Abstract

We address soliton transmission and reflection in nonlinear photonic lattices embedded into uniform Kerr nonlinear media. We show that by introducing disorder into the guiding lattice channels, one may achieve soliton transmission even under conditions where regular lattices reflect the input beam completely. In contrast, in the parameter range in which the lattice is almost transparent for incoming solitons, disorder may induce a significant reflection.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Abdullaev, Theory of Solitons in Inhomogeneous Media (Wiley, 1994).
  2. F. Abdullaev and J. Garnier, Prog. Opt. 48, 35 (2005).
    [CrossRef]
  3. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
    [CrossRef]
  4. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
    [CrossRef]
  5. T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
    [CrossRef] [PubMed]
  6. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, Nature 446, 52 (2007).
    [CrossRef] [PubMed]
  7. Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D. N. Christodoulides, and Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008).
    [CrossRef] [PubMed]
  8. 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] [PubMed]
  9. G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, Phys. Rev. Lett. 100, 084103 (2008).
    [CrossRef] [PubMed]
  10. Y. V. Kartashov and V. A. Vysloukh, Phys. Rev. E 72, 026606 (2005).
    [CrossRef]
  11. A. Sukhorukov, Phys. Rev. Lett. 96, 113902 (2006).
    [CrossRef] [PubMed]
  12. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. A 77, 051802(R) (2008).
    [CrossRef]
  13. V. Folli and C. Conti, Phys. Rev. Lett. 104, 193901 (2010).
    [CrossRef] [PubMed]
  14. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Express 15, 12409 (2007).
    [CrossRef] [PubMed]
  15. D. S. Wiersma, P. Bartolini, A. Lagendij, and R. Righini, Nature 390, 671 (1997).
    [CrossRef]
  16. F. J. P. Schuurmans, M. Megens, D. Vanmaekelbergh, and A. Lagendijk, Phys. Rev. Lett. 83, 2183 (1999).
    [CrossRef]
  17. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Express 14, 1576 (2006).
    [CrossRef] [PubMed]

2010 (2)

2009 (1)

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

2008 (4)

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

G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, Phys. Rev. Lett. 100, 084103 (2008).
[CrossRef] [PubMed]

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

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. A 77, 051802(R) (2008).
[CrossRef]

2007 (2)

2006 (2)

2005 (2)

Y. V. Kartashov and V. A. Vysloukh, Phys. Rev. E 72, 026606 (2005).
[CrossRef]

F. Abdullaev and J. Garnier, Prog. Opt. 48, 35 (2005).
[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] [PubMed]

1999 (1)

F. J. P. Schuurmans, M. Megens, D. Vanmaekelbergh, and A. Lagendijk, Phys. Rev. Lett. 83, 2183 (1999).
[CrossRef]

1997 (1)

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

Abdullaev, F.

F. Abdullaev and J. Garnier, Prog. Opt. 48, 35 (2005).
[CrossRef]

F. Abdullaev, Theory of Solitons in Inhomogeneous Media (Wiley, 1994).

Assanto, G.

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

Aubry, S.

G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, Phys. Rev. Lett. 100, 084103 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Bartal, G.

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

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] [PubMed]

Bartolini, P.

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

Christodoulides, D. N.

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] [PubMed]

Conti, C.

V. Folli and C. Conti, Phys. Rev. Lett. 104, 193901 (2010).
[CrossRef] [PubMed]

Dreisow, F.

Fishman, S.

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

Flach, S.

G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, Phys. Rev. Lett. 100, 084103 (2008).
[CrossRef] [PubMed]

Folli, V.

V. Folli and C. Conti, Phys. Rev. Lett. 104, 193901 (2010).
[CrossRef] [PubMed]

Garnier, J.

F. Abdullaev and J. Garnier, Prog. Opt. 48, 35 (2005).
[CrossRef]

Heinrich, M.

Kartashov, Y. V.

Keil, R.

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] [PubMed]

Komineas, S.

G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, Phys. Rev. Lett. 100, 084103 (2008).
[CrossRef] [PubMed]

Kopidakis, G.

G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, Phys. Rev. Lett. 100, 084103 (2008).
[CrossRef] [PubMed]

Lagendij, A.

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

Lagendijk, A.

F. J. P. Schuurmans, M. Megens, D. Vanmaekelbergh, and A. Lagendijk, Phys. Rev. Lett. 83, 2183 (1999).
[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] [PubMed]

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] [PubMed]

Megens, M.

