Abstract

We find that a surface soliton in nonlocal nonlinear media can be regarded as a half of a bulk soliton with an antisymmetric amplitude distribution. The analytical solutions for surface solitons and breathers in strongly nonlocal media are obtained, and the critical power and breather period are gotten analytically and confirmed by numerical simulations. In addition, the oscillating propagation of nonlocal surface solitons launched away from the stationary position is considered as interaction between the soliton and its out-of-phase image beam. Its trajectory and oscillating period obtained by our model are in good agreement with the numerical simulations.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Mitchell, M. Segev, and D. N. Christodoulides, "Observation of multihump multimode solitons," Phys. Rev. Lett. 80, 4657-4660 (1998).
    [CrossRef]
  2. M. Peccianti, K. A. Brzdkiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in nematic liquid crystals," Opt. Lett. 27, 1460-1462 (2002).
    [CrossRef]
  3. C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
    [CrossRef] [PubMed]
  4. 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]
  5. W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 07111 (2006).
    [CrossRef]
  6. C. Rotschild, O. Cohen, O. Manela, and M. Segev, "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]
  7. C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, "Two-dimensional multipole solitons in nonlocal nonlinear media," Opt. Lett. 31, 3312-3314 (2006).
    [CrossRef] [PubMed]
  8. S. Skupin, M. Saffman, and W. Krolikowski, "Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor," Phys. Rev. Lett. 98, 263902 (2007).
    [CrossRef] [PubMed]
  9. P. Pedri, and L. Santos, "Two-dimensional bright solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 95, 200404 (2005).
    [CrossRef] [PubMed]
  10. I. Tikhonenkov, B. A. Malomed, and A. Vardi, "Anisotropic solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 100, 090406 (2008).
    [CrossRef] [PubMed]
  11. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stability of vortex solitons in thermal nonlinear media with cylindrical symmetry," Opt. Express 15, 9378-9384 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-15-9378.
    [CrossRef] [PubMed]
  12. D. Q. Lu, and W. Hu, "Multiringed breathers and rotating breathers in strongly nonlocal nonlinear media under the off-waist incident condition," Phys. Rev. A 79, 043833 (2009).
    [CrossRef]
  13. Z. Xu, Y. V. Kartashov, and L. Torner, "Upper threshold for stability of multipole-mode solitons in nonlocal nonlinear media," Opt. Lett. 30, 3171-3173 (2005).
    [CrossRef] [PubMed]
  14. L. Dong, and F. Ye, "Stability of multipole-mode solitons in thermal nonlinear media," Phys. Rev. A 81, 013815 (2010).
    [CrossRef]
  15. S. Ouyang, Q. Guo, and W. Hu, "Perturbative analysis of generally nonlocal spatial optical solitons," Phys. Rev. E 74, 036622 (2006).
    [CrossRef]
  16. 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]
  17. D. Deng, X. Zhao, Q. Guo, and S. Lan, "Hermite-Gaussian breathers and solitons in strongly nonlocal nonlinear media," J. Opt. Soc. Am. B 24, 2537-2544 (2007).
    [CrossRef]
  18. D. Deng, and Q. Guo, "Propagation of Laguerre-Gaussian beams in nonlocal nonlinear media," J. Opt. A, Pure Appl. Opt. 10, 035101 (2008).
    [CrossRef]
  19. D. Deng, and Q. Guo, "Ince-Gaussian solitons in strongly nonlocal nonlinear media," Opt. Lett. 32, 3206-3208 (2007).
    [CrossRef] [PubMed]
  20. Y. V. Izdebskaya, A. S. Desyatnikov, G. Assanto, and Y. S. Kivshar, "Multimode nematicon waveguides," Opt. Lett. 36, 184-186 (2011).
    [CrossRef] [PubMed]
  21. Q. Guo, B. Luo, F. H. Yi, S. Chi, and Y. Q. Xie, "Large phase shift of nonlocal optical spatial solitons," Phys. Rev. E 69, 016602 (2004).
    [CrossRef]
  22. P. D. Rasmussen, O. Bang, and W. Królikowski, "Theory of nonlocal soliton interaction in nematic liquid crystals," Phys. Rev. E 72, 066611 (2005).
    [CrossRef]
  23. 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]
  24. N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical solitons," Opt. Lett. 29, 286-288 (2004).
    [CrossRef] [PubMed]
  25. D. Q. Lu, W. Hu, Y. J. Zheng, Y. B. Liang, L. G. Cao, S. Lan, and Q. Guo, "Self-induced fractional Fourier transform and revivable higher-order spatial solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 043815 (2008).
    [CrossRef]
  26. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, "Nonlocal surface-wave solitons," Phys. Rev. Lett. 98, 213901 (2007).
    [CrossRef] [PubMed]
  27. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Multipole surface solitons in thermal media," Opt. Lett. 34, 283-285 (2009).
    [CrossRef] [PubMed]
  28. F. Ye, Y. V. Kartashov, and L. Torner, "Nonlocal surface dipoles and vortices," Phys. Rev. A 77, 033829 (2008).
    [CrossRef]
  29. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Ring surface waves in thermal nonlinear media," Opt. Express 15, 16216-16221 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-16216.
    [CrossRef] [PubMed]
  30. B. Alfassi, C. Rotschild, and M. Segev, "Incoherent surface solitons in effectively instantaneous nonlocal nonlinear media," Phys. Rev. A 80, 041808 (2009).
    [CrossRef]
  31. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Optical surface waves supported and controlled by thermal waves," Opt. Lett. 33, 506-508 (2008).
    [CrossRef] [PubMed]
  32. W. Krolikowski, O. Bang, and J. Wyller, "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E 64, 016612 (2001).
    [CrossRef]
  33. N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, "Shocks in nonlocal media," Phys. Rev. Lett. 99, 043903 (2007).
    [CrossRef] [PubMed]
  34. C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, "Observation of a gradient catastrophe generating solitons," Phys. Rev. Lett. 102, 083902 (2009).
    [CrossRef] [PubMed]
  35. N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Królikowski, "Quadratic solitons as nonlocal solitons," Phys. Rev. E 68, 036614 (2003).
    [CrossRef]
  36. P. V. Larsen, M. P. Søensen, O. Bang, W. Z. Królikowski, and S. Trillo, "Nonlocal description of X waves in quadratic nonlinear materials," Phys. Rev. E 73, 036614 (2006).
    [CrossRef]
  37. Q. Shou, Y. B. Liang, Q. Jiang, Y. J. Zheng, S. Lan, W. Hu, and Q. Guo, "Boundary force exerted on spatial solitons in cylindrical strongly nonlocal media," Opt. Lett. 34, 3523-3523 (2009).
    [CrossRef] [PubMed]
  38. D. Anderson, "Variational approach to nonlinear pulse propagation in optical fibers," Phys. Rev. A 27, 3135-3145 (1983).
    [CrossRef]
  39. L. G. Cao, Y. Q. Zhu, D. Q. Lu, W. Hu, and Q. Guo, "Propagation of nonlocal optical solitons in lossy media with exponential-decay response," Opt. Commun. 281, 5004-5008 (2008).
    [CrossRef]

