Abstract

We theoretically study the properties of one-dimensional nonlinear saturable photonic lattices exhibiting multiple mobility windows for stationary solutions. The effective energy barrier decreases to a minimum in those power regions where a new intermediate stationary solution appears. As an application, we investigate the dynamics of high-power Gaussian-like beams finding several regions where the light transport is enhanced.

© 2011 Optical Society of America

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  1. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
    [CrossRef]
  2. S. Flach and A. V. Gorbach, Phys. Rep. 467, 1 (2008).
    [CrossRef]
  3. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Prog. Opt. 52, 63 (2009).
    [CrossRef]
  4. M. Stepić, D. Kip, L. Hadžievski, and A. Maluckov, Phys. Rev. E 69, 066618 (2004).
    [CrossRef]
  5. Lj. Hadžievski, A. Maluckov, M. Stepić, and D. Kip, Phys. Rev. Lett. 93, 033901 (2004).
    [CrossRef] [PubMed]
  6. Y. S. Kivshar and D. K. Campbell, Phys. Rev. E 48, 3077 (1993).
    [CrossRef]
  7. U. Peschel, R. Morandotti, J. M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, J. Opt. Soc. Am. B 19, 2637 (2002).
    [CrossRef]
  8. R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Opt. Lett. 28, 1942 (2003).
    [CrossRef] [PubMed]
  9. R. A. Vicencio and M. Johansson, Phys. Rev. E 73, 046602 (2006).
    [CrossRef]
  10. U. Naether, R. A. Vicencio, and M. Johansson, Phys. Rev. E 83, 036601 (2011).
    [CrossRef]
  11. M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
    [CrossRef] [PubMed]
  12. C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
    [CrossRef] [PubMed]
  13. T. R. O. Melvin, A. R. Champneys, P. G. Kevrekidis, and J. Cuevas, Phys. Rev. Lett. 97, 124101 (2006).
    [CrossRef] [PubMed]
  14. A. Khare, K. Ø. Rasmussen, M. R. Samuelsen, and A. Saxena, J. Phys. A 38, 807 (2005).
    [CrossRef]

2011 (1)

U. Naether, R. A. Vicencio, and M. Johansson, Phys. Rev. E 83, 036601 (2011).
[CrossRef]

2009 (1)

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

2008 (2)

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

S. Flach and A. V. Gorbach, Phys. Rep. 467, 1 (2008).
[CrossRef]

2006 (4)

R. A. Vicencio and M. Johansson, Phys. Rev. E 73, 046602 (2006).
[CrossRef]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

T. R. O. Melvin, A. R. Champneys, P. G. Kevrekidis, and J. Cuevas, Phys. Rev. Lett. 97, 124101 (2006).
[CrossRef] [PubMed]

2005 (1)

A. Khare, K. Ø. Rasmussen, M. R. Samuelsen, and A. Saxena, J. Phys. A 38, 807 (2005).
[CrossRef]

2004 (2)

M. Stepić, D. Kip, L. Hadžievski, and A. Maluckov, Phys. Rev. E 69, 066618 (2004).
[CrossRef]

Lj. Hadžievski, A. Maluckov, M. Stepić, and D. Kip, Phys. Rev. Lett. 93, 033901 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

1993 (1)

Y. S. Kivshar and D. K. Campbell, Phys. Rev. E 48, 3077 (1993).
[CrossRef]

Aitchison, J. S.

Arnold, J. M.

Assanto, G.

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

Campbell, D. K.

Y. S. Kivshar and D. K. Campbell, Phys. Rev. E 48, 3077 (1993).
[CrossRef]

Champneys, A. R.

T. R. O. Melvin, A. R. Champneys, P. G. Kevrekidis, and J. Cuevas, Phys. Rev. Lett. 97, 124101 (2006).
[CrossRef] [PubMed]

Christodoulides, D. N.

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

Cuevas, J.

T. R. O. Melvin, A. R. Champneys, P. G. Kevrekidis, and J. Cuevas, Phys. Rev. Lett. 97, 124101 (2006).
[CrossRef] [PubMed]

Eisenberg, H. S.

Flach, S.

S. Flach and A. V. Gorbach, Phys. Rep. 467, 1 (2008).
[CrossRef]

Gorbach, A. V.

S. Flach and A. V. Gorbach, Phys. Rep. 467, 1 (2008).
[CrossRef]

Hadžievski, L.

M. Stepić, D. Kip, L. Hadžievski, and A. Maluckov, Phys. Rev. E 69, 066618 (2004).
[CrossRef]

Hadžievski, Lj.

Lj. Hadžievski, A. Maluckov, M. Stepić, and D. Kip, Phys. Rev. Lett. 93, 033901 (2004).
[CrossRef] [PubMed]

Johansson, M.

U. Naether, R. A. Vicencio, and M. Johansson, Phys. Rev. E 83, 036601 (2011).
[CrossRef]

R. A. Vicencio and M. Johansson, Phys. Rev. E 73, 046602 (2006).
[CrossRef]

Kartashov, Y. V.

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

Kevrekidis, P. G.

T. R. O. Melvin, A. R. Champneys, P. G. Kevrekidis, and J. Cuevas, Phys. Rev. Lett. 97, 124101 (2006).
[CrossRef] [PubMed]

Khare, A.

A. Khare, K. Ø. Rasmussen, M. R. Samuelsen, and A. Saxena, J. Phys. A 38, 807 (2005).
[CrossRef]

Kip, D.

