Abstract

With the spectral renormalization method (the Fourier iteration method) we compute dark/gray soliton solutions in Kerr-type nonlocal media and find it agrees well with the analytical results. It is indicated when the characteristic nonlocal length is less than a certain critical value, the gray soliton’s maximal transverse velocity does not vary with the characteristic nonlocal length, otherwise such maximal velocity decreases with the characteristic nonlocal length.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Conti, M. Peccianti, and G. Assanto, "Route to Nonlocality and Observation of Accessible Solitons," Phys. Rev. Lett. 91, 073901 (2003).
    [CrossRef] [PubMed]
  2. C. Conti, M. Peccianti, and G. Assanto, "Observation of Optical Spatial Solitons in a Highly Nonlocal Medium," Phys. Rev. Lett. 92, 113902 (2004).
    [CrossRef] [PubMed]
  3. W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 071111 (2006).
    [CrossRef]
  4. C. Rotschild, O. Cohen, O. Manela, M. Segev and T. Carmon, "Solitons in Nonlinear Media with an Infinite Range of Nonlocality-First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons," Phys. Rev. Lett. 95, 213904 (2005).
    [CrossRef] [PubMed]
  5. Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, "Large phase shift of nonlocal optical spatial solitons," Phys. Rev. E,  69, 016602 (2004).
    [CrossRef]
  6. S. Ouyang, Q. Guo, and W. Hu, "Perturbative analysis of generally nonlocal spatial optical solitons," Phys. Rev. E  74, 036622 (2006).
    [CrossRef]
  7. S. Ouyang and Q. Guo, "(1+2)-dimensional strongly nonlocal solitons," Phys. Rev. A  76, 053833 (2007).
    [CrossRef]
  8. W. Zhong and L. Yi, "Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media," Phys. Rev. A  75, 061801 (2007).
    [CrossRef]
  9. D. Buccoliero, A. S. Desyatnikov,W. Krolikowski, and Y. S. Kivshar, "Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media," Phys. Rev. Lett. 98, 053901 (2007).
    [CrossRef] [PubMed]
  10. D. Deng and Q. Guo, "Ince-Gaussian solitons in strongly nonlocal nonlinear media," Opt. Lett,  32, 3206-3208 (2007).
    [CrossRef] [PubMed]
  11. A. W. Snyder and D. J. Mitchell, "accessible soliton," Science 276, 1538 (1997).
    [CrossRef]
  12. P. D. Rasmussen, O. Bang, W. Krolikowski, "Theory of nonlocal soliton interaction in nematic liquid crystal," Phys. Rev. E  72, 066611 (2005).
    [CrossRef]
  13. S. Ouyang, W. Hu, and Q. Guo, "Light steering in a strongly nonlocal nonlinear medium," Phys. Rev. A  76, 053832 (2007).
    [CrossRef]
  14. W. Hu, S. Ouyang, P. Yang, Q. Guo,and S. Lan, "Short-range interactions between strongly nonlocal spatial solitons," Phys. Rev. A  77, 033842 (2008).
    [CrossRef]
  15. A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of Attraction between Dark Solitons" Phys. Rev. Lett. 96, 043901 (2006).
    [CrossRef] [PubMed]
  16. N. I. Nikolov, D. Neshev, W. Krolikowski, O Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical soliton," Opt. Lett.  29, 286-288 (2004).
    [CrossRef]
  17. Y. V. Kartashov and L. Torner, "Gray spatial solitons in nonlocal nonlinear media," Opt. Lett. 32, 946-948 (2007)
    [CrossRef]
  18. M. J. Ablowitz and Z. H. Musslimani, "Spectral renormalization method for computing self-localized solutions to nonlinear systems," Opt. Lett.  30, 2140-2142 (2005).
    [CrossRef]
  19. Z. H. Musslimani, and J. Yang, "Self-trapping of light in a two-dimensional photonic lattice," J. Opt. Soc. Am. B. 21, 973-981 (2004).
    [CrossRef]
  20. A. A. Zozulya, D. Z. Anderson, A. V. Mamaev and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. E 57, 522-534 (1998).
  21. M. Stepic, L. Hadzievski, and M. M. Skoric, "Stability of one-dimensional array solitons," Phys. Rev. E  65, 026604 (2002)
    [CrossRef]
  22. J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, "Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics," Phys. Rev. E  67, 056618 (2003).
    [CrossRef]
  23. G. P. Agrawal, Nonlinear Fiber Optics, (New York: Academeic 1995).
  24. W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: Exact solutions," Phys. Rev. E  63, 016610 (2000).
    [CrossRef]
  25. W. Krolikowski, O. Bang, J. J. Rasmussen and J. Wyller "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E  64, 016612 (2001).
    [CrossRef]