2011 (1)

2010 (1)

L. Dong, and F. Ye, "Stability of multipole-mode solitons in thermal nonlinear media," Phys. Rev. A 81, 013815 (2010).
[CrossRef]

2009 (5)

D. Q. Lu, and W. Hu, "Multiringed breathers and rotating breathers in strongly nonlocal nonlinear media under the off-waist incident condition," Phys. Rev. A 79, 043833 (2009).
[CrossRef]

B. Alfassi, C. Rotschild, and M. Segev, "Incoherent surface solitons in effectively instantaneous nonlocal nonlinear media," Phys. Rev. A 80, 041808 (2009).
[CrossRef]

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, "Observation of a gradient catastrophe generating solitons," Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Multipole surface solitons in thermal media," Opt. Lett. 34, 283-285 (2009).
[CrossRef] [PubMed]

Q. Shou, Y. B. Liang, Q. Jiang, Y. J. Zheng, S. Lan, W. Hu, and Q. Guo, "Boundary force exerted on spatial solitons in cylindrical strongly nonlocal media," Opt. Lett. 34, 3523-3523 (2009).
[CrossRef] [PubMed]

2008 (6)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Optical surface waves supported and controlled by thermal waves," Opt. Lett. 33, 506-508 (2008).
[CrossRef] [PubMed]

F. Ye, Y. V. Kartashov, and L. Torner, "Nonlocal surface dipoles and vortices," Phys. Rev. A 77, 033829 (2008).
[CrossRef]

L. G. Cao, Y. Q. Zhu, D. Q. Lu, W. Hu, and Q. Guo, "Propagation of nonlocal optical solitons in lossy media with exponential-decay response," Opt. Commun. 281, 5004-5008 (2008).
[CrossRef]

D. Deng, and Q. Guo, "Propagation of Laguerre-Gaussian beams in nonlocal nonlinear media," J. Opt. A, Pure Appl. Opt. 10, 035101 (2008).
[CrossRef]

D. Q. Lu, W. Hu, Y. J. Zheng, Y. B. Liang, L. G. Cao, S. Lan, and Q. Guo, "Self-induced fractional Fourier transform and revivable higher-order spatial solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 043815 (2008).
[CrossRef]

I. Tikhonenkov, B. A. Malomed, and A. Vardi, "Anisotropic solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 100, 090406 (2008).
[CrossRef] [PubMed]

2007 (8)

S. Skupin, M. Saffman, and W. Krolikowski, "Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor," Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef] [PubMed]

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, "Nonlocal surface-wave solitons," Phys. Rev. Lett. 98, 213901 (2007).
[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]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, "Shocks in nonlocal media," Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stability of vortex solitons in thermal nonlinear media with cylindrical symmetry," Opt. Express 15, 9378-9384 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-15-9378.
[CrossRef] [PubMed]

