Abstract

In this paper, we discuss the evolution of the Gaussian-shaped soliton clusters in strongly nonlocal nonlinear media, which is modeled by the nonlinear Schrödinger equation. The influences of three initial incident parameters (the initial transverse velocity, the initial position, the input power) on propagation dynamics of the soliton clusters are all discussed in detail. The results show that the intensity distribution, the trajectory, the center distance, and the angular velocity of the clusters can be controlled by adjusting the initial incident parameters. A series of analytical solutions on the propagation dynamics of the clusters are derived by borrowing ideas from classical physics. The results in this paper may have potential applications in the beam controlling and all-optical interconnection with the interacting characteristics of (2+1)-dimensional soliton clusters.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Dynamics of rotating Laguerre-Gaussian soliton arrays

Limin Song, Zhenjun Yang, Shumin Zhang, and Xingliang Li
Opt. Express 27(19) 26331-26345 (2019)

Hermite-Gaussian breathers and solitons in strongly nonlocal nonlinear media

Dongmei Deng, Xin Zhao, Qi Guo, and Sheng Lan
J. Opt. Soc. Am. B 24(9) 2537-2544 (2007)

Ince-Gaussian solitons in strongly nonlocal nonlinear media

Dongmei Deng and Qi Guo
Opt. Lett. 32(21) 3206-3208 (2007)

