Abstract

We put forward new properties of lattice solitons in materials and geometries where both the linear refractive index and the nonlinearity are spatially modulated. We show that the interplay between linear and out-of-phase nonlinear refractive index modulations results in new soliton properties, including modifications of the soliton stability and transverse mobility, as well as shape transformations that may be controlled, e.g., by varying the light intensity.

© 2008 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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2008 (3)

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[Crossref]

Y. Sivan, G. Fibich, and B. Ilan, Phys. Rev. E 77, 045601(R) (2008).
[Crossref]

J. Zhou, C. Xue, Y. Qi, and S. Lou, Phys. Lett. A 372, 4395 (2008).
[Crossref]

2007 (4)

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[Crossref] [PubMed]

Y. V. Bludov, V. A. Brazhnyi, and V. V. Konotop, Phys. Rev. A 76, 023603 (2007).
[Crossref]

M. A. Porter, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, Physica D 229, 104 (2007).
[Crossref]

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[Crossref]

2006 (2)

2005 (2)

2004 (1)

2003 (3)

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

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

M. Öster, M. Johansson, and A. Eriksson, Phys. Rev. E 67, 056606 (2003).
[Crossref]

1998 (1)

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

Abdullaev, F. K.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[Crossref]

Aitchison, J. S.

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

Belmonte-Beitia, J.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[Crossref] [PubMed]

Blömer, D.

Bludov, Y. V.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[Crossref]

Y. V. Bludov, V. A. Brazhnyi, and V. V. Konotop, Phys. Rev. A 76, 023603 (2007).
[Crossref]

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616 (2006).
[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]

Brazhnyi, V. A.

Y. V. Bludov, V. A. Brazhnyi, and V. V. Konotop, Phys. Rev. A 76, 023603 (2007).
[Crossref]

Brocas, A.

Canioni, L.

Chen, F.

Christodoulides, D. N.

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

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

Dmitriev, S. V.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[Crossref]

Dreisow, F.

Efremidis, N. K.

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

Eisenberg, H. S.

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

Eriksson, A.

M. Öster, M. Johansson, and A. Eriksson, Phys. Rev. E 67, 056606 (2003).
[Crossref]

Fibich, G.

Y. Sivan, G. Fibich, and B. Ilan, Phys. Rev. E 77, 045601(R) (2008).
[Crossref]

Fleischer, J. W.

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

Frantzeskakis, D. J.

M. A. Porter, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, Physica D 229, 104 (2007).
[Crossref]

Ilan, B.

Y. Sivan, G. Fibich, and B. Ilan, Phys. Rev. E 77, 045601(R) (2008).
[Crossref]

Johansson, M.

M. Öster, M. Johansson, and A. Eriksson, Phys. Rev. E 67, 056606 (2003).
[Crossref]

Jones, C. K. R. T.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[Crossref]

Kartashov, Y. V.

Kevrekidis, P. G.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[Crossref]

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[Crossref]

M. A. Porter, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, Physica D 229, 104 (2007).
[Crossref]

Kip, D.

Konotop, V. V.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[Crossref]

Y. V. Bludov, V. A. Brazhnyi, and V. V. Konotop, Phys. Rev. A 76, 023603 (2007).
[Crossref]

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[Crossref]

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616 (2006).
[Crossref]

Lederer, F.

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

Lou, S.

J. Zhou, C. Xue, Y. Qi, and S. Lou, Phys. Lett. A 372, 4395 (2008).
[Crossref]

Malomed, B. A.

M. A. Porter, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, Physica D 229, 104 (2007).
[Crossref]

Manela, O.

Morandotti, R.

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

Nolte, S.

Öster, M.

M. Öster, M. Johansson, and A. Eriksson, Phys. Rev. E 67, 056606 (2003).
[Crossref]

Perez-Garcia, V. M.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[Crossref] [PubMed]

Pertsch, T.

Porter, M. A.

M. A. Porter, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, Physica D 229, 104 (2007).
[Crossref]

Qi, Y.

