Abstract

We predict new phenomena, such as soliton steering and soliton fission, in optical lattices that fade away exponentially along the propagation direction. Such lattices, featuring tunable decay rates, arise in photorefractive crystals in the wavelength range 360400nm. We show that the predicted phenomena offer different opportunities for soliton control.

© 2006 Optical Society of America

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References

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  1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  2. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef] [PubMed]
  3. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  4. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  5. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
    [CrossRef] [PubMed]
  6. Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 766 (2004).
    [CrossRef] [PubMed]
  7. Y. V. Kartashov, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 1102 (2004).
    [CrossRef] [PubMed]
  8. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. E 71, 036621 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. Y. V. Kartashov, L.-C. Crasovan, A. S. Zelenina, V. A. Vysloukh, A. Sanpera, M. Lewenstein, and L. Torner, Phys. Rev. Lett. 93, 143902 (2004).
    [CrossRef] [PubMed]

2006

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

2005

2004

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 766 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 1102 (2004).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, L.-C. Crasovan, A. S. Zelenina, V. A. Vysloukh, A. Sanpera, M. Lewenstein, and L. Torner, Phys. Rev. Lett. 93, 143902 (2004).
[CrossRef] [PubMed]

2003

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

2001

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

2000

M. Meyer, M. Wöhlecke, and O. F. Schirmer, Phys. Status Solidi 221, R1 (2000).
[CrossRef]

1995

J. Seglins and S. Kapphan, Phys. Status Solidi 188, K43 (1995).
[CrossRef]

1994

Ablowitz, M. J.

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

Afanasjev, V. V.

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Chen, Z.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Christodoulides, D. N.

Y. V. Kartashov, L. Torner, and D. N. Christodoulides, Opt. Lett. 30, 1378 (2005).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Crasovan, L.-C.

Y. V. Kartashov, L.-C. Crasovan, A. S. Zelenina, V. A. Vysloukh, A. Sanpera, M. Lewenstein, and L. Torner, Phys. Rev. Lett. 93, 143902 (2004).
[CrossRef] [PubMed]

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Eugenieva, E. D.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Fleischer, J. W.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Garanovich, I. L.

Herrero, R.

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Kapphan, S.

J. Seglins and S. Kapphan, Phys. Status Solidi 188, K43 (1995).
[CrossRef]

Kartashov, Y. V.

Kivshar, Y.

Kivshar, Y. S.

Krolikowski, W.

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Lewenstein, M.

Y. V. Kartashov, L.-C. Crasovan, A. S. Zelenina, V. A. Vysloukh, A. Sanpera, M. Lewenstein, and L. Torner, Phys. Rev. Lett. 93, 143902 (2004).
[CrossRef] [PubMed]

Martin, H.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Meyer, M.

M. Meyer, M. Wöhlecke, and O. F. Schirmer, Phys. Status Solidi 221, R1 (2000).
[CrossRef]

Musslimani, Z. H.

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

Neshev, D.

Ostrovskaya, E.

Sanpera, A.

Y. V. Kartashov, L.-C. Crasovan, A. S. Zelenina, V. A. Vysloukh, A. Sanpera, M. Lewenstein, and L. Torner, Phys. Rev. Lett. 93, 143902 (2004).
[CrossRef] [PubMed]

Schirmer, O. F.

M. Meyer, M. Wöhlecke, and O. F. Schirmer, Phys. Status Solidi 221, R1 (2000).
[CrossRef]

Segev, M.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Seglins, J.

J. Seglins and S. Kapphan, Phys. Status Solidi 188, K43 (1995).
[CrossRef]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Staliunas, K.

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Sukhorukov, A. A.

Torner, L.

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. E 71, 036621 (2005).
[CrossRef]

Y. V. Kartashov, L.-C. Crasovan, A. S. Zelenina, V. A. Vysloukh, A. Sanpera, M. Lewenstein, and L. Torner, Phys. Rev. Lett. 93, 143902 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 766 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 1102 (2004).
[CrossRef] [PubMed]

V. V. Afanasjev and V. A. Vysloukh, J. Opt. Soc. Am. B 11, 2385 (1994).
[CrossRef]

Wöhlecke, M.

M. Meyer, M. Wöhlecke, and O. F. Schirmer, Phys. Status Solidi 221, R1 (2000).
[CrossRef]

Zelenina, A. S.

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 766 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, L.-C. Crasovan, A. S. Zelenina, V. A. Vysloukh, A. Sanpera, M. Lewenstein, and L. Torner, Phys. Rev. Lett. 93, 143902 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B

Nature

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. E

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. E 71, 036621 (2005).
[CrossRef]

K. Staliunas and R. Herrero, Phys. Rev. E 73, 016601 (2006).
[CrossRef]

Phys. Rev. Lett.

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Y. V. Kartashov, L.-C. Crasovan, A. S. Zelenina, V. A. Vysloukh, A. Sanpera, M. Lewenstein, and L. Torner, Phys. Rev. Lett. 93, 143902 (2004).
[CrossRef] [PubMed]

Phys. Status Solidi

J. Seglins and S. Kapphan, Phys. Status Solidi 188, K43 (1995).
[CrossRef]

M. Meyer, M. Wöhlecke, and O. F. Schirmer, Phys. Status Solidi 221, R1 (2000).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Propagation dynamics of solitons in decaying lattices with δ = 0.14 (a) and δ = 0.2 (b) at p = 1 , Ω = 1 , χ = 3 , η 0 = π 4 Ω . (c) Profile of a decaying lattice with δ = 0.2 and Ω = 1 .

Fig. 2
Fig. 2

Integral soliton center shift versus (a) lattice frequency at p = 1 , χ = 2 , η 0 = π 4 Ω ; (b) initial soliton displacement at p = 1 , Ω = 2 , δ = 0.5 ; (c) soliton form factor at p = 1 , Ω = 2 , η 0 = π 4 Ω ; (d) lattice decay rate at p = 1 , Ω = 2 , η 0 = π 4 Ω , χ = 2 .

Fig. 3
Fig. 3

Dynamics of decay of three-soliton bound states in lattice with (a) Ω = 1 and (b) Ω = 1.6 at p = 2 , δ = 2 . Labels χ k denote solitons with initial form factors k = 1 , 3 , 5 . Output angles for solitons emerging after the decay of the bound state (c) versus the lattice frequency at p δ = 1 and (d) versus p δ at Ω = 2 .

Equations (4)

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

i q ξ = 1 2 2 q η 2 q q 2 p R ( η , ξ ) q .
δ χ = χ sech [ χ ( η η 0 ) ] Re ( δ q ) d η ,
δ α = χ sech [ χ ( η η 0 ) ] tanh [ χ ( η η 0 ) ] Im ( δ q ) d η .
δ q = q r q s = [ J 0 ( μ ) 1 + 2 i J 1 ( μ ) cos ( 2 Ω η ) ] q s ,

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