2008 (1)

W. Hu, S. Ouyang, P. Yang, Q. Guo,and S. Lan, "Short-range interactions between strongly nonlocal spatial solitons," Phys. Rev. A  77, 033842 (2008).
[CrossRef]

2007 (6)

Y. V. Kartashov and L. Torner, "Gray spatial solitons in nonlocal nonlinear media," Opt. Lett. 32, 946-948 (2007)
[CrossRef]

S. Ouyang and Q. Guo, "(1+2)-dimensional strongly nonlocal solitons," Phys. Rev. A  76, 053833 (2007).
[CrossRef]

W. Zhong and L. Yi, "Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media," Phys. Rev. A  75, 061801 (2007).
[CrossRef]

D. Buccoliero, A. S. Desyatnikov,W. Krolikowski, and Y. S. Kivshar, "Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media," Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

D. Deng and Q. Guo, "Ince-Gaussian solitons in strongly nonlocal nonlinear media," Opt. Lett,  32, 3206-3208 (2007).
[CrossRef] [PubMed]

S. Ouyang, W. Hu, and Q. Guo, "Light steering in a strongly nonlocal nonlinear medium," Phys. Rev. A  76, 053832 (2007).
[CrossRef]

2006 (3)

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of Attraction between Dark Solitons" Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

S. Ouyang, Q. Guo, and W. Hu, "Perturbative analysis of generally nonlocal spatial optical solitons," Phys. Rev. E  74, 036622 (2006).
[CrossRef]

2005 (3)

P. D. Rasmussen, O. Bang, W. Krolikowski, "Theory of nonlocal soliton interaction in nematic liquid crystal," Phys. Rev. E  72, 066611 (2005).
[CrossRef]

M. J. Ablowitz and Z. H. Musslimani, "Spectral renormalization method for computing self-localized solutions to nonlinear systems," Opt. Lett.  30, 2140-2142 (2005).
[CrossRef]

C. Rotschild, O. Cohen, O. Manela, M. Segev and T. Carmon, "Solitons in Nonlinear Media with an Infinite Range of Nonlocality-First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

2004 (4)

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, "Large phase shift of nonlocal optical spatial solitons," Phys. Rev. E,  69, 016602 (2004).
[CrossRef]

C. Conti, M. Peccianti, and G. Assanto, "Observation of Optical Spatial Solitons in a Highly Nonlocal Medium," Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

Z. H. Musslimani, and J. Yang, "Self-trapping of light in a two-dimensional photonic lattice," J. Opt. Soc. Am. B. 21, 973-981 (2004).
[CrossRef]

N. I. Nikolov, D. Neshev, W. Krolikowski, O Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical soliton," Opt. Lett.  29, 286-288 (2004).
[CrossRef]

2003 (2)

C. Conti, M. Peccianti, and G. Assanto, "Route to Nonlocality and Observation of Accessible Solitons," Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, "Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics," Phys. Rev. E  67, 056618 (2003).
[CrossRef]

2002 (1)

M. Stepic, L. Hadzievski, and M. M. Skoric, "Stability of one-dimensional array solitons," Phys. Rev. E  65, 026604 (2002)
[CrossRef]

2001 (1)

W. Krolikowski, O. Bang, J. J. Rasmussen and J. Wyller "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E  64, 016612 (2001).
[CrossRef]

2000 (1)

W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: Exact solutions," Phys. Rev. E  63, 016610 (2000).
[CrossRef]

1998 (1)

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. E 57, 522-534 (1998).

1997 (1)

A. W. Snyder and D. J. Mitchell, "accessible soliton," Science 276, 1538 (1997).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz and Z. H. Musslimani, "Spectral renormalization method for computing self-localized solutions to nonlinear systems," Opt. Lett.  30, 2140-2142 (2005).
[CrossRef]

Anderson, D. Z.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. E 57, 522-534 (1998).

Assanto, G.

