. Ertmer, L. Santos, and J. J. Arlt, New J. Phys. 10, 045027 (2008).
    [CrossRef]
  18. N. Chiodo, G. Della Valle, R. Osellame, S. Longhi, G. Cerullo, R. Ramponi, P. Laporta, and U. Morgner, Opt. Lett. 31, 1651 (2006).
    [CrossRef]

2012 (1)

R. El-Ganainy, M.-A. Miri, and D. Christodoulides, Europhys. Lett. 99, 64004 (2012).
[CrossRef]

2010 (1)

S. Longhi, Phys. Rev. B 81, 195118 (2010).
[CrossRef]

2008 (4)

A. R. Kolovsky, Phys. Rev. Lett. 101, 190602 (2008).
[CrossRef]

T. Schulte, S. Drenkelforth, G. Kleine Büning, W. Ertmer, J. Arlt, M. Lewenstein, and L. Santos, Phys. Rev. A 77, 023610 (2008).
[CrossRef]

S. Drenkelforth, G. Kleine Büning, J. Will, T. Schulte, N. Murray, W. Ertmer, L. Santos, and J. J. Arlt, New J. Phys. 10, 045027 (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]

2007 (1)

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

2006 (2)

1999 (3)

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

1998 (2)

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

E. Diez, F. Domínguez-Adame, and A. Sánchez, Microelectron. Eng. 43–44117 (1998).
[CrossRef]

1997 (1)

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
[CrossRef]

1985 (1)

F. Bentosela, V. Grecchi, and F. Zironi, Phys. Rev. B 31, 6909 (1985).
[CrossRef]

1983 (1)

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, and R. Weder, Commun. Math. Phys. 88, 387 (1983).
[CrossRef]

1960 (1)

G. H. Wannier, Phys. Rev. 117, 432 (1960).
[CrossRef]

Aitchison, J. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Arlt, J.

T. Schulte, S. Drenkelforth, G. Kleine Büning, W. Ertmer, J. Arlt, M. Lewenstein, and L. Santos, Phys. Rev. A 77, 023610 (2008).
[CrossRef]

Arlt, J. J.

S. Drenkelforth, G. Kleine Büning, J. Will, T. Schulte, N. Murray, W. Ertmer, L. Santos, and J. J. Arlt, New J. Phys. 10, 045027 (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]

Bartolini, P.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
[CrossRef]

Bentosela, F.

F. Bentosela, V. Grecchi, and F. Zironi, Phys. Rev. B 31, 6909 (1985).
[CrossRef]

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, and R. Weder, Commun. Math. Phys. 88, 387 (1983).
[CrossRef]

Bräuer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Carmona, R.

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, and R. Weder, Commun. Math. Phys. 88, 387 (1983).
[CrossRef]

Cerullo, G.

Chiodo, N.

Christodoulides, D.

R. El-Ganainy, M.-A. Miri, and D. Christodoulides, Europhys. Lett. 99, 64004 (2012).
[CrossRef]

Christodoulides, D. N.

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

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

de Sterke, C. M.

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

Della Valle, G.

Diez, E.

E. Diez, F. Domínguez-Adame, and A. Sánchez, Microelectron. Eng. 43–44117 (1998).
[CrossRef]

Domínguez-Adame, F.

E. Diez, F. Domínguez-Adame, and A. Sánchez, Microelectron. Eng. 43–44117 (1998).
[CrossRef]

Drenkelforth, S.

T. Schulte, S. Drenkelforth, G. Kleine Büning, W. Ertmer, J. Arlt, M. Lewenstein, and L. Santos, Phys. Rev. A 77, 023610 (2008).
[CrossRef]

S. Drenkelforth, G. Kleine Büning, J. Will, T. Schulte, N. Murray, W. Ertmer, L. Santos, and J. J. Arlt, New J. Phys. 10, 045027 (2008).
[CrossRef]

Duclos, P.

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, and R. Weder, Commun. Math. Phys. 88, 387 (1983).
[CrossRef]

Eisenberg, H. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

El-Ganainy, R.

