Abstract

We observe experimentally higher-order solitons in waveguide arrays with defocusing saturable nonlinearity. Such solitons can comprise several in-phase bright spots and are stable above a critical power threshold. We elucidate the impact of the nonlinearity saturation on the domains of existence and stability of the observed complex soliton states.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. F. Chen, M. Stepic, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, Opt. Express 13, 4314 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  20. P. G. Kevrekidis, H. Susanto, and Z. Chen, Phys. Rev. E 74, 066606 (2006).
    [CrossRef]

2006 (5)

2005 (1)

2004 (6)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Express 12, 2831 (2004).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, Opt. Lett. 29, 1918 (2004).
[CrossRef] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

L. Hadzievski, A. Maluckov, M. Stepic, and D. Kip, Phys. Rev. Lett. 93, 033901 (2004).
[CrossRef] [PubMed]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

2003 (6)

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

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

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. A 67, 063608 (2003).
[CrossRef]

1998 (2)

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

S. Darmanyan, A. Kobyakov, and F. Lederer, J. Exp. Theor. Phys. 86, 682 (1998).
[CrossRef]

Aitchison, J. S.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

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

Austin, M. W.

Bezryadina, A.

Boyd, A. R.

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

Carmon, T.

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

Champneys, A. R.

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

Chen, F.

Chen, Z.

Christodoulides, D. N.

Y. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, Opt. Lett. 29, 1918 (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]

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]

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. A 67, 063608 (2003).
[CrossRef]

Cuevas, J.

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

Darmanyan, S.

S. Darmanyan, A. Kobyakov, and F. Lederer, J. Exp. Theor. Phys. 86, 682 (1998).
[CrossRef]

Efremidis, N. K.

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

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. A 67, 063608 (2003).
[CrossRef]

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

Egorov, A. A.

Eisenberg, H. S.

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

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]

Hadzievski, L.

L. Hadzievski, A. Maluckov, M. Stepic, and D. Kip, Phys. Rev. Lett. 93, 033901 (2004).
[CrossRef] [PubMed]

Hanna, B.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

Hizanidis, K.

Kartashov, Y. V.

Kevrekidis, P. G.

P. G. Kevrekidis, H. Susanto, and Z. Chen, Phys. Rev. E 74, 066606 (2006).
[CrossRef]

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

C. Lou, J. Xu, L. Tang, Z. Chen, and P. G. Kevrekidis, Opt. Lett. 31, 492 (2006).
[CrossRef] [PubMed]

Kip, D.

Kivshar, Y.

Kivshar, Y. S.

M. Matuszewski, C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, A. Mitchell, M. Trippenbach, M. W. Austin, W. Krolikowski, and Y. S. Kivshar, Opt. Express 14, 254 (2006).
[CrossRef] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Kobyakov, A.

S. Darmanyan, A. Kobyakov, and F. Lederer, J. Exp. Theor. Phys. 86, 682 (1998).
[CrossRef]

Kominis, Y.

Krolikowski, W.

Lederer, F.

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

S. Darmanyan, A. Kobyakov, and F. Lederer, J. Exp. Theor. Phys. 86, 682 (1998).
[CrossRef]

Lou, C.

Louis, P. J. Y.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Makasyuk, I.

Maluckov, A.

L. Hadzievski, A. Maluckov, M. Stepic, and D. Kip, Phys. Rev. Lett. 93, 033901 (2004).
[CrossRef] [PubMed]

Mandelik, D.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

Manela, O.

Matuszewski, M.

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.

Morandotti, R.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

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

Neshev, D.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

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

Neshev, D. N.

Ostrovskaya, E.

Ostrovskaya, E. A.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Rosberg, C. R.

Runde, D.

Rüter, C. E.

Savage, C. M.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Segev, M.

F. Chen, M. Stepic, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, Opt. Express 13, 4314 (2005).
[CrossRef] [PubMed]

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]

Shandarov, V.

Silberberg, Y.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

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]

Stepic, M.

Sukhorukov, A. A.

Susanto, H.

P. G. Kevrekidis, H. Susanto, and Z. Chen, Phys. Rev. E 74, 066606 (2006).
[CrossRef]

Tang, L.

Torner, L.

Trippenbach, M.

Vysloukh, V. A.

Xu, J.

Yang, J.

J. Exp. Theor. Phys. (1)

S. Darmanyan, A. Kobyakov, and F. Lederer, J. Exp. Theor. Phys. 86, 682 (1998).
[CrossRef]

Nature (2)

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]

Opt. Express (3)

Opt. Lett. (5)

Phys. Rev. A (2)

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. A 67, 063608 (2003).
[CrossRef]

Phys. Rev. E (1)

P. G. Kevrekidis, H. Susanto, and Z. Chen, Phys. Rev. E 74, 066606 (2006).
[CrossRef]

Phys. Rev. Lett. (6)

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

L. Hadzievski, A. Maluckov, M. Stepic, and D. Kip, Phys. Rev. Lett. 93, 033901 (2004).
[CrossRef] [PubMed]

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

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

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (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]

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Figures (3)

Fig. 1
Fig. 1

Profiles of even solitons with (a) b = 11.34 and (b) b = 10 at p = 17 and S = 0.5 . (c) Energy flow versus propagation constant at p = 17 . (d) Domains of existence for even solitons on the ( S , b ) plane at p = 17 and (e) on the ( p , b ) plane at S = 0.5 . The (red dashed) curve in (d) indicates the upper border of the stability domain. (f) Real part of perturbation growth rate versus propagation constant at p = 17 , S = 0.5 .

Fig. 2
Fig. 2

Experimental observation of discrete diffraction, an even soliton, and a three-soliton train. Experimental images at the output crystal face are superimposed on the theoretical plots, showing the propagation dynamics inside the crystal. (a) Discrete diffraction in the linear regime. (b) Excitation of an even soliton with two Gaussian beams with amplitude A = 5 and width W = 0.5 launched into adjacent channels. (c) Excitation of such a soliton by a single beam with A = 5 and W = 1 launched in between channels. (d) Excitation of a three-soliton train with a broad super-Gaussian beam with A = 5 and W = 2.3 . In all cases p = 17 and S = 0.5 .

Fig. 3
Fig. 3

Observed temporal dynamics of the formation of even solitons. (a) Discrete diffraction and (b) temporal buildup of the even soliton for excitation with two in-phase Gaussian beams. In (c) the input beam on the right-hand side is blocked at t = 0 s . Light energy starts to oscillate in the directional-coupler-like waveguiding structure and finally forms a narrow odd soliton in the excited channel.

Equations (1)

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i q ξ = 1 2 2 q η 2 + q q 2 1 + S q 2 p R q .

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