References

  • View by:
  • |
  • |
  • |

  1. A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science,  2761538–1541 (1997).
    [Crossref]
  2. R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
    [Crossref]
  3. A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearité optique de kerr,” Opt. Commun. 55(3), 201–206 (1985).
    [Crossref]
  4. G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
    [Crossref] [PubMed]
  5. G. I. Stegeman and M. Segve, “Optical spatial solitons and their interactions: universality and diversity,” Science,  2861518–1523 (1999).
    [Crossref] [PubMed]
  6. A. S. Desyatnikov and Y. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88(5), 053901 (2002).
    [Crossref] [PubMed]
  7. C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nature Physics,  2 (10), 769–774 (2006).
    [Crossref]
  8. Z. Yang, X. Ma, D. Lu, Y. Zheng, X. Gao, and W. Hu, “Relation between surface solitons and bulk solitons in nonlocal nonlinear media,” Opt. Express 19, 4890–4901 (2011).
    [Crossref] [PubMed]
  9. R. Guo, Y. Liu, H. Hao, and F. Qi, “Coherently coupled solitons, breathers and rogue waves for polarized optical waves in an isotropic medium,” Nonlinear. Dyn. 80, 1221–1230 (2015).
    [Crossref]
  10. Z. Dai, Z. Yang, X. Ling, S. Zhang, Z. Pang, and J. Li, “Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality,” Ann. Phys. 366, 13–21 (2016).
    [Crossref]
  11. X. Zhao, R. Guo, and H. Hao, “N-fold Darboux transformation and discrete soliton solutions for the discrete Hirota equation,” Appl. Math. Lett. 75, 114–120 (2018).
    [Crossref]
  12. J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92(16), 163902 (2004).
    [Crossref] [PubMed]
  13. T. Mayteevarunyoo, B. A. Malomed, and A. Roeksabutr, “Solitons and vortices in nonlinear two-dimensional photonic crystals of the Kronig-Penney type,” Opt. Express 19(18), 17834–17851 (2011).
    [Crossref] [PubMed]
  14. F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, “Light bullets in Bessel optical lattices with spatially modulated nonlinearity,” Opt. Express 17(14), 11328–11334 (2009).
    [Crossref] [PubMed]
  15. S. Xu, J. Cheng, M. R. Belić, Z. Hu, and Y. Zhao, “Dynamics of nonlinear waves in two-dimensional cubic-quintic nonlinear Schrödinger equation with spatially modulated nonlinearities and potentials,” Opt. Express 24(9), 10066–10077 (2016).
    [Crossref] [PubMed]
  16. S. Ouyang, W. Hu, and Q. Guo, “Light steering in a strongly nonlocal nonlinear medium,” Phys. Rev. A 76, 053832 (2007).
    [Crossref]
  17. Y. Wang and Q. Guo, “Rotating soliton clusters in nonlocal nonlinear media,” Chin. Phys. B 17, 2527–2534 (2008).
    [Crossref]
  18. D. Lu and W. Hu, “Theory of multibeam interactions in strongly nonlocal nonlinear media,” Phys. Rev. A 80, 053818 (2009).
    [Crossref]
  19. L. Cao, Y. Zheng, W. Hu, P. Yang, and Q. Guo, “Long-range interactions between nematicons,” Chin. Phys. Lett. 26(6), 064209 (2009).
    [Crossref]
  20. Y. Zhu and W. Hu, “Related factors of interactions between nonlocal spatial solitons,” Acta Opt. Sin. 35, 0819001 (2015).
    [Crossref]
  21. S. Xu, G. Zhao, M. R. Belić, J. He, and L. Xue, “Light bullets in coupled nonlinear Schrödinger equations with variable coefficients and a trapping potential,” Opt. Express 25(8), 9094 (2017).
    [Crossref] [PubMed]
  22. W. Krolikowski, O. Bang, J. J. Rasmussenet, and J. Wyller, “Modulational instability in nonlocal nonlinear Kerr media,” Phys. Rev. E 64, 016612 (2001).
    [Crossref]
  23. 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]
  24. Z. J. Yang, S. M. Zhang, X. L. Li, and Z. G. Pang, “Variable sinh-Gaussian solitons in nonlocal nonlinear Schröinger equation,” Appl. Math. Lett. 82, 64–70 (2018).
    [Crossref]
  25. D. M. Deng and Q. Guo, “Ince-Gaussian solitons in strongly nonlocal nonlinear media,” Opt. Lett. 32, 3206 (2007).
    [Crossref] [PubMed]
  26. G. Liang, W. Cheng, Z. Dai, T. Jia, M. Wang, and H. Li, “Spiraling elliptic solitons in lossy nonlocal nonlinear media,” Opt. Express 25 (10), 11717–11724 (2017).
    [Crossref] [PubMed]
  27. Z. Yang, D. Lu, W. Hu, Y. Zheng, X. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).
    [Crossref]
  28. B. Ren, Q. Guo, S. Lan, and X. Yang, “The interaction of multi-spatial solitons in strongly nonlocal media,” Acta Opt. Sin. 27, 1668–1674 (2007) (in Chinese).
  29. Z. J. Yang, Z. F. Yang, J. X. Li, Z. P. Dai, S. M. Zhang, and X. L. Li, “Interaction between anomalous vortex beams in nonlocal media,” Results. Phys. 7, 1485–1486 (2017).
    [Crossref]
  30. Z. Dai, Z. Yang, X. Ling, S. Zhang, and Z. Pang, “Motion of soliton center of interactional solitons in nonlinear media with an exponential nonlocal response,” Opt. Commun. 367, 305–311 (2016).
    [Crossref]
  31. M. Shin, M. Segev, and G. Salamo, “Three-dimensional spiraling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551 (1997).
    [Crossref]
  32. G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express 23 (19), 24612–24625 (2015).
    [Crossref] [PubMed]
  33. X. Ma, Oleg A. Egorov, and Stefan Schumacher, “Creation and manipulation of stable dark solitons and vortices in microcavity polariton condensates,” Phys. Rev. Lett. 118, 157401 (2017).
    [Crossref] [PubMed]
  34. B. K. Esbensen, M. Bache, W. Krolikowski, and O. Bang, “Quadratic solitons for negative effective second-harmonic diffraction as nonlocal solitons with periodic nonlocal response function,” Phys. Rev. A 86, 023849 (2012).
    [Crossref]
  35. N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
    [Crossref]

2018 (2)

X. Zhao, R. Guo, and H. Hao, “N-fold Darboux transformation and discrete soliton solutions for the discrete Hirota equation,” Appl. Math. Lett. 75, 114–120 (2018).
[Crossref]

Z. J. Yang, S. M. Zhang, X. L. Li, and Z. G. Pang, “Variable sinh-Gaussian solitons in nonlocal nonlinear Schröinger equation,” Appl. Math. Lett. 82, 64–70 (2018).
[Crossref]

2017 (4)

S. Xu, G. Zhao, M. R. Belić, J. He, and L. Xue, “Light bullets in coupled nonlinear Schrödinger equations with variable coefficients and a trapping potential,” Opt. Express 25(8), 9094 (2017).
[Crossref] [PubMed]