Lj. Hadžievski, A. Maluckov, M. Stepić, and D. Kip, Phys. Rev. Lett. 93, 033901 (2004).
[CrossRef] [PubMed]

M. Stepić, D. Kip, L. Hadžievski, and A. Maluckov, Phys. Rev. E 69, 066618 (2004).
[CrossRef]

Kivshar, Y. S.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Opt. Lett. 28, 1942 (2003).
[CrossRef] [PubMed]

Y. S. Kivshar and D. K. Campbell, Phys. Rev. E 48, 3077 (1993).
[CrossRef]

Krolikowski, W.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[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]

U. Peschel, R. Morandotti, J. M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, J. Opt. Soc. Am. B 19, 2637 (2002).
[CrossRef]

Maluckov, A.

Lj. Hadžievski, A. Maluckov, M. Stepić, and D. Kip, Phys. Rev. Lett. 93, 033901 (2004).
[CrossRef] [PubMed]

M. Stepić, D. Kip, L. Hadžievski, and A. Maluckov, Phys. Rev. E 69, 066618 (2004).
[CrossRef]

Melvin, T. R. O.

T. R. O. Melvin, A. R. Champneys, P. G. Kevrekidis, and J. Cuevas, Phys. Rev. Lett. 97, 124101 (2006).
[CrossRef] [PubMed]

Mitchell, A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Molina, M. I.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Opt. Lett. 28, 1942 (2003).
[CrossRef] [PubMed]

Morandotti, R.

Naether, U.

U. Naether, R. A. Vicencio, and M. Johansson, Phys. Rev. E 83, 036601 (2011).
[CrossRef]

Neshev, D. N.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Pertsch, T.

Peschel, U.

Rasmussen, K. Ø.

A. Khare, K. Ø. Rasmussen, M. R. Samuelsen, and A. Saxena, J. Phys. A 38, 807 (2005).
[CrossRef]

Rosberg, C. R.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Samuelsen, M. R.

A. Khare, K. Ø. Rasmussen, M. R. Samuelsen, and A. Saxena, J. Phys. A 38, 807 (2005).
[CrossRef]

Saxena, A.

A. Khare, K. Ø. Rasmussen, M. R. Samuelsen, and A. Saxena, J. Phys. A 38, 807 (2005).
[CrossRef]

Segev, M.

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

Silberberg, Y.

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

U. Peschel, R. Morandotti, J. M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, J. Opt. Soc. Am. B 19, 2637 (2002).
[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]

Stepic, M.

Lj. Hadžievski, A. Maluckov, M. Stepić, and D. Kip, Phys. Rev. Lett. 93, 033901 (2004).
[CrossRef] [PubMed]

M. Stepić, D. Kip, L. Hadžievski, and A. Maluckov, Phys. Rev. E 69, 066618 (2004).
[CrossRef]

Torner, L.

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

Vicencio, R. A.

U. Naether, R. A. Vicencio, and M. Johansson, Phys. Rev. E 83, 036601 (2011).
[CrossRef]

M. I. Molina, R. A. Vicencio, and Y. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

R. A. Vicencio and M. Johansson, Phys. Rev. E 73, 046602 (2006).
[CrossRef]

R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Opt. Lett. 28, 1942 (2003).
[CrossRef] [PubMed]

Vysloukh, V. A.

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

J. Opt. Soc. Am. B (1)

J. Phys. A (1)

A. Khare, K. Ø. Rasmussen, M. R. Samuelsen, and A. Saxena, J. Phys. A 38, 807 (2005).
[CrossRef]

Opt. Lett. (2)

Phys. Rep. (2)

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

S. Flach and A. V. Gorbach, Phys. Rep. 467, 1 (2008).
[CrossRef]

Phys. Rev. E (4)

M. Stepić, D. Kip, L. Hadžievski, and A. Maluckov, Phys. Rev. E 69, 066618 (2004).
[CrossRef]

Y. S. Kivshar and D. K. Campbell, Phys. Rev. E 48, 3077 (1993).
[CrossRef]

R. A. Vicencio and M. Johansson, Phys. Rev. E 73, 046602 (2006).
[CrossRef]

U. Naether, R. A. Vicencio, and M. Johansson, Phys. Rev. E 83, 036601 (2011).
[CrossRef]

Phys. Rev. Lett. (3)

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

T. R. O. Melvin, A. R. Champneys, P. G. Kevrekidis, and J. Cuevas, Phys. Rev. Lett. 97, 124101 (2006).
[CrossRef] [PubMed]

Lj. Hadžievski, A. Maluckov, M. Stepić, and D. Kip, Phys. Rev. Lett. 93, 033901 (2004).
[CrossRef] [PubMed]

Prog. Opt. (1)

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

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Figures (3)

Fig. 1
Fig. 1

P versus λ for odd solutions, even solutions, and ISs in full, dashed, and thin curves, respectively. Inset: profiles corresponding to filled circles.

Fig. 2
Fig. 2

(a) g versus P for odd solutions, even solutions, and ISs in full, dashed, and thin curves, respectively. Inset: H versus P. (b)  Δ H 0 (thick curve) and Δ H (thin curve) versus P. (c) Energy surface where light (dark) color denotes a high (low) H value.

Fig. 3
Fig. 3

(a) Output X f versus input P. (b), (c), (d) Dynamical examples for P = 54 , 300, and 550, respectively. γ = 10 , n c = 26 , k = 0.3 , α = 1 / 3 , z f = 50 .

Equations (1)

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i d u n d z + ( u n + 1 + u n 1 ) γ u n 1 + | u n | 2 = 0 ,

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