R. El-Ganainy, M.-A. Miri, and D. Christodoulides, Europhys. Lett. 99, 64004 (2012).
[CrossRef]

Ertmer, W.

T. Schulte, S. Drenkelforth, G. Kleine Büning, W. Ertmer, J. Arlt, M. Lewenstein, and L. Santos, Phys. Rev. A 77, 023610 (2008).
[CrossRef]

S. Drenkelforth, G. Kleine Büning, J. Will, T. Schulte, N. Murray, W. Ertmer, L. Santos, and J. J. Arlt, New J. Phys. 10, 045027 (2008).
[CrossRef]

Fishman, S.

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

Grecchi, V.

F. Bentosela, V. Grecchi, and F. Zironi, Phys. Rev. B 31, 6909 (1985).
[CrossRef]

Kleine Büning, G.

T. Schulte, S. Drenkelforth, G. Kleine Büning, W. Ertmer, J. Arlt, M. Lewenstein, and L. Santos, Phys. Rev. A 77, 023610 (2008).
[CrossRef]

S. Drenkelforth, G. Kleine Büning, J. Will, T. Schulte, N. Murray, W. Ertmer, L. Santos, and J. J. Arlt, New J. Phys. 10, 045027 (2008).
[CrossRef]

Kolovsky, A. R.

A. R. Kolovsky, Phys. Rev. Lett. 101, 190602 (2008).
[CrossRef]

Lagendijk, A.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
[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]

Laporta, P.

Lederer, F.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

Lenz, G.

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

Lewenstein, M.

T. Schulte, S. Drenkelforth, G. Kleine Büning, W. Ertmer, J. Arlt, M. Lewenstein, and L. Santos, Phys. Rev. A 77, 023610 (2008).
[CrossRef]

Longhi, S.

Miri, M.-A.

R. El-Ganainy, M.-A. Miri, and D. Christodoulides, Europhys. Lett. 99, 64004 (2012).
[CrossRef]

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]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Morgner, U.

Murray, N.

S. Drenkelforth, G. Kleine Büning, J. Will, T. Schulte, N. Murray, W. Ertmer, L. Santos, and J. J. Arlt, New J. Phys. 10, 045027 (2008).
[CrossRef]

Osellame, R.

Pertsch, T.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

Peschel, U.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[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]

Ramponi, R.

Righini, R.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
[CrossRef]

Sánchez, A.

E. Diez, F. Domínguez-Adame, and A. Sánchez, Microelectron. Eng. 43–44117 (1998).
[CrossRef]

Santos, L.

T. Schulte, S. Drenkelforth, G. Kleine Büning, W. Ertmer, J. Arlt, M. Lewenstein, and L. Santos, Phys. Rev. A 77, 023610 (2008).
[CrossRef]

S. Drenkelforth, G. Kleine Büning, J. Will, T. Schulte, N. Murray, W. Ertmer, L. Santos, and J. J. Arlt, New J. Phys. 10, 045027 (2008).
[CrossRef]

Schulte, T.

S. Drenkelforth, G. Kleine Büning, J. Will, T. Schulte, N. Murray, W. Ertmer, L. Santos, and J. J. Arlt, New J. Phys. 10, 045027 (2008).
[CrossRef]

T. Schulte, S. Drenkelforth, G. Kleine Büning, W. Ertmer, J. Arlt, M. Lewenstein, and L. Santos, Phys. Rev. A 77, 023610 (2008).
[CrossRef]

Schwartz, T.

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

Segev, M.

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]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Simon, B.

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, and R. Weder, Commun. Math. Phys. 88, 387 (1983).
[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]

Souillard, B.

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, and R. Weder, Commun. Math. Phys. 88, 387 (1983).
[CrossRef]

Talanina, I.

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

Ulloa, S. E.

W. Zhang and S. E. Ulloa, Phys. Rev. B 74, 115304 (2006).
[CrossRef]

Wannier, G. H.

G. H. Wannier, Phys. Rev. 117, 432 (1960).
[CrossRef]

Weder, R.