G. Liang, W. Cheng, Z. Dai, T. Jia, M. Wang, and H. Li, “Spiraling elliptic solitons in lossy nonlocal nonlinear media,” Opt. Express 25 (10), 11717–11724 (2017).
[Crossref] [PubMed]

Z. J. Yang, Z. F. Yang, J. X. Li, Z. P. Dai, S. M. Zhang, and X. L. Li, “Interaction between anomalous vortex beams in nonlocal media,” Results. Phys. 7, 1485–1486 (2017).
[Crossref]

X. Ma, Oleg A. Egorov, and Stefan Schumacher, “Creation and manipulation of stable dark solitons and vortices in microcavity polariton condensates,” Phys. Rev. Lett. 118, 157401 (2017).
[Crossref] [PubMed]

2016 (3)

Z. Dai, Z. Yang, X. Ling, S. Zhang, and Z. Pang, “Motion of soliton center of interactional solitons in nonlinear media with an exponential nonlocal response,” Opt. Commun. 367, 305–311 (2016).
[Crossref]

Z. Dai, Z. Yang, X. Ling, S. Zhang, Z. Pang, and J. Li, “Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality,” Ann. Phys. 366, 13–21 (2016).
[Crossref]

S. Xu, J. Cheng, M. R. Belić, Z. Hu, and Y. Zhao, “Dynamics of nonlinear waves in two-dimensional cubic-quintic nonlinear Schrödinger equation with spatially modulated nonlinearities and potentials,” Opt. Express 24(9), 10066–10077 (2016).
[Crossref] [PubMed]

2015 (3)

R. Guo, Y. Liu, H. Hao, and F. Qi, “Coherently coupled solitons, breathers and rogue waves for polarized optical waves in an isotropic medium,” Nonlinear. Dyn. 80, 1221–1230 (2015).
[Crossref]

G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express 23 (19), 24612–24625 (2015).
[Crossref] [PubMed]

Y. Zhu and W. Hu, “Related factors of interactions between nonlocal spatial solitons,” Acta Opt. Sin. 35, 0819001 (2015).
[Crossref]

2012 (1)

B. K. Esbensen, M. Bache, W. Krolikowski, and O. Bang, “Quadratic solitons for negative effective second-harmonic diffraction as nonlocal solitons with periodic nonlocal response function,” Phys. Rev. A 86, 023849 (2012).
[Crossref]

2011 (2)

2010 (1)

Z. Yang, D. Lu, W. Hu, Y. Zheng, X. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).
[Crossref]

2009 (3)

D. Lu and W. Hu, “Theory of multibeam interactions in strongly nonlocal nonlinear media,” Phys. Rev. A 80, 053818 (2009).
[Crossref]

L. Cao, Y. Zheng, W. Hu, P. Yang, and Q. Guo, “Long-range interactions between nematicons,” Chin. Phys. Lett. 26(6), 064209 (2009).
[Crossref]

F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, “Light bullets in Bessel optical lattices with spatially modulated nonlinearity,” Opt. Express 17(14), 11328–11334 (2009).
[Crossref] [PubMed]

2008 (1)

Y. Wang and Q. Guo, “Rotating soliton clusters in nonlocal nonlinear media,” Chin. Phys. B 17, 2527–2534 (2008).
[Crossref]

2007 (3)

D. M. Deng and Q. Guo, “Ince-Gaussian solitons in strongly nonlocal nonlinear media,” Opt. Lett. 32, 3206 (2007).
[Crossref] [PubMed]

B. Ren, Q. Guo, S. Lan, and X. Yang, “The interaction of multi-spatial solitons in strongly nonlocal media,” Acta Opt. Sin. 27, 1668–1674 (2007) (in Chinese).