D. Deng, X. Zhao, Q. Guo, and S. Lan, "Hermite-Gaussian breathers and solitons in strongly nonlocal nonlinear media," J. Opt. Soc. Am. B 24, 2537-2544 (2007).
[CrossRef]

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

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Ring surface waves in thermal nonlinear media," Opt. Express 15, 16216-16221 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-16216.
[CrossRef] [PubMed]

2006 (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]

P. V. Larsen, M. P. Søensen, O. Bang, W. Z. Królikowski, and S. Trillo, "Nonlocal description of X waves in quadratic nonlinear materials," Phys. Rev. E 73, 036614 (2006).
[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, X. Li, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 07111 (2006).
[CrossRef]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, "Two-dimensional multipole solitons in nonlocal nonlinear media," Opt. Lett. 31, 3312-3314 (2006).
[CrossRef] [PubMed]

2005 (4)

Z. Xu, Y. V. Kartashov, and L. Torner, "Upper threshold for stability of multipole-mode solitons in nonlocal nonlinear media," Opt. Lett. 30, 3171-3173 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, and M. Segev, "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]

P. Pedri, and L. Santos, "Two-dimensional bright solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 95, 200404 (2005).
[CrossRef] [PubMed]

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

2004 (3)

Q. Guo, B. Luo, F. H. Yi, S. Chi, and Y. Q. 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]

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

2003 (2)

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Królikowski, "Quadratic solitons as nonlocal solitons," Phys. Rev. E 68, 036614 (2003).
[CrossRef]

C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

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

1998 (1)

M. Mitchell, M. Segev, and D. N. Christodoulides, "Observation of multihump multimode solitons," Phys. Rev. Lett. 80, 4657-4660 (1998).
[CrossRef]

1983 (1)

D. Anderson, "Variational approach to nonlinear pulse propagation in optical fibers," Phys. Rev. A 27, 3135-3145 (1983).
[CrossRef]

Alfassi, B.

B. Alfassi, C. Rotschild, and M. Segev, "Incoherent surface solitons in effectively instantaneous nonlocal nonlinear media," Phys. Rev. A 80, 041808 (2009).
[CrossRef]

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, "Nonlocal surface-wave solitons," Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

Anderson, D.

D. Anderson, "Variational approach to nonlinear pulse propagation in optical fibers," Phys. Rev. A 27, 3135-3145 (1983).
[CrossRef]

Assanto, G.

Y. V. Izdebskaya, A. S. Desyatnikov, G. Assanto, and Y. S. Kivshar, "Multimode nematicon waveguides," Opt. Lett. 36, 184-186 (2011).
[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]

C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

M. Peccianti, K. A. Brzdkiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in nematic liquid crystals," Opt. Lett. 27, 1460-1462 (2002).
[CrossRef]

Bang, O.

P. V. Larsen, M. P. Søensen, O. Bang, W. Z. Królikowski, and S. Trillo, "Nonlocal description of X waves in quadratic nonlinear materials," Phys. Rev. E 73, 036614 (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]

P. D. Rasmussen, O. Bang, and W. Królikowski, "Theory of nonlocal soliton interaction in nematic liquid crystals," 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 solitons," Opt. Lett. 29, 286-288 (2004).
[CrossRef] [PubMed]

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Królikowski, "Quadratic solitons as nonlocal solitons," Phys. Rev. E 68, 036614 (2003).
[CrossRef]

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

Brzdkiewicz, K. A.

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]

Cao, L. G.

D. Q. Lu, W. Hu, Y. J. Zheng, Y. B. Liang, L. G. Cao, S. Lan, and Q. Guo, "Self-induced fractional Fourier transform and revivable higher-order spatial solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 043815 (2008).
[CrossRef]

L. G. Cao, Y. Q. Zhu, D. Q. Lu, W. Hu, and Q. Guo, "Propagation of nonlocal optical solitons in lossy media with exponential-decay response," Opt. Commun. 281, 5004-5008 (2008).
[CrossRef]

Chi, S.

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

Christiansen, P. L.

Christodoulides, D. N.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, "Nonlocal surface-wave solitons," Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

M. Mitchell, M. Segev, and D. N. Christodoulides, "Observation of multihump multimode solitons," Phys. Rev. Lett. 80, 4657-4660 (1998).
[CrossRef]

Cohen, O.

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, "Two-dimensional multipole solitons in nonlocal nonlinear media," Opt. Lett. 31, 3312-3314 (2006).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, and M. Segev, "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, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, "Observation of a gradient catastrophe generating solitons," Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, "Shocks in nonlocal media," Phys. Rev. Lett. 99, 043903 (2007).
[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]

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.

Desyatnikov, A. S.

Y. V. Izdebskaya, A. S. Desyatnikov, G. Assanto, and Y. S. Kivshar, "Multimode nematicon waveguides," Opt. Lett. 36, 184-186 (2011).
[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]

Dong, L.

