Abstract

We report on, for the first time to our knowledge, the existence of (1+1)-dimensional dipole solitons. We numerically find that such solitons can be supported by one-dimensional optical lattice in Kerr-type nonlinear media. Two dipoles of solitons are completely located at a broad optical lattice whose transverse modulation period is larger than ~1.5 times of the soliton width. The inherent repulsive interaction between dipoles can be effectively overcome by the lattice. The stable swing motion of dipole solitons in such lattice is also demonstrated.

© 2006 Optical Society of America

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  1. R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beam," Phys. Rev. Lett. 13, 479 (1964).
    [CrossRef]
  2. J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrovskaya, and Y. S. Kivshar, "Dipole-mode vector solitons," Phys. Rev. Lett. 85, 82 (2000).
    [CrossRef] [PubMed]
  3. W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424 (2000).
    [CrossRef] [PubMed]
  4. T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. Christodoulides, "Observation of two-dimensional multimode solitons," Opt. Lett. 25, 1113 (2000).
    [CrossRef]
  5. A. S. Desyatnikov, D. Neshev, E. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. M. Pérez-García, "Multipole spatial vector solitons," Opt. Lett. 26, 435 (2001).
    [CrossRef]
  6. A. S. Desyatnikov, D. Neshev, E. A. Osrovskaya, Y. S. Kivshar, G. McCarthy, W. Krolikowski, and B. Luther-Davies, "Multipole composite spatial solitons: theory and experiment," J. Opt. Soc. Am. B 19, 586 (2002).
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    [CrossRef]
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    [CrossRef]
  9. J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: Theory and experiment," Studies in Applied Mathematics 113, 389 (2004).
    [CrossRef]
  10. Y. V. Kartashov, R. Carretero-González, B. A. Malomed, V. A. Vysloukh, and L. Torner, "Multipole-mode solitons in Bessel optical lattices," Opt. Express 13,10703 (2005).
    [CrossRef] [PubMed]
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  12. J. Yang and D. E. Pelinovsky, "Stable vortex and dipole vector solitons in a saturable nonlinear medium," Phys. Rev. E 67, 016608 (2003).
    [CrossRef]
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  14. J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole solitons in optically induced two-dimensional photonic lattices," Opt. Lett. 29, 1662 (2004).
    [CrossRef] [PubMed]
  15. Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and J. Yang, "Formation of discrete solitons in light-induced photonic lattices," Opt. Express 13, 1816 (2005).
    [CrossRef] [PubMed]
  16. D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  17. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  18. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
    [CrossRef] [PubMed]
  19. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
    [CrossRef]
  20. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef] [PubMed]
  21. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  22. D. Neshev, E. Ostrovskaya, Y. S. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  23. R. Scharf and A. R. Bishop, "Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials," Phys. Rev. E 47, 1375 (1993).
    [CrossRef]
  24. Y. V. Kartashov A. S. Zelenina, L. Torner, and V. A. Vysloukh, "Spatial soliton switching in quasi-continuous optical arrays," Opt. Lett. 29, 766 (2004).
    [CrossRef] [PubMed]
  25. Y. V. Kartashov, L. Torner, and V. A. Vysloukh, "Parametric amplification of soliton steering in optical lattices," Opt. Lett. 29, 1102 (2004).
    [CrossRef] [PubMed]
  26. V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, "Dynamics of matter solitons in weakly modulated optical lattices," Phys. Rev. A 70, 043604 (2004).
    [CrossRef]
  27. F. Kh. Abdullaev and J. Garnier, "Propagation of matter-wave solitons in periodic and random nonlinear potentials," Phys. Rev. A 72, 061605 (2005).
    [CrossRef]
  28. Y. S. Kivashar and B. A. Malomed, "Dynamics of solitons in nearly integrable systems," Rev. Mod. Phys. 61, 763 (1989).
    [CrossRef]
  29. J. A. Fleck, J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser-beams through atmosphere," Appl. Phys. 10, 129 (1976).
    [CrossRef]
  30. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
    [CrossRef] [PubMed]
  31. Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
    [CrossRef] [PubMed]

2006 (1)

2005 (4)

2004 (8)

Y. V. Kartashov A. S. Zelenina, L. Torner, and V. A. Vysloukh, "Spatial soliton switching in quasi-continuous optical arrays," Opt. Lett. 29, 766 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, "Parametric amplification of soliton steering in optical lattices," Opt. Lett. 29, 1102 (2004).
[CrossRef] [PubMed]