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

2006 (1)

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nature Physics,  2 (10), 769–774 (2006).
[Crossref]

2004 (2)

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92(16), 163902 (2004).
[Crossref] [PubMed]

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]

2003 (1)

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
[Crossref]

2002 (1)

A. S. Desyatnikov and Y. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88(5), 053901 (2002).
[Crossref] [PubMed]

2001 (1)

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

1999 (1)

G. I. Stegeman and M. Segve, “Optical spatial solitons and their interactions: universality and diversity,” Science,  2861518–1523 (1999).
[Crossref] [PubMed]

1997 (2)

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science,  2761538–1541 (1997).
[Crossref]

M. Shin, M. Segev, and G. Salamo, “Three-dimensional spiraling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551 (1997).
[Crossref]

1993 (1)

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[Crossref] [PubMed]

1985 (1)

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearité optique de kerr,” Opt. Commun. 55(3), 201–206 (1985).
[Crossref]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[Crossref]

Aitchison, J. S.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92(16), 163902 (2004).
[Crossref] [PubMed]

Alfassi, B.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nature Physics,  2 (10), 769–774 (2006).
[Crossref]

Bache, M.

B. K. Esbensen, M. Bache, W. Krolikowski, and O. Bang, “Quadratic solitons for negative effective second-harmonic diffraction as nonlocal solitons with periodic nonlocal response function,” Phys. Rev. A 86, 023849 (2012).
[Crossref]

Bang, O.

B. K. Esbensen, M. Bache, W. Krolikowski, and O. Bang, “Quadratic solitons for negative effective second-harmonic diffraction as nonlocal solitons with periodic nonlocal response function,” Phys. Rev. A 86, 023849 (2012).
[Crossref]

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
[Crossref]

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

Barthelemy, A.

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearité optique de kerr,” Opt. Commun. 55(3), 201–206 (1985).
[Crossref]

Belic, M. R.

Cao, H.

Cao, L.

L. Cao, Y. Zheng, W. Hu, P. Yang, and Q. Guo, “Long-range interactions between nematicons,” Chin. Phys. Lett. 26(6), 064209 (2009).
[Crossref]

Cheng, J.

Cheng, W.

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]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[Crossref]

Christodoulides, D. N.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92(16), 163902 (2004).
[Crossref] [PubMed]

Cohen, O.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nature Physics,  2 (10), 769–774 (2006).
[Crossref]

Crosignani, B.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[Crossref] [PubMed]

Dai, Z.

G. Liang, W. Cheng, Z. Dai, T. Jia, M. Wang, and H. Li, “Spiraling elliptic solitons in lossy nonlocal nonlinear media,” Opt. Express 25 (10), 11717–11724 (2017).
[Crossref] [PubMed]

Z. Dai, Z. Yang, X. Ling, S. Zhang, and Z. Pang, “Motion of soliton center of interactional solitons in nonlinear media with an exponential nonlocal response,” Opt. Commun. 367, 305–311 (2016).
[Crossref]

Z. Dai, Z. Yang, X. Ling, S. Zhang, Z. Pang, and J. Li, “Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality,” Ann. Phys. 366, 13–21 (2016).
[Crossref]

Dai, Z. P.

Z. J. Yang, Z. F. Yang, J. X. Li, Z. P. Dai, S. M. Zhang, and X. L. Li, “Interaction between anomalous vortex beams in nonlocal media,” Results. Phys. 7, 1485–1486 (2017).
[Crossref]

Deng, D. M.

Desyatnikov, A. S.

A. S. Desyatnikov and Y. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88(5), 053901 (2002).
[Crossref] [PubMed]

Duree, G. C.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[Crossref] [PubMed]

Egorov, Oleg A.

X. Ma, Oleg A. Egorov, and Stefan Schumacher, “Creation and manipulation of stable dark solitons and vortices in microcavity polariton condensates,” Phys. Rev. Lett. 118, 157401 (2017).
[Crossref] [PubMed]

Esbensen, B. K.

B. K. Esbensen, M. Bache, W. Krolikowski, and O. Bang, “Quadratic solitons for negative effective second-harmonic diffraction as nonlocal solitons with periodic nonlocal response function,” Phys. Rev. A 86, 023849 (2012).
[Crossref]

Froehly, C.

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearité optique de kerr,” Opt. Commun. 55(3), 201–206 (1985).
[Crossref]

Gao, X.

Z. Yang, X. Ma, D. Lu, Y. Zheng, X. Gao, and W. Hu, “Relation between surface solitons and bulk solitons in nonlocal nonlinear media,” Opt. Express 19, 4890–4901 (2011).
[Crossref] [PubMed]

Z. Yang, D. Lu, W. Hu, Y. Zheng, X. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).
[Crossref]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[Crossref]

Guo, Q.