C. Conti, M. Peccianti, and G. Assanto, "Observation of Optical Spatial Solitons in a Highly Nonlocal Medium," Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, "Route to Nonlocality and Observation of Accessible Solitons," Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

Bang, O

N. I. Nikolov, D. Neshev, W. Krolikowski, O Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical soliton," Opt. Lett.  29, 286-288 (2004).
[CrossRef]

Bang, O.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of Attraction between Dark Solitons" Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

P. D. Rasmussen, O. Bang, W. Krolikowski, "Theory of nonlocal soliton interaction in nematic liquid crystal," Phys. Rev. E  72, 066611 (2005).
[CrossRef]

W. Krolikowski, O. Bang, J. J. Rasmussen and J. Wyller "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E  64, 016612 (2001).
[CrossRef]

W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: Exact solutions," Phys. Rev. E  63, 016610 (2000).
[CrossRef]

Buccoliero, D.

D. Buccoliero, A. S. Desyatnikov,W. Krolikowski, and Y. S. Kivshar, "Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media," Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

Carmon, T.

C. Rotschild, O. Cohen, O. Manela, M. Segev and T. Carmon, "Solitons in Nonlinear Media with an Infinite Range of Nonlocality-First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Chi, S.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, "Large phase shift of nonlocal optical spatial solitons," Phys. Rev. E,  69, 016602 (2004).
[CrossRef]

Christiansen, P. L.

N. I. Nikolov, D. Neshev, W. Krolikowski, O Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical soliton," Opt. Lett.  29, 286-288 (2004).
[CrossRef]

Christodoulides, D. N.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, "Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics," Phys. Rev. E  67, 056618 (2003).
[CrossRef]

Cohen, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev and T. Carmon, "Solitons in Nonlinear Media with an Infinite Range of Nonlocality-First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Conti, C.

C. Conti, M. Peccianti, and G. Assanto, "Observation of Optical Spatial Solitons in a Highly Nonlocal Medium," Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, "Route to Nonlocality and Observation of Accessible Solitons," Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

Deng, D.

D. Deng and Q. Guo, "Ince-Gaussian solitons in strongly nonlocal nonlinear media," Opt. Lett,  32, 3206-3208 (2007).
[CrossRef] [PubMed]

Desyatnikov, A. S.

D. Buccoliero, A. S. Desyatnikov,W. Krolikowski, and Y. S. Kivshar, "Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media," Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

Dreischuh, A.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of Attraction between Dark Solitons" Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

Guo, Q.

W. Hu, S. Ouyang, P. Yang, Q. Guo,and S. Lan, "Short-range interactions between strongly nonlocal spatial solitons," Phys. Rev. A  77, 033842 (2008).
[CrossRef]

S. Ouyang, W. Hu, and Q. Guo, "Light steering in a strongly nonlocal nonlinear medium," Phys. Rev. A  76, 053832 (2007).
[CrossRef]

D. Deng and Q. Guo, "Ince-Gaussian solitons in strongly nonlocal nonlinear media," Opt. Lett,  32, 3206-3208 (2007).
[CrossRef] [PubMed]

S. Ouyang and Q. Guo, "(1+2)-dimensional strongly nonlocal solitons," Phys. Rev. A  76, 053833 (2007).
[CrossRef]

S. Ouyang, Q. Guo, and W. Hu, "Perturbative analysis of generally nonlocal spatial optical solitons," Phys. Rev. E  74, 036622 (2006).
[CrossRef]

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, "Large phase shift of nonlocal optical spatial solitons," Phys. Rev. E,  69, 016602 (2004).
[CrossRef]

Hadzievski, L.

M. Stepic, L. Hadzievski, and M. M. Skoric, "Stability of one-dimensional array solitons," Phys. Rev. E  65, 026604 (2002)
[CrossRef]

Hu, W.

W. Hu, S. Ouyang, P. Yang, Q. Guo,and S. Lan, "Short-range interactions between strongly nonlocal spatial solitons," Phys. Rev. A  77, 033842 (2008).
[CrossRef]

S. Ouyang, W. Hu, and Q. Guo, "Light steering in a strongly nonlocal nonlinear medium," Phys. Rev. A  76, 053832 (2007).
[CrossRef]

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

S. Ouyang, Q. Guo, and W. Hu, "Perturbative analysis of generally nonlocal spatial optical solitons," Phys. Rev. E  74, 036622 (2006).
[CrossRef]

Hudock, J.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, "Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics," Phys. Rev. E  67, 056618 (2003).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov and L. Torner, "Gray spatial solitons in nonlocal nonlinear media," Opt. Lett. 32, 946-948 (2007)
[CrossRef]

Kevrekidis, P. G.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, "Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics," Phys. Rev. E  67, 056618 (2003).
[CrossRef]

Kivshar, Y. S.