L. Dong, and F. Ye, "Stability of multipole-mode solitons in thermal nonlinear media," Phys. Rev. A 81, 013815 (2010).
[CrossRef]

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]

Fratalocchi, A.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, "Observation of a gradient catastrophe generating solitons," Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

Ghofraniha, N.

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, "Shocks in nonlocal media," Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef] [PubMed]

Guo, Q.

Q. Shou, Y. B. Liang, Q. Jiang, Y. J. Zheng, S. Lan, W. Hu, and Q. Guo, "Boundary force exerted on spatial solitons in cylindrical strongly nonlocal media," Opt. Lett. 34, 3523-3523 (2009).
[CrossRef] [PubMed]

D. Deng, and Q. Guo, "Propagation of Laguerre-Gaussian beams in nonlocal nonlinear media," J. Opt. A, Pure Appl. Opt. 10, 035101 (2008).
[CrossRef]

D. Q. Lu, W. Hu, Y. J. Zheng, Y. B. Liang, L. G. Cao, S. Lan, and Q. Guo, "Self-induced fractional Fourier transform and revivable higher-order spatial solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 043815 (2008).
[CrossRef]

L. G. Cao, Y. Q. Zhu, D. Q. Lu, W. Hu, and Q. Guo, "Propagation of nonlocal optical solitons in lossy media with exponential-decay response," Opt. Commun. 281, 5004-5008 (2008).
[CrossRef]

D. Deng, X. Zhao, Q. Guo, and S. Lan, "Hermite-Gaussian breathers and solitons in strongly nonlocal nonlinear media," J. Opt. Soc. Am. B 24, 2537-2544 (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, 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, X. Li, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 07111 (2006).
[CrossRef]

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

Hu, W.

D. Q. Lu, and W. Hu, "Multiringed breathers and rotating breathers in strongly nonlocal nonlinear media under the off-waist incident condition," Phys. Rev. A 79, 043833 (2009).
[CrossRef]

Q. Shou, Y. B. Liang, Q. Jiang, Y. J. Zheng, S. Lan, W. Hu, and Q. Guo, "Boundary force exerted on spatial solitons in cylindrical strongly nonlocal media," Opt. Lett. 34, 3523-3523 (2009).
[CrossRef] [PubMed]

D. Q. Lu, W. Hu, Y. J. Zheng, Y. B. Liang, L. G. Cao, S. Lan, and Q. Guo, "Self-induced fractional Fourier transform and revivable higher-order spatial solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 043815 (2008).
[CrossRef]

L. G. Cao, Y. Q. Zhu, D. Q. Lu, W. Hu, and Q. Guo, "Propagation of nonlocal optical solitons in lossy media with exponential-decay response," Opt. Commun. 281, 5004-5008 (2008).
[CrossRef]

W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 07111 (2006).
[CrossRef]

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

Izdebskaya, Y. V.

Jiang, Q.

Kartashov, Y. V.

Kivshar, Y. S.

Y. V. Izdebskaya, A. S. Desyatnikov, G. Assanto, and Y. S. Kivshar, "Multimode nematicon waveguides," Opt. Lett. 36, 184-186 (2011).
[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]

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]

S. Skupin, M. Saffman, and W. Krolikowski, "Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor," Phys. Rev. Lett. 98, 263902 (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]

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

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

Królikowski, W.

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

Królikowski, W. Z.

P. V. Larsen, M. P. Søensen, O. Bang, W. Z. Królikowski, and S. Trillo, "Nonlocal description of X waves in quadratic nonlinear materials," Phys. Rev. E 73, 036614 (2006).
[CrossRef]

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Królikowski, "Quadratic solitons as nonlocal solitons," Phys. Rev. E 68, 036614 (2003).
[CrossRef]

Lan, S.

Q. Shou, Y. B. Liang, Q. Jiang, Y. J. Zheng, S. Lan, W. Hu, and Q. Guo, "Boundary force exerted on spatial solitons in cylindrical strongly nonlocal media," Opt. Lett. 34, 3523-3523 (2009).
[CrossRef] [PubMed]

D. Q. Lu, W. Hu, Y. J. Zheng, Y. B. Liang, L. G. Cao, S. Lan, and Q. Guo, "Self-induced fractional Fourier transform and revivable higher-order spatial solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 043815 (2008).
[CrossRef]

D. Deng, X. Zhao, Q. Guo, and S. Lan, "Hermite-Gaussian breathers and solitons in strongly nonlocal nonlinear media," J. Opt. Soc. Am. B 24, 2537-2544 (2007).
[CrossRef]

W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 07111 (2006).
[CrossRef]

Larsen, P. V.

P. V. Larsen, M. P. Søensen, O. Bang, W. Z. Królikowski, and S. Trillo, "Nonlocal description of X waves in quadratic nonlinear materials," Phys. Rev. E 73, 036614 (2006).
[CrossRef]

Li, X.