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, "Dynamics of matter solitons in weakly modulated optical lattices," Phys. Rev. A 70, 043604 (2004).
[CrossRef]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole solitons in optically induced two-dimensional photonic lattices," Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Rotary dipole-mode solitons in Bessel optical lattices," J. Opt. B: Quantum Semiclassical Opt. 6, 444 (2004).
[CrossRef]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: Theory and experiment," Studies in Applied Mathematics 113, 389 (2004).
[CrossRef]

2003 (5)

J. Yang and D. E. Pelinovsky, "Stable vortex and dipole vector solitons in a saturable nonlinear medium," Phys. Rev. E 67, 016608 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

D. Neshev, E. Ostrovskaya, Y. S. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

2002 (3)

2001 (2)

A. S. Desyatnikov, D. Neshev, E. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. M. Pérez-García, "Multipole spatial vector solitons," Opt. Lett. 26, 435 (2001).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

2000 (3)

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrovskaya, and Y. S. Kivshar, "Dipole-mode vector solitons," Phys. Rev. Lett. 85, 82 (2000).
[CrossRef] [PubMed]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. Christodoulides, "Observation of two-dimensional multimode solitons," Opt. Lett. 25, 1113 (2000).
[CrossRef]

1998 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

1993 (1)

R. Scharf and A. R. Bishop, "Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials," Phys. Rev. E 47, 1375 (1993).
[CrossRef]

1989 (1)

Y. S. Kivashar and B. A. Malomed, "Dynamics of solitons in nearly integrable systems," Rev. Mod. Phys. 61, 763 (1989).
[CrossRef]

1976 (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser-beams through atmosphere," Appl. Phys. 10, 129 (1976).
[CrossRef]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beam," Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Abdullaev, F. Kh.

F. Kh. Abdullaev and J. Garnier, "Propagation of matter-wave solitons in periodic and random nonlinear potentials," Phys. Rev. A 72, 061605 (2005).
[CrossRef]

Aitchison, J. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Anastassiou, C.

Bezryadina, A.

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: Theory and experiment," Studies in Applied Mathematics 113, 389 (2004).
[CrossRef]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole solitons in optically induced two-dimensional photonic lattices," Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Bishop, A. R.

R. Scharf and A. R. Bishop, "Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials," Phys. Rev. E 47, 1375 (1993).
[CrossRef]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Brazhnyi, V. A.

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, "Dynamics of matter solitons in weakly modulated optical lattices," Phys. Rev. A 70, 043604 (2004).
[CrossRef]

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. Christodoulides, "Observation of two-dimensional multimode solitons," Opt. Lett. 25, 1113 (2000).
[CrossRef]

Carretero-González, R.

Chen, Z.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and J. Yang, "Formation of discrete solitons in light-induced photonic lattices," Opt. Express 13, 1816 (2005).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: Theory and experiment," Studies in Applied Mathematics 113, 389 (2004).
[CrossRef]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole solitons in optically induced two-dimensional photonic lattices," Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beam," Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Christodoulides, D.

Christodoulides, D. N.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Denz, C.

Desyatnikov, A. S.

Efremidis, N. K.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Egorov, A. A.

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Rotary dipole-mode solitons in Bessel optical lattices," J. Opt. B: Quantum Semiclassical Opt. 6, 444 (2004).
[CrossRef]

Eisenberg, H. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Eugenieva, E. D.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and J. Yang, "Formation of discrete solitons in light-induced photonic lattices," Opt. Express 13, 1816 (2005).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Feit, M. D.

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser-beams through atmosphere," Appl. Phys. 10, 129 (1976).
[CrossRef]

Fleck, J. A.

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser-beams through atmosphere," Appl. Phys. 10, 129 (1976).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

García-Ripoll, J. J.

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beam," Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Garnier, J.

F. Kh. Abdullaev and J. Garnier, "Propagation of matter-wave solitons in periodic and random nonlinear potentials," Phys. Rev. A 72, 061605 (2005).
[CrossRef]

Geisser, M.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

Jander, P.

Kaiser, F.

Kartashov, Y. V.

Kip, D.

Kivashar, Y. S.

Y. S. Kivashar and B. A. Malomed, "Dynamics of solitons in nearly integrable systems," Rev. Mod. Phys. 61, 763 (1989).
[CrossRef]

Kivshar, Y. S.

Konotop, V. V.