D. Buccoliero, A. S. Desyatnikov,W. Krolikowski, and Y. S. Kivshar, "Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media," Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

Krolikowski, W.

D. Buccoliero, A. S. Desyatnikov,W. Krolikowski, and Y. S. Kivshar, "Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media," Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of Attraction between Dark Solitons" Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

P. D. Rasmussen, O. Bang, W. Krolikowski, "Theory of nonlocal soliton interaction in nematic liquid crystal," Phys. Rev. E  72, 066611 (2005).
[CrossRef]

N. I. Nikolov, D. Neshev, W. Krolikowski, O Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical soliton," Opt. Lett.  29, 286-288 (2004).
[CrossRef]

W. Krolikowski, O. Bang, J. J. Rasmussen and J. Wyller "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E  64, 016612 (2001).
[CrossRef]

W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: Exact solutions," Phys. Rev. E  63, 016610 (2000).
[CrossRef]

Lan, S.

W. Hu, S. Ouyang, P. Yang, Q. Guo,and S. Lan, "Short-range interactions between strongly nonlocal spatial solitons," Phys. Rev. A  77, 033842 (2008).
[CrossRef]

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

Luo, B.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, "Large phase shift of nonlocal optical spatial solitons," Phys. Rev. E,  69, 016602 (2004).
[CrossRef]

Malomed, B. A.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, "Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics," Phys. Rev. E  67, 056618 (2003).
[CrossRef]

Mamaev, A. V.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. E 57, 522-534 (1998).

Manela, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev and T. Carmon, "Solitons in Nonlinear Media with an Infinite Range of Nonlocality-First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Mitchell, D. J.

A. W. Snyder and D. J. Mitchell, "accessible soliton," Science 276, 1538 (1997).
[CrossRef]

Musslimani, Z. H.

M. J. Ablowitz and Z. H. Musslimani, "Spectral renormalization method for computing self-localized solutions to nonlinear systems," Opt. Lett.  30, 2140-2142 (2005).
[CrossRef]

Z. H. Musslimani, and J. Yang, "Self-trapping of light in a two-dimensional photonic lattice," J. Opt. Soc. Am. B. 21, 973-981 (2004).
[CrossRef]

Neshev, D.

N. I. Nikolov, D. Neshev, W. Krolikowski, O Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical soliton," Opt. Lett.  29, 286-288 (2004).
[CrossRef]

Neshev, D. N.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of Attraction between Dark Solitons" Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

Nikolov, N. I.

N. I. Nikolov, D. Neshev, W. Krolikowski, O Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical soliton," Opt. Lett.  29, 286-288 (2004).
[CrossRef]

Ouyang, S.

W. Hu, S. Ouyang, P. Yang, Q. Guo,and S. Lan, "Short-range interactions between strongly nonlocal spatial solitons," Phys. Rev. A  77, 033842 (2008).
[CrossRef]

S. Ouyang, W. Hu, and Q. Guo, "Light steering in a strongly nonlocal nonlinear medium," Phys. Rev. A  76, 053832 (2007).
[CrossRef]

S. Ouyang and Q. Guo, "(1+2)-dimensional strongly nonlocal solitons," Phys. Rev. A  76, 053833 (2007).
[CrossRef]

S. Ouyang, Q. Guo, and W. Hu, "Perturbative analysis of generally nonlocal spatial optical solitons," Phys. Rev. E  74, 036622 (2006).
[CrossRef]

Peccianti, M.

C. Conti, M. Peccianti, and G. Assanto, "Observation of Optical Spatial Solitons in a Highly Nonlocal Medium," Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, "Route to Nonlocality and Observation of Accessible Solitons," Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

Petersen, D. E.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of Attraction between Dark Solitons" Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

Rasmussen, J. J.