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, and R. Weder, Commun. Math. Phys. 88, 387 (1983).
[CrossRef]

Wiersma, D. S.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
[CrossRef]

Will, J.

S. Drenkelforth, G. Kleine Büning, J. Will, T. Schulte, N. Murray, W. Ertmer, L. Santos, and J. J. Arlt, New J. Phys. 10, 045027 (2008).
[CrossRef]

Zhang, W.

W. Zhang and S. E. Ulloa, Phys. Rev. B 74, 115304 (2006).
[CrossRef]

Zironi, F.

F. Bentosela, V. Grecchi, and F. Zironi, Phys. Rev. B 31, 6909 (1985).
[CrossRef]

Commun. Math. Phys. (1)

F. Bentosela, R. Carmona, P. Duclos, B. Simon, B. Souillard, and R. Weder, Commun. Math. Phys. 88, 387 (1983).
[CrossRef]

Europhys. Lett. (1)

R. El-Ganainy, M.-A. Miri, and D. Christodoulides, Europhys. Lett. 99, 64004 (2012).
[CrossRef]

Microelectron. Eng. (1)

E. Diez, F. Domínguez-Adame, and A. Sánchez, Microelectron. Eng. 43–44117 (1998).
[CrossRef]

Nature (2)

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, Nature 390, 671 (1997).
[CrossRef]

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

New J. Phys. (1)

S. Drenkelforth, G. Kleine Büning, J. Will, T. Schulte, N. Murray, W. Ertmer, L. Santos, and J. J. Arlt, New J. Phys. 10, 045027 (2008).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

G. H. Wannier, Phys. Rev. 117, 432 (1960).
[CrossRef]

Phys. Rev. A (1)

T. Schulte, S. Drenkelforth, G. Kleine Büning, W. Ertmer, J. Arlt, M. Lewenstein, and L. Santos, Phys. Rev. A 77, 023610 (2008).
[CrossRef]

Phys. Rev. B (3)

F. Bentosela, V. Grecchi, and F. Zironi, Phys. Rev. B 31, 6909 (1985).
[CrossRef]

S. Longhi, Phys. Rev. B 81, 195118 (2010).
[CrossRef]

W. Zhang and S. E. Ulloa, Phys. Rev. B 74, 115304 (2006).
[CrossRef]

Phys. Rev. Lett. (5)

A. R. Kolovsky, Phys. Rev. Lett. 101, 190602 (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]

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[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 (6)

Fig. 1.
Fig. 1.

Narrow excitation: (a) σav versus nd at α=0.173 (curve 1) and α=0.3 (curve 2). (b) σav versus α at nd=0.5 (curve 1) and nd=1.5 (curve 2). Red curve shows xB(α)/2 dependence for regular array. Broad excitation: σav and xav versus nd at α=0.173 (c) and versus α at nd=0.5. The circles in (a), (b) and (c), (d) correspond to distributions in Figs. 2 and 3, respectively.

Fig. 2.
Fig. 2.

Averaged intensity distributions for narrow input at α=0.173 for (a) nd=0.2, (b) nd=0.3, and (c) nd=2.5. Averaged intensity distributions at nd=0.5 for (d) α=0.09, (e) α=0.173, and (f) α=0.6. Propagation distance is z=100.

Fig. 3.
Fig. 3.

Same as in Fig. 2, but for broad input excitation.

Fig. 4.
Fig. 4.

Averaged output intensity distributions at z=200, α=0.04 (a) for nd=0.5 and (b) nd=1.5.

Fig. 5.
Fig. 5.

Experimentally observed averaged intensity distributions in 70 mm sample showing hybrid Anderson–Bloch localization. (a) vd=0mm/min, (b) vd=14mm/min, (c) vd=28mm/min. Blue lines indicate input beam center.

Fig. 6.
Fig. 6.

Wave packet evolution for broad input in a 75 mm sample. Top row: cross section of the intensity distribution in ln scale; red lines indicate the position of integral beam center.

Equations (1)

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

iψz=122ψx2R(x)ψαxψ,

Metrics