F. J. P. Schuurmans, M. Megens, D. Vanmaekelbergh, and A. Lagendijk, Phys. Rev. Lett. 83, 2183 (1999).
[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] [PubMed]

Nolte, S.

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] [PubMed]

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

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] [PubMed]

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] [PubMed]

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] [PubMed]

Righini, R.

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

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] [PubMed]

Schuurmans, F. J. P.

F. J. P. Schuurmans, M. Megens, D. Vanmaekelbergh, and A. Lagendijk, Phys. Rev. Lett. 83, 2183 (1999).
[CrossRef]

Schwartz, T.

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

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] [PubMed]

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] [PubMed]

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] [PubMed]

Stegeman, G. I.

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

Sukhorukov, A.

A. Sukhorukov, Phys. Rev. Lett. 96, 113902 (2006).
[CrossRef] [PubMed]

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] [PubMed]

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

Vanmaekelbergh, D.

F. J. P. Schuurmans, M. Megens, D. Vanmaekelbergh, and A. Lagendijk, Phys. Rev. Lett. 83, 2183 (1999).
[CrossRef]

Vysloukh, V. A.

Wiersma, D. S.

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

Zeil, P.

Nature (1)

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

Nature (1)

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

Opt. Express (2)

Opt. Lett. (1)

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. A (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. A 77, 051802(R) (2008).
[CrossRef]

Phys. Rev. E (1)

Y. V. Kartashov and V. A. Vysloukh, Phys. Rev. E 72, 026606 (2005).
[CrossRef]

Phys. Rev. Lett. (6)

A. Sukhorukov, Phys. Rev. Lett. 96, 113902 (2006).
[CrossRef] [PubMed]

V. Folli and C. Conti, Phys. Rev. Lett. 104, 193901 (2010).
[CrossRef] [PubMed]

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

F. J. P. Schuurmans, M. Megens, D. Vanmaekelbergh, and A. Lagendijk, Phys. Rev. Lett. 83, 2183 (1999).
[CrossRef]

G. Kopidakis, S. Komineas, S. Flach, and S. Aubry, Phys. Rev. Lett. 100, 084103 (2008).
[CrossRef] [PubMed]

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

Prog. Opt. (2)

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

F. Abdullaev and J. Garnier, Prog. Opt. 48, 35 (2005).
[CrossRef]

Other (1)

F. Abdullaev, Theory of Solitons in Inhomogeneous Media (Wiley, 1994).

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 (4)

Fig. 1
Fig. 1

Averaged (over 10 3 realizations) propagation dynamics of broad solitons with χ = 0.05 colliding with disordered arrays of waveguides at (a)  α = 5.26 , S d = 0.00 ; (b)  α = 5.26 , S d = 0.30 ; (c)  α = 5.26 , S d = 0.42 ; (d)  α = 4.80 , S d = 0.00 ; (e)  α = 4.80 , S d = 0.30 ; and (f)  α = 5.26 , S d = 0.30 . In (a)–(e) n = 15 , while in (f) n = 31 . Dashed lines indicate the mean positions of the central waveguide in the array.

Fig. 2
Fig. 2

(a) Reflection coefficient in the regular arrays versus input angle for different numbers of waveguides. (b) Reflection and transmission coefficients versus number of waveguides at α = 5.26 . In all cases the input soliton has form factor χ = 0.05 .

Fig. 3
Fig. 3

(a) Reflection coefficient versus disorder level for n = 15 at α = 5.26 (curve 1) and α = 4.80 (curve 2). (b) Reflection coefficient versus disorder level for n = 31 at α = 5.26 (curve 1) and α = 4.68 (curve 2). (c) Reflection and transmission coefficients versus n at α = 5.26 , S d = 0.30 . In all cases χ = 0.05 .

Fig. 4
Fig. 4

Histograms of the reflection coefficient calculated for 1300 realizations of disordered waveguide arrays for χ = 0.05 , n = 15 , α = 5.26 at S d = 0.2 (a) and 0.3 (b). (c) Reflection coefficient versus disorder level for n = 15 , α = 5.26 at χ = 0.05 (curve 1), 0.50 (curve 2), and 1.00 (curve 3).

Equations (1)

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

i q ξ = 1 2 2 q η 2 p Q ( η ) q | q | 2 q .

Metrics