W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 07111 (2006).
[CrossRef]

Liang, Y. B.

Q. Shou, Y. B. Liang, Q. Jiang, Y. J. Zheng, S. Lan, W. Hu, and Q. Guo, "Boundary force exerted on spatial solitons in cylindrical strongly nonlocal media," Opt. Lett. 34, 3523-3523 (2009).
[CrossRef] [PubMed]

D. Q. Lu, W. Hu, Y. J. Zheng, Y. B. Liang, L. G. Cao, S. Lan, and Q. Guo, "Self-induced fractional Fourier transform and revivable higher-order spatial solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 043815 (2008).
[CrossRef]

Lu, D. Q.

D. Q. Lu, and W. Hu, "Multiringed breathers and rotating breathers in strongly nonlocal nonlinear media under the off-waist incident condition," Phys. Rev. A 79, 043833 (2009).
[CrossRef]

D. Q. Lu, W. Hu, Y. J. Zheng, Y. B. Liang, L. G. Cao, S. Lan, and Q. Guo, "Self-induced fractional Fourier transform and revivable higher-order spatial solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 043815 (2008).
[CrossRef]

L. G. Cao, Y. Q. Zhu, D. Q. Lu, W. Hu, and Q. Guo, "Propagation of nonlocal optical solitons in lossy media with exponential-decay response," Opt. Commun. 281, 5004-5008 (2008).
[CrossRef]

Luo, B.

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

Malomed, B. A.

I. Tikhonenkov, B. A. Malomed, and A. Vardi, "Anisotropic solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 100, 090406 (2008).
[CrossRef] [PubMed]

Manela, O.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, "Nonlocal surface-wave solitons," Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, and M. Segev, "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, M.

M. Mitchell, M. Segev, and D. N. Christodoulides, "Observation of multihump multimode solitons," Phys. Rev. Lett. 80, 4657-4660 (1998).
[CrossRef]

Neshev, D.

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

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Królikowski, "Quadratic solitons as nonlocal solitons," Phys. Rev. E 68, 036614 (2003).
[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 solitons," Opt. Lett. 29, 286-288 (2004).
[CrossRef] [PubMed]

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Królikowski, "Quadratic solitons as nonlocal solitons," Phys. Rev. E 68, 036614 (2003).
[CrossRef]

Ouyang, S.

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, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, "Observation of a gradient catastrophe generating solitons," Phys. Rev. Lett. 102, 083902 (2009).
[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]

C. Conti, M. Peccianti, and G. Assanto, "Route to nonlocality and observation of accessible solitons," Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

M. Peccianti, K. A. Brzdkiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in nematic liquid crystals," Opt. Lett. 27, 1460-1462 (2002).
[CrossRef]

Pedri, P.

P. Pedri, and L. Santos, "Two-dimensional bright solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 95, 200404 (2005).
[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.

Rasmussen, P. D.

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

Rotschild, C.

B. Alfassi, C. Rotschild, and M. Segev, "Incoherent surface solitons in effectively instantaneous nonlocal nonlinear media," Phys. Rev. A 80, 041808 (2009).
[CrossRef]

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, "Nonlocal surface-wave solitons," Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, "Two-dimensional multipole solitons in nonlocal nonlinear media," Opt. Lett. 31, 3312-3314 (2006).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, and M. Segev, "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]

Ruocco, G.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, "Observation of a gradient catastrophe generating solitons," Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, "Shocks in nonlocal media," Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef] [PubMed]

Saffman, M.

S. Skupin, M. Saffman, and W. Krolikowski, "Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor," Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef] [PubMed]

Santos, L.

P. Pedri, and L. Santos, "Two-dimensional bright solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 95, 200404 (2005).
[CrossRef] [PubMed]

Segev, M.

B. Alfassi, C. Rotschild, and M. Segev, "Incoherent surface solitons in effectively instantaneous nonlocal nonlinear media," Phys. Rev. A 80, 041808 (2009).
[CrossRef]

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, "Nonlocal surface-wave solitons," Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, "Two-dimensional multipole solitons in nonlocal nonlinear media," Opt. Lett. 31, 3312-3314 (2006).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, and M. Segev, "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]

M. Mitchell, M. Segev, and D. N. Christodoulides, "Observation of multihump multimode solitons," Phys. Rev. Lett. 80, 4657-4660 (1998).
[CrossRef]

Shou, Q.

Skupin, S.

S. Skupin, M. Saffman, and W. Krolikowski, "Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor," Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef] [PubMed]

Søensen, M. P.

P. V. Larsen, M. P. Søensen, O. Bang, W. Z. Królikowski, and S. Trillo, "Nonlocal description of X waves in quadratic nonlinear materials," Phys. Rev. E 73, 036614 (2006).
[CrossRef]

Tikhonenkov, I.

I. Tikhonenkov, B. A. Malomed, and A. Vardi, "Anisotropic solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 100, 090406 (2008).
[CrossRef] [PubMed]

Torner, L.