G. Liang, Q. Guo, W. Cheng, N. Yin, P. Wu, and H. Cao, “Spiraling elliptic beam in nonlocal nonlinear media,” Opt. Express 23 (19), 24612–24625 (2015).
[Crossref] [PubMed]

Z. Yang, D. Lu, W. Hu, Y. Zheng, X. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).
[Crossref]

L. Cao, Y. Zheng, W. Hu, P. Yang, and Q. Guo, “Long-range interactions between nematicons,” Chin. Phys. Lett. 26(6), 064209 (2009).
[Crossref]

Y. Wang and Q. Guo, “Rotating soliton clusters in nonlocal nonlinear media,” Chin. Phys. B 17, 2527–2534 (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. M. Deng and Q. Guo, “Ince-Gaussian solitons in strongly nonlocal nonlinear media,” Opt. Lett. 32, 3206 (2007).
[Crossref] [PubMed]

B. Ren, Q. Guo, S. Lan, and X. Yang, “The interaction of multi-spatial solitons in strongly nonlocal media,” Acta Opt. Sin. 27, 1668–1674 (2007) (in Chinese).

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]

Guo, R.

X. Zhao, R. Guo, and H. Hao, “N-fold Darboux transformation and discrete soliton solutions for the discrete Hirota equation,” Appl. Math. Lett. 75, 114–120 (2018).
[Crossref]

R. Guo, Y. Liu, H. Hao, and F. Qi, “Coherently coupled solitons, breathers and rogue waves for polarized optical waves in an isotropic medium,” Nonlinear. Dyn. 80, 1221–1230 (2015).
[Crossref]

Hao, H.

X. Zhao, R. Guo, and H. Hao, “N-fold Darboux transformation and discrete soliton solutions for the discrete Hirota equation,” Appl. Math. Lett. 75, 114–120 (2018).
[Crossref]

R. Guo, Y. Liu, H. Hao, and F. Qi, “Coherently coupled solitons, breathers and rogue waves for polarized optical waves in an isotropic medium,” Nonlinear. Dyn. 80, 1221–1230 (2015).
[Crossref]

He, J.

Hu, B.

Hu, W.

Y. Zhu and W. Hu, “Related factors of interactions between nonlocal spatial solitons,” Acta Opt. Sin. 35, 0819001 (2015).
[Crossref]

Z. Yang, X. Ma, D. Lu, Y. Zheng, X. Gao, and W. Hu, “Relation between surface solitons and bulk solitons in nonlocal nonlinear media,” Opt. Express 19, 4890–4901 (2011).
[Crossref] [PubMed]

Z. Yang, D. Lu, W. Hu, Y. Zheng, X. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).
[Crossref]

L. Cao, Y. Zheng, W. Hu, P. Yang, and Q. Guo, “Long-range interactions between nematicons,” Chin. Phys. Lett. 26(6), 064209 (2009).
[Crossref]

D. Lu and W. Hu, “Theory of multibeam interactions in strongly nonlocal nonlinear media,” Phys. Rev. A 80, 053818 (2009).
[Crossref]

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

Hu, Z.

Jia, T.

Kartashov, Y. V.

Kivshar, Y. S.

A. S. Desyatnikov and Y. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88(5), 053901 (2002).
[Crossref] [PubMed]

Krolikowski, W.

B. K. Esbensen, M. Bache, W. Krolikowski, and O. Bang, “Quadratic solitons for negative effective second-harmonic diffraction as nonlocal solitons with periodic nonlocal response function,” Phys. Rev. A 86, 023849 (2012).
[Crossref]

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

Krolikowski, W. Z.

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
[Crossref]

Lan, S.

B. Ren, Q. Guo, S. Lan, and X. Yang, “The interaction of multi-spatial solitons in strongly nonlocal media,” Acta Opt. Sin. 27, 1668–1674 (2007) (in Chinese).

Li, H.

Li, J.

Z. Dai, Z. Yang, X. Ling, S. Zhang, Z. Pang, and J. Li, “Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality,” Ann. Phys. 366, 13–21 (2016).
[Crossref]

Li, J. X.

Z. J. Yang, Z. F. Yang, J. X. Li, Z. P. Dai, S. M. Zhang, and X. L. Li, “Interaction between anomalous vortex beams in nonlocal media,” Results. Phys. 7, 1485–1486 (2017).
[Crossref]

Li, X. L.