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, "Dynamics of matter solitons in weakly modulated optical lattices," Phys. Rev. A 70, 043604 (2004).
[CrossRef]

Krolikowski, W.

Kuzmiak, V.

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, "Dynamics of matter solitons in weakly modulated optical lattices," Phys. Rev. A 70, 043604 (2004).
[CrossRef]

Lan, S.

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
[CrossRef] [PubMed]

Luther-Davies, B.

Makasyuk, I.

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: Theory and experiment," Studies in Applied Mathematics 113, 389 (2004).
[CrossRef]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole solitons in optically induced two-dimensional photonic lattices," Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

Malomed, B. A.

Martin, H.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and J. Yang, "Formation of discrete solitons in light-induced photonic lattices," Opt. Express 13, 1816 (2005).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

McCarthy, G.

A. S. Desyatnikov, D. Neshev, E. A. Osrovskaya, Y. S. Kivshar, G. McCarthy, W. Krolikowski, and B. Luther-Davies, "Multipole composite spatial solitons: theory and experiment," J. Opt. Soc. Am. B 19, 586 (2002).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

Mihalache, D.

Morandotti, R.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser-beams through atmosphere," Appl. Phys. 10, 129 (1976).
[CrossRef]

Motzek, K.

Musslimani, Z. H.

Neshev, D.

Osrovskaya, E. A.

Ostrovskaya, E.

Ostrovskaya, E. A.

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrovskaya, and Y. S. Kivshar, "Dipole-mode vector solitons," Phys. Rev. Lett. 85, 82 (2000).
[CrossRef] [PubMed]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

Pelinovsky, D. E.

J. Yang and D. E. Pelinovsky, "Stable vortex and dipole vector solitons in a saturable nonlinear medium," Phys. Rev. E 67, 016608 (2003).
[CrossRef]

Pérez-García, V. M.

Richter, T.

Scharf, R.

R. Scharf and A. R. Bishop, "Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials," Phys. Rev. E 47, 1375 (1993).
[CrossRef]

Schroder, J.

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Segev, M.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. Christodoulides, "Observation of two-dimensional multimode solitons," Opt. Lett. 25, 1113 (2000).
[CrossRef]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Sorel, M.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

Torner, L.

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beam," Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Vysloukh, V. A.

Weilnau, C.

A. S. Desyatnikov and Y. S. Kivshar, K. Motzek, F. Kaiser, C. Weilnau, and C. Denz, "Multicomponent dipole-mode spatial solitons," Opt. Lett. 27, 634 (2002).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

Xu, J.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and J. Yang, "Formation of discrete solitons in light-induced photonic lattices," Opt. Express 13, 1816 (2005).
[CrossRef] [PubMed]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Yang, J.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and J. Yang, "Formation of discrete solitons in light-induced photonic lattices," Opt. Express 13, 1816 (2005).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: Theory and experiment," Studies in Applied Mathematics 113, 389 (2004).
[CrossRef]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole solitons in optically induced two-dimensional photonic lattices," Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

J. Yang and D. E. Pelinovsky, "Stable vortex and dipole vector solitons in a saturable nonlinear medium," Phys. Rev. E 67, 016608 (2003).
[CrossRef]

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time-dependent propagation of high-energy laser-beams through atmosphere," Appl. Phys. 10, 129 (1976).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt. (1)

Y. V. Kartashov, A. A. Egorov, V. A. Vysloukh, and L. Torner, "Rotary dipole-mode solitons in Bessel optical lattices," J. Opt. B: Quantum Semiclassical Opt. 6, 444 (2004).
[CrossRef]

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

Nature (2)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (9)

Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, "Multipole vector solitons in nonlocal nonlinear media," Opt. Lett. 31, 1483 (2006).
[CrossRef] [PubMed]

J. Schroder, P. Jander, C. Denz, T. Richter, K. Motzek, and F. Kaiser, "Counterpropagating dipole-mode vector soliton," Opt. Lett. 30, 1042 (2005).
[CrossRef] [PubMed]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole solitons in optically induced two-dimensional photonic lattices," Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

A. S. Desyatnikov and Y. S. Kivshar, K. Motzek, F. Kaiser, C. Weilnau, and C. Denz, "Multicomponent dipole-mode spatial solitons," Opt. Lett. 27, 634 (2002).
[CrossRef]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. Christodoulides, "Observation of two-dimensional multimode solitons," Opt. Lett. 25, 1113 (2000).
[CrossRef]