Trillo, S.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, "Observation of a gradient catastrophe generating solitons," Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, "Shocks in nonlocal media," Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef] [PubMed]

P. V. Larsen, M. P. Søensen, O. Bang, W. Z. Królikowski, and S. Trillo, "Nonlocal description of X waves in quadratic nonlinear materials," Phys. Rev. E 73, 036614 (2006).
[CrossRef]

Vardi, A.

I. Tikhonenkov, B. A. Malomed, and A. Vardi, "Anisotropic solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 100, 090406 (2008).
[CrossRef] [PubMed]

Vysloukh, V. A.

Wyller, J.

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

Xie, Y. Q.

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

Xu, Z.

Ye, F.

L. Dong, and F. Ye, "Stability of multipole-mode solitons in thermal nonlinear media," Phys. Rev. A 81, 013815 (2010).
[CrossRef]

F. Ye, Y. V. Kartashov, and L. Torner, "Nonlocal surface dipoles and vortices," Phys. Rev. A 77, 033829 (2008).
[CrossRef]

Yi, F. H.

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

Zhang, T.

W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 07111 (2006).
[CrossRef]

Zhao, X.

Zheng, Y. J.

Q. Shou, Y. B. Liang, Q. Jiang, Y. J. Zheng, S. Lan, W. Hu, and Q. Guo, "Boundary force exerted on spatial solitons in cylindrical strongly nonlocal media," Opt. Lett. 34, 3523-3523 (2009).
[CrossRef] [PubMed]

D. Q. Lu, W. Hu, Y. J. Zheng, Y. B. Liang, L. G. Cao, S. Lan, and Q. Guo, "Self-induced fractional Fourier transform and revivable higher-order spatial solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 043815 (2008).
[CrossRef]

Zhu, Y. Q.

L. G. Cao, Y. Q. Zhu, D. Q. Lu, W. Hu, and Q. Guo, "Propagation of nonlocal optical solitons in lossy media with exponential-decay response," Opt. Commun. 281, 5004-5008 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

W. Hu, T. Zhang, Q. Guo, X. Li, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 07111 (2006).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

D. Deng, and Q. Guo, "Propagation of Laguerre-Gaussian beams in nonlocal nonlinear media," J. Opt. A, Pure Appl. Opt. 10, 035101 (2008).
[CrossRef]

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

Opt. Commun. (1)

L. G. Cao, Y. Q. Zhu, D. Q. Lu, W. Hu, and Q. Guo, "Propagation of nonlocal optical solitons in lossy media with exponential-decay response," Opt. Commun. 281, 5004-5008 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (9)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Optical surface waves supported and controlled by thermal waves," Opt. Lett. 33, 506-508 (2008).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Multipole surface solitons in thermal media," Opt. Lett. 34, 283-285 (2009).
[CrossRef] [PubMed]

Q. Shou, Y. B. Liang, Q. Jiang, Y. J. Zheng, S. Lan, W. Hu, and Q. Guo, "Boundary force exerted on spatial solitons in cylindrical strongly nonlocal media," Opt. Lett. 34, 3523-3523 (2009).
[CrossRef] [PubMed]

Y. V. Izdebskaya, A. S. Desyatnikov, G. Assanto, and Y. S. Kivshar, "Multimode nematicon waveguides," Opt. Lett. 36, 184-186 (2011).
[CrossRef] [PubMed]

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

M. Peccianti, K. A. Brzdkiewicz, and G. Assanto, "Nonlocal spatial soliton interactions in nematic liquid crystals," Opt. Lett. 27, 1460-1462 (2002).
[CrossRef]

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

Z. Xu, Y. V. Kartashov, and L. Torner, "Upper threshold for stability of multipole-mode solitons in nonlocal nonlinear media," Opt. Lett. 30, 3171-3173 (2005).
[CrossRef] [PubMed]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, "Two-dimensional multipole solitons in nonlocal nonlinear media," Opt. Lett. 31, 3312-3314 (2006).
[CrossRef] [PubMed]

Phys. Rev. A (6)

D. Q. Lu, W. Hu, Y. J. Zheng, Y. B. Liang, L. G. Cao, S. Lan, and Q. Guo, "Self-induced fractional Fourier transform and revivable higher-order spatial solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 043815 (2008).
[CrossRef]

D. Anderson, "Variational approach to nonlinear pulse propagation in optical fibers," Phys. Rev. A 27, 3135-3145 (1983).
[CrossRef]

D. Q. Lu, and W. Hu, "Multiringed breathers and rotating breathers in strongly nonlocal nonlinear media under the off-waist incident condition," Phys. Rev. A 79, 043833 (2009).
[CrossRef]

L. Dong, and F. Ye, "Stability of multipole-mode solitons in thermal nonlinear media," Phys. Rev. A 81, 013815 (2010).
[CrossRef]