N. I. Nikolov, D. Neshev, W. Krolikowski, O Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical soliton," Opt. Lett.  29, 286-288 (2004).
[CrossRef]

W. Krolikowski, O. Bang, J. J. Rasmussen and J. Wyller "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E  64, 016612 (2001).
[CrossRef]

Rasmussen, P. D.

P. D. Rasmussen, O. Bang, W. Krolikowski, "Theory of nonlocal soliton interaction in nematic liquid crystal," Phys. Rev. E  72, 066611 (2005).
[CrossRef]

Rotschild, C.

C. Rotschild, O. Cohen, O. Manela, M. Segev and T. Carmon, "Solitons in Nonlinear Media with an Infinite Range of Nonlocality-First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Saffman, M.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. E 57, 522-534 (1998).

Segev, M.

C. Rotschild, O. Cohen, O. Manela, M. Segev and T. Carmon, "Solitons in Nonlinear Media with an Infinite Range of Nonlocality-First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Skoric, M. M.

M. Stepic, L. Hadzievski, and M. M. Skoric, "Stability of one-dimensional array solitons," Phys. Rev. E  65, 026604 (2002)
[CrossRef]

Snyder, A. W.

A. W. Snyder and D. J. Mitchell, "accessible soliton," Science 276, 1538 (1997).
[CrossRef]

Stepic, M.

M. Stepic, L. Hadzievski, and M. M. Skoric, "Stability of one-dimensional array solitons," Phys. Rev. E  65, 026604 (2002)
[CrossRef]

Torner, L.

Y. V. Kartashov and L. Torner, "Gray spatial solitons in nonlocal nonlinear media," Opt. Lett. 32, 946-948 (2007)
[CrossRef]

Wyller, J.

W. Krolikowski, O. Bang, J. J. Rasmussen and J. Wyller "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E  64, 016612 (2001).
[CrossRef]

Xie, Y.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, "Large phase shift of nonlocal optical spatial solitons," Phys. Rev. E,  69, 016602 (2004).
[CrossRef]

Xuan, L.

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

Yang, J.

Z. H. Musslimani, and J. Yang, "Self-trapping of light in a two-dimensional photonic lattice," J. Opt. Soc. Am. B. 21, 973-981 (2004).
[CrossRef]

Yang, P.

W. Hu, S. Ouyang, P. Yang, Q. Guo,and S. Lan, "Short-range interactions between strongly nonlocal spatial solitons," Phys. Rev. A  77, 033842 (2008).
[CrossRef]

Yi, F.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, "Large phase shift of nonlocal optical spatial solitons," Phys. Rev. E,  69, 016602 (2004).
[CrossRef]

Yi, L.

W. Zhong and L. Yi, "Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media," Phys. Rev. A  75, 061801 (2007).
[CrossRef]

Zhang, T.

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

Zhong, W.

W. Zhong and L. Yi, "Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media," Phys. Rev. A  75, 061801 (2007).
[CrossRef]

Zozulya, A. A.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. E 57, 522-534 (1998).

Appl. Phys. Lett. (1)

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

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

Z. H. Musslimani, and J. Yang, "Self-trapping of light in a two-dimensional photonic lattice," J. Opt. Soc. Am. B. 21, 973-981 (2004).
[CrossRef]

Opt. Lett (4)

D. Deng and Q. Guo, "Ince-Gaussian solitons in strongly nonlocal nonlinear media," Opt. Lett,  32, 3206-3208 (2007).
[CrossRef] [PubMed]

N. I. Nikolov, D. Neshev, W. Krolikowski, O Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical soliton," Opt. Lett.  29, 286-288 (2004).
[CrossRef]

Y. V. Kartashov and L. Torner, "Gray spatial solitons in nonlocal nonlinear media," Opt. Lett. 32, 946-948 (2007)
[CrossRef]

M. J. Ablowitz and Z. H. Musslimani, "Spectral renormalization method for computing self-localized solutions to nonlinear systems," Opt. Lett.  30, 2140-2142 (2005).
[CrossRef]

Phys. Rev. A (4)

S. Ouyang, W. Hu, and Q. Guo, "Light steering in a strongly nonlocal nonlinear medium," Phys. Rev. A  76, 053832 (2007).
[CrossRef]

W. Hu, S. Ouyang, P. Yang, Q. Guo,and S. Lan, "Short-range interactions between strongly nonlocal spatial solitons," Phys. Rev. A  77, 033842 (2008).
[CrossRef]