A. S. Desyatnikov, D. Neshev, E. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. M. Pérez-García, "Multipole spatial vector solitons," Opt. Lett. 26, 435 (2001).
[CrossRef]

D. Neshev, E. Ostrovskaya, Y. S. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

Y. V. Kartashov A. S. Zelenina, L. Torner, and V. A. Vysloukh, "Spatial soliton switching in quasi-continuous optical arrays," Opt. Lett. 29, 766 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, "Parametric amplification of soliton steering in optical lattices," Opt. Lett. 29, 1102 (2004).
[CrossRef] [PubMed]

Phys. Rev. A (2)

V. A. Brazhnyi, V. V. Konotop, and V. Kuzmiak, "Dynamics of matter solitons in weakly modulated optical lattices," Phys. Rev. A 70, 043604 (2004).
[CrossRef]

F. Kh. Abdullaev and J. Garnier, "Propagation of matter-wave solitons in periodic and random nonlinear potentials," Phys. Rev. A 72, 061605 (2005).
[CrossRef]

Phys. Rev. E (3)

R. Scharf and A. R. Bishop, "Length-scale competition for the one-dimensional nonlinear Schrödinger equation with spatially periodic potentials," Phys. Rev. E 47, 1375 (1993).
[CrossRef]

J. Yang and D. E. Pelinovsky, "Stable vortex and dipole vector solitons in a saturable nonlinear medium," Phys. Rev. E 67, 016608 (2003).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Phys. Rev. Lett. (8)

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Observation of discrete solitons in optical waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, "Self-focusing and defocusing in waveguide arrays," Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beam," Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrovskaya, and Y. S. Kivshar, "Dipole-mode vector solitons," Phys. Rev. Lett. 85, 82 (2000).
[CrossRef] [PubMed]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. Luther-Davies, "Observation of dipole-mode vector solitons," Phys. Rev. Lett. 85, 1424 (2000).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

Y. S. Kivashar and B. A. Malomed, "Dynamics of solitons in nearly integrable systems," Rev. Mod. Phys. 61, 763 (1989).
[CrossRef]

Studies in Applied Mathematics (1)

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, "Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: Theory and experiment," Studies in Applied Mathematics 113, 389 (2004).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Profiles of dipoles solitons (DSs) for (a) the first-order DS A=1 and (b) the second-order DS A=2. (c) Lattice modulation depth p versus modulation period T for A=1 and A=2, to achieve the stabilization of DSs.

Fig. 2.
Fig. 2.

(Color online) Evolutions of unstable DSs along direction z. (a) T=3, p=0 and A=1. (b) T=3, p=0 and A=2. (c) T=6, p=5 and A=1. (d) T=6, p=10 and A=2.

Fig. 3.
Fig. 3.

(Color online) Evolutions of DSs trapped by lattice for z=200. The first-order DSs A=1 for (a) T=3, p=10, (c) T=6, p=40 and (e) T=8, p=70. The second-order DSs A=2 for (b) T=3, p=50, (d) T=6, p=190 and (f) T=8, p=340.

Fig. 4.
Fig. 4.

(Color online) Critical incident angle (a) and critical center position (b) versus period T for both A=1 and A=2. Evolutions of DSs exhibit stable swing motion around the center of lattice: (c) T=3, p=10, x 0=0.2 and A=1, (d) T=6, p=40, ∫=0.5 and A=1, (e) T=6, p=190, x 0=0.3 and A=2, (f) T=6, p=190, ∫=0.5 and A=2, (g) T=3, p=10, x 0=0.2, ∫=0.1 and A=1, and (i) T=6, p=190, x 0=0.2, ∫=0.1 and A=2. Evolutions of DSs exhibit unstable swing motion: (h) T=3, p=10, x 0=0.8, ∫=0.2 and A=1, and (j) T=6, p=190, x 0=0.3, ∫=1.5 and A=2.

Equations (6)

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

i u z = 1 2 u xx u 2 u p V ( x ) u ,
U = u 2 dx ,
H = 1 2 [ u x 2 2 p V ( x ) u 2 u 4 ] dx .
u ( z = 0 , x ) = A sec h [ A ( x x 0 ) ] × sin ( x x 0 ) × exp [ i α ( x x 0 ) ] .
d 2 x 0 dz 2 = 0.69 V eff ( x 0 ) ,
V eff ( x 0 ) = p V ( x ) u ( x x 0 ) 2 dx .

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