F. Ye, Y. V. Kartashov, and L. Torner, "Nonlocal surface dipoles and vortices," Phys. Rev. A 77, 033829 (2008).
[CrossRef]

B. Alfassi, C. Rotschild, and M. Segev, "Incoherent surface solitons in effectively instantaneous nonlocal nonlinear media," Phys. Rev. A 80, 041808 (2009).
[CrossRef]

Phys. Rev. E (6)

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

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

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

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

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Królikowski, "Quadratic solitons as nonlocal solitons," Phys. Rev. E 68, 036614 (2003).
[CrossRef]

P. V. Larsen, M. P. Søensen, O. Bang, W. Z. Królikowski, and S. Trillo, "Nonlocal description of X waves in quadratic nonlinear materials," Phys. Rev. E 73, 036614 (2006).
[CrossRef]

Phys. Rev. Lett. (12)

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, "Nonlocal surface-wave solitons," Phys. Rev. Lett. 98, 213901 (2007).
[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, and M. Segev, "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]

S. Skupin, M. Saffman, and W. Krolikowski, "Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor," Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef] [PubMed]

P. Pedri, and L. Santos, "Two-dimensional bright solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 95, 200404 (2005).
[CrossRef] [PubMed]

I. Tikhonenkov, B. A. Malomed, and A. Vardi, "Anisotropic solitons in dipolar Bose-Einstein condensates," Phys. Rev. Lett. 100, 090406 (2008).
[CrossRef] [PubMed]

M. Mitchell, M. Segev, and D. N. Christodoulides, "Observation of multihump multimode solitons," Phys. Rev. Lett. 80, 4657-4660 (1998).
[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]

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]

N. Ghofraniha, C. Conti, G. Ruocco, and S. Trillo, "Shocks in nonlocal media," Phys. Rev. Lett. 99, 043903 (2007).
[CrossRef] [PubMed]

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, "Observation of a gradient catastrophe generating solitons," Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

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 (8)

Fig. 1
Fig. 1

Sketches of (a) a nonlocal surface soliton, and (b) a nonlocal antisymmetric bulk soliton. Red solid and green dashed lines represent the distributions of the amplitude and the nonlinear refraction index, respectively.

Fig. 2
Fig. 2

Comparison between the fundamental surface solitons and the first-order Hermite-Gaussian bulk solitons with the degree of nonlocality α = 10. (a) and (c) are simulated intensity distribution for surface solitons during propagation with w0 = 1.0 and 2.0, respectively; (b) and (d) are simulated intensity distribution for bulk solitons with w0 = 1.0 and 2.0, respectively. (e)–(h) are, respectively, the transverse intensity distributions (red solid line) and the refractive index distributions (green dashed line) corresponding to row 1.

Fig. 3
Fig. 3

Simulated propagation of surface solitons in the presence of 3% white noise at a fixed nonlocal degree α = 10. (a) and (b) give the propagation of surface solitons with different soliton widths w0 = 1.0 and 2.0, respectively. (c) and (d) give the incident intensity distribution (left) and the output intensity distribution at z = 2000 (right) corresponding to (a) and (b), respectively.

Fig. 4
Fig. 4

Variations of the surface soliton power with the soliton width under different conditions. (a) and (c) are the results with a fixed degree of nonlocality α = 30, 6, respectively. (b) and (d) are the results with a fixed width of the nonlocal response wm = 100, 10, respectively. Solid lines represent the analytical results based on Eq. (17); the triangles represent the numerical results.

Fig. 5
Fig. 5

Variations of the surface soliton power with the propagation constant for (a) wm = 30 and (b) wm = 10. Solid lines represent the analytical results based on Eqs. (17) and (18); the triangles represent the numerical results.

Fig. 6
Fig. 6

Comparison between the surface solitons and the bulk solitons for the weakly nonlocal case (α = 0.2). (a) and (d) are the simulated intensity distributions for the surface soliton and the bulk soliton during propagation with w0 = 1.0, wm = 0.5, respectively; (b) and (e) are the transverse intensity distributions (red solid line) and the refractive index distributions (green dashed line) corresponding to (a) and (d), respectively. (c) and (f) are the transverse amplitude distributions (blue dashed-dotted line) and the refractive index distributions (green dashed line) corresponding to (a) and (d), respectively.

Fig. 7
Fig. 7

Comparison between the surface breathers and the bulk breathers with α = 10. (a) and (c) are, respectively, the simulated propagations of the surface breather and the bulk breather with input power being twice soliton power. (b) and (d) give the analytical trajectories of the maximal intensity corresponding to (a) and (c), respectively. Row 2 is the same as row 1 except that the input power is a half of soliton power.

Fig. 8
Fig. 8

(a) Simulated propagations of a Gaussian surface wave launched 2.5w0 away from the surface. (b) Simulated propagations of two out-of-phase Gaussian solitons with a separated distance 5.0w0. (c) The trajectories of surface wave and two Gaussian solitons. (d) The oscillation period of surface wave. (e) Distribution of Δn′. The red solid line and the blue dashed-dotted line are the results based on Eqs. (28) and (29), respectively. The green dashed line and green triangles are the simulated results directly based on Eqs. (4)(6). All cases are with the parameters wm = 50.0, w0 = 1.0.