Z. J. Yang, S. M. Zhang, X. L. Li, and Z. G. Pang, “Variable sinh-Gaussian solitons in nonlocal nonlinear Schröinger equation,” Appl. Math. Lett. 82, 64–70 (2018).
[Crossref]

Z. J. Yang, Z. F. Yang, J. X. Li, Z. P. Dai, S. M. Zhang, and X. L. Li, “Interaction between anomalous vortex beams in nonlocal media,” Results. Phys. 7, 1485–1486 (2017).
[Crossref]

Liang, G.

Ling, X.

Z. Dai, Z. Yang, X. Ling, S. Zhang, and Z. Pang, “Motion of soliton center of interactional solitons in nonlinear media with an exponential nonlocal response,” Opt. Commun. 367, 305–311 (2016).
[Crossref]

Z. Dai, Z. Yang, X. Ling, S. Zhang, Z. Pang, and J. Li, “Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality,” Ann. Phys. 366, 13–21 (2016).
[Crossref]

Liu, Y.

R. Guo, Y. Liu, H. Hao, and F. Qi, “Coherently coupled solitons, breathers and rogue waves for polarized optical waves in an isotropic medium,” Nonlinear. Dyn. 80, 1221–1230 (2015).
[Crossref]

Lu, D.

Z. Yang, X. Ma, D. Lu, Y. Zheng, X. Gao, and W. Hu, “Relation between surface solitons and bulk solitons in nonlocal nonlinear media,” Opt. Express 19, 4890–4901 (2011).
[Crossref] [PubMed]

Z. Yang, D. Lu, W. Hu, Y. Zheng, X. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).
[Crossref]

D. Lu and W. Hu, “Theory of multibeam interactions in strongly nonlocal nonlinear media,” Phys. Rev. A 80, 053818 (2009).
[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]

Ma, X.

X. Ma, Oleg A. Egorov, and Stefan Schumacher, “Creation and manipulation of stable dark solitons and vortices in microcavity polariton condensates,” Phys. Rev. Lett. 118, 157401 (2017).
[Crossref] [PubMed]

Z. Yang, X. Ma, D. Lu, Y. Zheng, X. Gao, and W. Hu, “Relation between surface solitons and bulk solitons in nonlocal nonlinear media,” Opt. Express 19, 4890–4901 (2011).
[Crossref] [PubMed]

Malomed, B. A.

Maneuf, S.

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearité optique de kerr,” Opt. Commun. 55(3), 201–206 (1985).
[Crossref]

Mayteevarunyoo, T.

Meier, J.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92(16), 163902 (2004).
[Crossref] [PubMed]

Mitchell, D. J.

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science,  2761538–1541 (1997).
[Crossref]

Morandotti, R.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92(16), 163902 (2004).
[Crossref] [PubMed]

Neshev, D.

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
[Crossref]

Neurgaonkar, R. R.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[Crossref] [PubMed]

Nikolov, N. I.

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
[Crossref]

Ouyang, S.

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

Pang, Z.

Z. Dai, Z. Yang, X. Ling, S. Zhang, Z. Pang, and J. Li, “Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality,” Ann. Phys. 366, 13–21 (2016).
[Crossref]

Z. Dai, Z. Yang, X. Ling, S. Zhang, and Z. Pang, “Motion of soliton center of interactional solitons in nonlinear media with an exponential nonlocal response,” Opt. Commun. 367, 305–311 (2016).
[Crossref]

Pang, Z. G.

Z. J. Yang, S. M. Zhang, X. L. Li, and Z. G. Pang, “Variable sinh-Gaussian solitons in nonlocal nonlinear Schröinger equation,” Appl. Math. Lett. 82, 64–70 (2018).
[Crossref]

Porto, P. D.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[Crossref] [PubMed]

Qi, F.

R. Guo, Y. Liu, H. Hao, and F. Qi, “Coherently coupled solitons, breathers and rogue waves for polarized optical waves in an isotropic medium,” Nonlinear. Dyn. 80, 1221–1230 (2015).
[Crossref]

Rasmussenet, J. J.

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

Ren, B.