J. Zhou, C. Xue, Y. Qi, and S. Lou, Phys. Lett. A 372, 4395 (2008).
[Crossref]

Rapti, Z.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[Crossref]

Richardson, M.

Runde, D.

Rüter, C. E.

Sarger, L.

Segev, M.

Shandarov, V.

Silberberg, Y.

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

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

Sivan, Y.

Y. Sivan, G. Fibich, and B. Ilan, Phys. Rev. E 77, 045601(R) (2008).
[Crossref]

Stepic, M.

Szameit, A.

Torner, L.

Torres, P. J.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[Crossref] [PubMed]

Tünnermann, A.

Vekslerchik, V.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[Crossref] [PubMed]

Vysloukh, V. A.

Xue, C.

J. Zhou, C. Xue, Y. Qi, and S. Lou, Phys. Lett. A 372, 4395 (2008).
[Crossref]

Zelenina, A. S.

Zhou, J.

J. Zhou, C. Xue, Y. Qi, and S. Lou, Phys. Lett. A 372, 4395 (2008).
[Crossref]

Zoubir, A.

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

J. Phys. A (1)

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[Crossref]

Nature (2)

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 (2)

Opt. Lett. (1)

Phys. Lett. A (1)

J. Zhou, C. Xue, Y. Qi, and S. Lou, Phys. Lett. A 372, 4395 (2008).
[Crossref]

Phys. Rev. A (2)

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616 (2006).
[Crossref]

Y. V. Bludov, V. A. Brazhnyi, and V. V. Konotop, Phys. Rev. A 76, 023603 (2007).
[Crossref]

Phys. Rev. E (3)

Y. Sivan, G. Fibich, and B. Ilan, Phys. Rev. E 77, 045601(R) (2008).
[Crossref]

M. Öster, M. Johansson, and A. Eriksson, Phys. Rev. E 67, 056606 (2003).
[Crossref]

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[Crossref]

Phys. Rev. Lett. (2)

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

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[Crossref] [PubMed]

Physica D (1)

M. A. Porter, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, Physica D 229, 104 (2007).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Profiles of odd solitons with (a) b = 5.5 and (b) b = 12 at σ = 0.85 . Profiles of even solitons with (c) b = 3.7 and (d) b = 7 at σ = 0.3 . Profiles of (e) dipole and (f) triple-mode solitons with b = 4 at σ = 0.4 . In shaded regions R 1 2 , while in white regions R < 1 2 . Curves marked with a γ show the profile of the nonlinearity coefficient γ = 1 σ R .

Fig. 2
Fig. 2

U versus b for (a) odd soliton at σ = 0.85 and (b) even soliton at σ = 0.3 . Points marked by circles in (a) correspond to solitons in Figs. 1a, 1b, while points marked by circles in (b) correspond to solitons in Figs. 1c, 1d (c) Critical b values for stabilization of odd and even solitons versus σ. In shaded area both odd and even solitons are unstable. (d) δ r versus b for odd soliton at σ = 0.85 (curve 1) and even soliton at σ = 0.3 (curve 2). (e) Domains of instability (shaded region) and stability (white region embedded inside shaded one) on ( σ , b ) plane for dipole solitons. (f) δ r versus b for dipole soliton at σ = 0.4 .

Fig. 3
Fig. 3

Dynamics of soliton excitation by Gaussian input beams at (a) A = 2 , σ = 0.2 ; (b) A = 3.1 , σ = 0.6 ; (c) A = 5.6 , σ = 0.2 ; and (d) A = 5 , σ = 0.9 .

Fig. 4
Fig. 4

Critical angle versus b for (a) odd and (b) even solitons. (c) Propagation dynamics of odd solitons with b = 9.8 launched in the lattice at two different angles. The field modulus distributions corresponding to different input angles are superimposed. In all cases σ = 0.4 .

Equations (1)

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i q ξ = 1 2 2 q η 2 [ 1 σ R ( η ) ] q 2 q p R ( η ) q .

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