Equations (36)

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

2 i n 0 k 0 A Z + 2 A X 2 + 2 n 0 Δ N k 0 2 A = 0 ,
Δ N W m 2 2 Δ N X 2 n 2 | A | 2 = 0 ;
2 i n 0 k 0 A Z + 2 A X 2 ( n 0 2 n L 2 ) k 0 2 A = 0 ,
i q z + 1 2 2 q x 2 + Δ n q = 0 ,
Δ n w m 2 2 Δ n x 2 = | q | 2 ;
i q z + 1 2 2 q x 2 n d q = 0 .
q ( x ) = q ( 0 ) = 0 ,
Δ n x | x = 0 = 0 .
q ( 0 ) = q ( + 0 ) = 0 ,
q ( x ± ) = 0 ,
Δ n x | x = 0 = 0 .
q ( x , z ) = a ( z ) x exp [ x 2 w 2 ( z ) + i c ( z ) x 2 ] e i θ ( z ) ,
δ 0 + [ L ] d z = 0 ,
[ L ] = + L ( q , q * , q x , q * x , q z , q * z ) d x .
L = i 2 ( q * q z q q * z ) 1 2 | q x | 2 + 1 2 | q | 2 + R ( x x ) | q ( x ) | 2 d x ,
R ( x ) 1 2 w m ( 1 | x | w m + x 2 2 w m 2 ) .
[ L ] = 3 8 π 2 a 2 w ( 1 + c 2 w 4 ) 1 16 π 2 a 2 w 3 ( 3 w 2 d c d z + 4 d θ d z ) + a 4 w 6 512 w m 3 ( 4 π w m 2 7 π w m w + 3 π w 2 ) .
2 w d a d z + 3 a d w d z = 0 ,
2 w d a d z + a ( 5 d w d z 4 c w ) = 0 ,
a 2 w 5 w m 3 ( 4 π w m 2 7 π w m w + 3 π w 2 ) 48 2 π ( 1 + c 2 w 4 ) 8 2 π w 2 ( 3 w 2 d c d z + 4 d θ d z ) = 0 ,
480 2 w m 3 c 2 w 4 + a 2 w 5 ( 24 π w m 2 + 49 w m w 24 π w 2 ) + 48 2 w m 3 ( 4 w 2 d θ d z + 5 w 4 d c d z + 2 ) = 0 .
q ( x , z ) = a 0 x exp ( x 2 w 0 2 ) e i β z ,
P c = 48 π w m 3 w 0 3 ( 7 w m 6 π w 0 ) ,
β = 105 w m w 0 6 π ( 8 w m 2 + 9 w 0 2 ) 2 w 0 3 ( 6 π w 0 7 w m ) .
q ( x , z ) = { a 0 x exp ( x 2 w 0 2 ) e i β z for x 0 , 0 for x > 0 .
x s = 2 w 0 2 .
d 2 w d z 2 = 2 2 w 3 7 a 2 w 3 96 2 w m 2 + π a 2 w 4 16 w m 3 .
V ( w ) = 2 w 2 a 2 π w 5 80 w m 3 + 7 a 2 w 4 384 w m 2 + c 0 ,
w ( z ) = 2 2 [ g b + ( 2 w 0 g + b ) cos ( 12 ( g b ) 4 + 1 3 w 0 p z ) ] ,
g = 7 w m 12 2 π + t + 49 w m 2 288 π , b = g 2 2 t 2 t 2 + 3 w 0 p , t = ( h + p 3 + h 2 ) 1 3 + ( h p 3 + h 2 ) 1 3 , h = 49 w 0 w m 2 192 π , p = w 0 2 P c ( 6 π w 0 7 w m ) 18 π P 0 .
Δ z = 2 π [ 12 ( g b ) 4 6 π P s 0 w 0 3 P s ( 7 w m 6 π w 0 ) ] 1 2 ,
q ± ( x , z ) = ± a 0 exp [ [ x ± x c ( z ) ] 2 w 0 2 ± i u ( z ) x ] e i θ ( z ) ,
d 2 x c d z 2 = d ( Δ n ) d x | x = x c Δ n ,
Δ n = + R ( x x ) | q ( x , z ) | 2 d x .
d 2 x c d z 2 = π a 2 w 0 4 2 w m 2 exp ( w 0 2 16 w m x c 8 w m 2 ) × [ exp ( 4 x c w m ) erfc ( w 0 2 + 8 w m x c 2 2 w 0 w m ) + erf ( w 0 2 8 w m x c 2 2 w 0 w m ) 1 ] ,
d 2 x c d z 2 a 2 π w 0 2 2 w m 2 erf ( 4 x c 2 w 0 ) .

Metrics