S. Ouyang and Q. Guo, "(1+2)-dimensional strongly nonlocal solitons," Phys. Rev. A  76, 053833 (2007).
[CrossRef]

W. Zhong and L. Yi, "Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media," Phys. Rev. A  75, 061801 (2007).
[CrossRef]

Phys. Rev. E (8)

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, "Large phase shift of nonlocal optical spatial solitons," Phys. Rev. E,  69, 016602 (2004).
[CrossRef]

S. Ouyang, Q. Guo, and W. Hu, "Perturbative analysis of generally nonlocal spatial optical solitons," Phys. Rev. E  74, 036622 (2006).
[CrossRef]

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. E 57, 522-534 (1998).

M. Stepic, L. Hadzievski, and M. M. Skoric, "Stability of one-dimensional array solitons," Phys. Rev. E  65, 026604 (2002)
[CrossRef]

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, "Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics," Phys. Rev. E  67, 056618 (2003).
[CrossRef]

W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: Exact solutions," Phys. Rev. E  63, 016610 (2000).
[CrossRef]

W. Krolikowski, O. Bang, J. J. Rasmussen and J. Wyller "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E  64, 016612 (2001).
[CrossRef]

P. D. Rasmussen, O. Bang, W. Krolikowski, "Theory of nonlocal soliton interaction in nematic liquid crystal," Phys. Rev. E  72, 066611 (2005).
[CrossRef]

Phys. Rev. Lett. (5)

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of Attraction between Dark Solitons" Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

D. Buccoliero, A. S. Desyatnikov,W. Krolikowski, and Y. S. Kivshar, "Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media," Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev and T. Carmon, "Solitons in Nonlinear Media with an Infinite Range of Nonlocality-First Observation of Coherent Elliptic Solitons and of Vortex-Ring Solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, "Route to Nonlocality and Observation of Accessible Solitons," Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, "Observation of Optical Spatial Solitons in a Highly Nonlocal Medium," Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

Science (1)

A. W. Snyder and D. J. Mitchell, "accessible soliton," Science 276, 1538 (1997).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, (New York: Academeic 1995).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

(a), (b) Gray soliton solutions computed with the exponentially decaying or Gaussian nonlocal response respectively when μ = 1/3 and w = 0 (black line) or w = 1 (red line), or w = 3 (green line), or w = 5 (blue line). (c), (d) Numerical simulations computed with the exponentially decaying or Gaussian nonlocal response respectively when w = 5.

Fig. 2.
Fig. 2.

(a) The gray soliton (black line) computed with an exponentially decaying nonlocal response when μ = 0.43,w = 5, and its fitting functions (red line) 1 - 0.137exp(-0.0753∣x∣)cos(0.596∣x∣ + 0.055); (b) The gray soliton (black line) computed with a Gaussian nonlocal response when μ = 0.4, w = 5, and its fitting function (red line) 1 -0.238exp(-0.0733∣x∣)cos(0.713∣x∣ + 0.107).

Fig. 3.
Fig. 3.

Areas below red lines are the existing parameter-spaces for gray soliton in a Kerr-type nonlinear media with (a) an exponentially decaying or (b) a Gaussian nonlocal response. Areas on the left sides or right sides of blue lines correspond to gray solitons with exponentially decaying or exponentially decaying oscillatory tails respectively.

Fig. 4.
Fig. 4.

(a) Dark solitons computed with a Gaussian nonlocal response when w = 0(black line), or w = 1(red line ), or w = 3(green line), or w = 5(blue line). (b) The numerical simulation of a dark soliton computed with a Gaussian nonlocal response when w = 5.

Equations (5)

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

i u z + 1 2 2 u x 2 u R ( x ξ ) u ( ξ , z ) 2 = 0 ,
1 2 d 2 ψ d x 2 + μ 2 + 2 2 ψ μ 2 2 ψ 3 ψ ∫R ( x ξ ) ψ 2 ( ξ ) = 0 ,
χ / 2 + N ( χ ) = 0 ,
1 2 χ 2 μ 2 χ + 2 R ( x ξ ) χ ( ξ ) = 0 .
1 2 d 2 ψ d x 2 + ψ ψ∫ R ( x ξ ) ψ 2 ( ξ ) = 0 .

Metrics