B. Ren, Q. Guo, S. Lan, and X. Yang, “The interaction of multi-spatial solitons in strongly nonlocal media,” Acta Opt. Sin. 27, 1668–1674 (2007) (in Chinese).

Roeksabutr, A.

Rotschild, C.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nature Physics,  2 (10), 769–774 (2006).
[Crossref]

Salamo, G.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92(16), 163902 (2004).
[Crossref] [PubMed]

M. Shin, M. Segev, and G. Salamo, “Three-dimensional spiraling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551 (1997).
[Crossref]

Salamo, G. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[Crossref] [PubMed]

Schumacher, Stefan

X. Ma, Oleg A. Egorov, and Stefan Schumacher, “Creation and manipulation of stable dark solitons and vortices in microcavity polariton condensates,” Phys. Rev. Lett. 118, 157401 (2017).
[Crossref] [PubMed]

Segev, M.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nature Physics,  2 (10), 769–774 (2006).
[Crossref]

M. Shin, M. Segev, and G. Salamo, “Three-dimensional spiraling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551 (1997).
[Crossref]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[Crossref] [PubMed]

Segve, M.

G. I. Stegeman and M. Segve, “Optical spatial solitons and their interactions: universality and diversity,” Science,  2861518–1523 (1999).
[Crossref] [PubMed]

Sharp, E. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[Crossref] [PubMed]

Shin, M.

M. Shin, M. Segev, and G. Salamo, “Three-dimensional spiraling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551 (1997).
[Crossref]

Shultz, J. L.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[Crossref] [PubMed]

Silberberg, Y.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92(16), 163902 (2004).
[Crossref] [PubMed]

Snyder, A. W.

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science,  2761538–1541 (1997).
[Crossref]

Sorel, M.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92(16), 163902 (2004).
[Crossref] [PubMed]

Stegeman, G. I.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92(16), 163902 (2004).
[Crossref] [PubMed]

G. I. Stegeman and M. Segve, “Optical spatial solitons and their interactions: universality and diversity,” Science,  2861518–1523 (1999).
[Crossref] [PubMed]

Torner, L.

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[Crossref]

Wang, M.

Wang, Y.

Y. Wang and Q. Guo, “Rotating soliton clusters in nonlocal nonlinear media,” Chin. Phys. B 17, 2527–2534 (2008).
[Crossref]

Wu, P.

Wyller, J.

W. Krolikowski, O. Bang, J. J. Rasmussenet, 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]

Xu, S.

Xue, L.

Yang, H.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92(16), 163902 (2004).
[Crossref] [PubMed]

Yang, P.

L. Cao, Y. Zheng, W. Hu, P. Yang, and Q. Guo, “Long-range interactions between nematicons,” Chin. Phys. Lett. 26(6), 064209 (2009).
[Crossref]

Yang, X.

B. Ren, Q. Guo, S. Lan, and X. Yang, “The interaction of multi-spatial solitons in strongly nonlocal media,” Acta Opt. Sin. 27, 1668–1674 (2007) (in Chinese).

Yang, Z.

Z. Dai, Z. Yang, X. Ling, S. Zhang, and Z. Pang, “Motion of soliton center of interactional solitons in nonlinear media with an exponential nonlocal response,” Opt. Commun. 367, 305–311 (2016).
[Crossref]

Z. Dai, Z. Yang, X. Ling, S. Zhang, Z. Pang, and J. Li, “Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality,” Ann. Phys. 366, 13–21 (2016).
[Crossref]

Z. Yang, X. Ma, D. Lu, Y. Zheng, X. Gao, and W. Hu, “Relation between surface solitons and bulk solitons in nonlocal nonlinear media,” Opt. Express 19, 4890–4901 (2011).
[Crossref] [PubMed]

Z. Yang, D. Lu, W. Hu, Y. Zheng, X. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).
[Crossref]

Yang, Z. F.

Z. J. Yang, Z. F. Yang, J. X. Li, Z. P. Dai, S. M. Zhang, and X. L. Li, “Interaction between anomalous vortex beams in nonlocal media,” Results. Phys. 7, 1485–1486 (2017).
[Crossref]

Yang, Z. J.

