Abstract

We study the trapping process of moving discrete solitons by linear and nonlinear impurities embedded in a one-dimensional nonlinear cubic array. We show that there exist specific values for the strength of the impurity and for the angle where a strong trapping is obtained. We introduce a criterion for studying the scattering dynamics of localized waves in nonlinear extended systems where the trapping of energy takes place.

© 2006 Optical Society of America

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References

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  1. D. K. Cambpell, S. Flach, and Y. S. Kivshar, Phys. Today 57, 43 (2004).
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  4. R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Opt. Lett. 29, 2905 (2004).
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  5. W. Królikowski and Y. S. Kivshar, J. Opt. Soc. Am. B 13, 876 (1996).
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  6. R. H. Goodman, R. E. Slusher, and M. I. Weinstein, J. Opt. Soc. Am. B 19, 1635 (2002).
    [CrossRef]
  7. R. Morandoti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, Opt. Lett. 28, 834 (2003).
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  8. Z. Xu, Y. V. Kartashov, and L. Torner, Opt. Express 13, 1774 (2005).
    [CrossRef] [PubMed]
  9. G. Kalosakas, A. V. Zolotaryuk, G. P. Tsironis, and E. N. Economou, Phys. Rev. E 56, 1088 (1997).
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  10. C. Lee and J. Brand, Europhys. Lett. 73, 321 (2006).
    [CrossRef]
  11. R. H. Goodman, P. J. Holmes, and M. I. Weinstein, Physica D 192, 215 (2004).
    [CrossRef]

2006 (1)

C. Lee and J. Brand, Europhys. Lett. 73, 321 (2006).
[CrossRef]

2005 (1)

2004 (3)

D. K. Cambpell, S. Flach, and Y. S. Kivshar, Phys. Today 57, 43 (2004).
[CrossRef]

R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Opt. Lett. 29, 2905 (2004).
[CrossRef]

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, Physica D 192, 215 (2004).
[CrossRef]

2003 (1)

2002 (1)

1998 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

1997 (1)

G. Kalosakas, A. V. Zolotaryuk, G. P. Tsironis, and E. N. Economou, Phys. Rev. E 56, 1088 (1997).
[CrossRef]

1996 (1)

1988 (1)

Aitchison, J. S.

R. Morandoti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, Opt. Lett. 28, 834 (2003).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Brand, J.

C. Lee and J. Brand, Europhys. Lett. 73, 321 (2006).
[CrossRef]

Cambpell, D. K.

D. K. Cambpell, S. Flach, and Y. S. Kivshar, Phys. Today 57, 43 (2004).
[CrossRef]

Christodoulides, D. N.

Economou, E. N.

G. Kalosakas, A. V. Zolotaryuk, G. P. Tsironis, and E. N. Economou, Phys. Rev. E 56, 1088 (1997).
[CrossRef]

Eisenberg, H. S.

R. Morandoti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, Opt. Lett. 28, 834 (2003).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Flach, S.

D. K. Cambpell, S. Flach, and Y. S. Kivshar, Phys. Today 57, 43 (2004).
[CrossRef]

Goodman, R. H.

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, Physica D 192, 215 (2004).
[CrossRef]

R. H. Goodman, R. E. Slusher, and M. I. Weinstein, J. Opt. Soc. Am. B 19, 1635 (2002).
[CrossRef]

Holmes, P. J.

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, Physica D 192, 215 (2004).
[CrossRef]

Joseph, R. I.

Kalosakas, G.

G. Kalosakas, A. V. Zolotaryuk, G. P. Tsironis, and E. N. Economou, Phys. Rev. E 56, 1088 (1997).
[CrossRef]

Kartashov, Y. V.

Kivshar, Y. S.

Królikowski, W.

Lee, C.

C. Lee and J. Brand, Europhys. Lett. 73, 321 (2006).
[CrossRef]

Mandelik, D.

Modotto, D.

Molina, M. I.

Morandoti, R.

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Silberberg, Y.

R. Morandoti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, Opt. Lett. 28, 834 (2003).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Slusher, R. E.

Sorel, M.

Stanley, C. R.

Torner, L.

Tsironis, G. P.

G. Kalosakas, A. V. Zolotaryuk, G. P. Tsironis, and E. N. Economou, Phys. Rev. E 56, 1088 (1997).
[CrossRef]

Vicencio, R. A.

Weinstein, M. I.

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, Physica D 192, 215 (2004).
[CrossRef]

R. H. Goodman, R. E. Slusher, and M. I. Weinstein, J. Opt. Soc. Am. B 19, 1635 (2002).
[CrossRef]

Xu, Z.

Zolotaryuk, A. V.

G. Kalosakas, A. V. Zolotaryuk, G. P. Tsironis, and E. N. Economou, Phys. Rev. E 56, 1088 (1997).
[CrossRef]

Europhys. Lett. (1)

C. Lee and J. Brand, Europhys. Lett. 73, 321 (2006).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. E (1)

G. Kalosakas, A. V. Zolotaryuk, G. P. Tsironis, and E. N. Economou, Phys. Rev. E 56, 1088 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Phys. Today (1)

D. K. Cambpell, S. Flach, and Y. S. Kivshar, Phys. Today 57, 43 (2004).
[CrossRef]

Physica D (1)

R. H. Goodman, P. J. Holmes, and M. I. Weinstein, Physica D 192, 215 (2004).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

(a) and (b) L versus k and ϵ for the linear and the nonlinear impurity, respectively. (c) and (d) Power versus frequency diagram for the linear and the nonlinear impurity modes, respectively.

Fig. 2
Fig. 2

(a) Trapping L versus ϵ for k = 0.2 depicted by a dashed white line in Figs. 1a, 1b. The results are depicted by stars and diamonds for the linear and nonlinear cases, respectively. (b)–(e) Intensity evolution for different points in (a): (b) ϵ 1 = 0.3 (A), (c) ϵ 1 = 1 (B), (d) ϵ 2 = 0.42 (C), (e) ϵ 2 = 0.92 (D).

Equations (2)

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i d u n d ξ + ( u n + 1 + u n 1 ) + ϵ 1 u n δ n , i 0 + ( 1 + ϵ 2 δ n , i 0 ) u n 2 u n = 0 ,
R + T + L = 1 ,

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