Abstract

We show that two-dimensional photonic Kerr nonlinear lattices can support stable soliton complexes composed of several solitons packed together with appropriately engineered phases. This may open up new prospects for encoding pixellike images made of robust discrete or lattice solitons.

© 2004 Optical Society of America

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References

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  1. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
    [Crossref] [PubMed]
  2. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [Crossref] [PubMed]
  3. Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 24, 766 (2004).
    [Crossref]
  4. Y. V. Kartashov, L. Torner, and V. A. Vysloukh, Opt. Lett. 24, 1102 (2004).
    [Crossref]
  5. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
    [Crossref]
  6. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
    [Crossref]
  7. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [Crossref] [PubMed]
  8. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
    [Crossref] [PubMed]
  9. N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
    [Crossref]
  10. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Express (to be published), http://www.opticsexpress.org .
  11. J. Yang and Z. Musslimani, Opt. Lett. 28, 2094 (2003).
    [Crossref] [PubMed]
  12. S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
    [Crossref]
  13. E. A. Ostrovskaya and Y. S. Kivshar, Phys. Rev. Lett. 90, 160407 (2003).
    [Crossref]
  14. B. B. Baizakov and M. Salerno, Phys. Rev. A 69, 013602 (2004).
    [Crossref]

2004 (3)

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 24, 766 (2004).
[Crossref]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, Opt. Lett. 24, 1102 (2004).
[Crossref]

B. B. Baizakov and M. Salerno, Phys. Rev. A 69, 013602 (2004).
[Crossref]

2003 (7)

E. A. Ostrovskaya and Y. S. Kivshar, Phys. Rev. Lett. 90, 160407 (2003).
[Crossref]

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]

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]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[Crossref]

J. Yang and Z. Musslimani, Opt. Lett. 28, 2094 (2003).
[Crossref] [PubMed]

2002 (1)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[Crossref]

1998 (1)

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[Crossref]

1988 (1)

Baizakov, B. B.

B. B. Baizakov and M. Salerno, Phys. Rev. A 69, 013602 (2004).
[Crossref]

Carmon, T.

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

Christodoulides, D. N.

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]

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

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[Crossref]

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 794 (1988).
[Crossref] [PubMed]

Cohen, O.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[Crossref]

Darmanyan, S.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (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, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[Crossref]

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

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[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]

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

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[Crossref]

Hudock, J.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[Crossref]

Joseph, R. I.

Kartashov, Y. V.

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 24, 766 (2004).
[Crossref]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, Opt. Lett. 24, 1102 (2004).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Express (to be published), http://www.opticsexpress.org .

Kivshar, Y.

Kivshar, Y. S.

E. A. Ostrovskaya and Y. S. Kivshar, Phys. Rev. Lett. 90, 160407 (2003).
[Crossref]

Kobyakov, A.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[Crossref]

Krolikowski, W.

Lederer, F.

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

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[Crossref]

Musslimani, Z.

Neshev, D.

Ostrovskaya, E.

Ostrovskaya, E. A.

E. A. Ostrovskaya and Y. S. Kivshar, Phys. Rev. Lett. 90, 160407 (2003).
[Crossref]

Salerno, M.

B. B. Baizakov and M. Salerno, Phys. Rev. A 69, 013602 (2004).
[Crossref]

Schmidt, E.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[Crossref]

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[Crossref]

Segev, M.

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

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

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[Crossref]

Silberberg, Y.

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

Torner, L.

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 24, 766 (2004).
[Crossref]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, Opt. Lett. 24, 1102 (2004).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Express (to be published), http://www.opticsexpress.org .

Vysloukh, V. A.

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, Opt. Lett. 24, 1102 (2004).
[Crossref]

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 24, 766 (2004).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Express (to be published), http://www.opticsexpress.org .

Yang, J.

Zelenina, A. S.

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 24, 766 (2004).
[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. Lett. (5)

Phys. Rev. A (1)

B. B. Baizakov and M. Salerno, Phys. Rev. A 69, 013602 (2004).
[Crossref]

Phys. Rev. E (2)

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[Crossref]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602 (2002).
[Crossref]

Phys. Rev. Lett. (3)

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

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, Phys. Rev. Lett. 91, 213906 (2003).
[Crossref]

E. A. Ostrovskaya and Y. S. Kivshar, Phys. Rev. Lett. 90, 160407 (2003).
[Crossref]

Other (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Soliton trains in photonic lattices,” Opt. Express (to be published), http://www.opticsexpress.org .

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Figures (3)

Fig. 1
Fig. 1

Profiles of (a) single-hump and (b) two-hump lattice solitons at b=2.5. (c) Energy flow versus propagation constant for single- (curve 1) and two-hump (curve 2) solitons. (d) Real part of the perturbation growth rate for single- (inset) and two-hump lattice solitons versus propagation constant. Guiding parameter p=10.

Fig. 2
Fig. 2

(a) Profile of a stable twisted mode corresponding to a point marked by a circle in dispersion diagram (b). For (a) and (b), guiding parameter p=10. (c) Cutoff on propagation constant versus guiding parameter. (d) Real part of perturbation growth rate versus propagation constant at p=10.

Fig. 3
Fig. 3

Simplest stable combinations of lattice solitons at p=10 corresponding to (a), (b) b=8 and (c) b=11. Example of stable soliton letter Y composed from nine lowest-order lattice solitons at b=16 with p=20.

Equations (1)

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iqξ=-122qη2+2qζ2+σqq2-pRη,ζq,

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