Z. J. Yang, S. M. Zhang, X. L. Li, and Z. G. Pang, “Variable sinh-Gaussian solitons in nonlocal nonlinear Schröinger equation,” Appl. Math. Lett. 82, 64–70 (2018).
[Crossref]

Z. J. Yang, Z. F. Yang, J. X. Li, Z. P. Dai, S. M. Zhang, and X. L. Li, “Interaction between anomalous vortex beams in nonlocal media,” Results. Phys. 7, 1485–1486 (2017).
[Crossref]

Yariv, A.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[Crossref] [PubMed]

Ye, F.

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]

Yin, N.

Zhang, S.

Z. Dai, Z. Yang, X. Ling, S. Zhang, and Z. Pang, “Motion of soliton center of interactional solitons in nonlinear media with an exponential nonlocal response,” Opt. Commun. 367, 305–311 (2016).
[Crossref]

Z. Dai, Z. Yang, X. Ling, S. Zhang, Z. Pang, and J. Li, “Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality,” Ann. Phys. 366, 13–21 (2016).
[Crossref]

Zhang, S. M.

Z. J. Yang, S. M. Zhang, X. L. Li, and Z. G. Pang, “Variable sinh-Gaussian solitons in nonlocal nonlinear Schröinger equation,” Appl. Math. Lett. 82, 64–70 (2018).
[Crossref]

Z. J. Yang, Z. F. Yang, J. X. Li, Z. P. Dai, S. M. Zhang, and X. L. Li, “Interaction between anomalous vortex beams in nonlocal media,” Results. Phys. 7, 1485–1486 (2017).
[Crossref]

Zhao, G.

Zhao, X.

X. Zhao, R. Guo, and H. Hao, “N-fold Darboux transformation and discrete soliton solutions for the discrete Hirota equation,” Appl. Math. Lett. 75, 114–120 (2018).
[Crossref]

Zhao, Y.

Zheng, Y.

Z. Yang, X. Ma, D. Lu, Y. Zheng, X. Gao, and W. Hu, “Relation between surface solitons and bulk solitons in nonlocal nonlinear media,” Opt. Express 19, 4890–4901 (2011).
[Crossref] [PubMed]

Z. Yang, D. Lu, W. Hu, Y. Zheng, X. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).
[Crossref]

L. Cao, Y. Zheng, W. Hu, P. Yang, and Q. Guo, “Long-range interactions between nematicons,” Chin. Phys. Lett. 26(6), 064209 (2009).
[Crossref]

Zhu, Y.

Y. Zhu and W. Hu, “Related factors of interactions between nonlocal spatial solitons,” Acta Opt. Sin. 35, 0819001 (2015).
[Crossref]

Acta Opt. Sin. (2)

Y. Zhu and W. Hu, “Related factors of interactions between nonlocal spatial solitons,” Acta Opt. Sin. 35, 0819001 (2015).
[Crossref]

B. Ren, Q. Guo, S. Lan, and X. Yang, “The interaction of multi-spatial solitons in strongly nonlocal media,” Acta Opt. Sin. 27, 1668–1674 (2007) (in Chinese).

Ann. Phys. (1)

Z. Dai, Z. Yang, X. Ling, S. Zhang, Z. Pang, and J. Li, “Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality,” Ann. Phys. 366, 13–21 (2016).
[Crossref]

Appl. Math. Lett. (2)

X. Zhao, R. Guo, and H. Hao, “N-fold Darboux transformation and discrete soliton solutions for the discrete Hirota equation,” Appl. Math. Lett. 75, 114–120 (2018).
[Crossref]

Z. J. Yang, S. M. Zhang, X. L. Li, and Z. G. Pang, “Variable sinh-Gaussian solitons in nonlocal nonlinear Schröinger equation,” Appl. Math. Lett. 82, 64–70 (2018).
[Crossref]

Chin. Phys. B (1)

Y. Wang and Q. Guo, “Rotating soliton clusters in nonlocal nonlinear media,” Chin. Phys. B 17, 2527–2534 (2008).
[Crossref]

Chin. Phys. Lett. (1)

L. Cao, Y. Zheng, W. Hu, P. Yang, and Q. Guo, “Long-range interactions between nematicons,” Chin. Phys. Lett. 26(6), 064209 (2009).
[Crossref]

Nature Physics (1)

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nature Physics,  2 (10), 769–774 (2006).
[Crossref]

Nonlinear. Dyn. (1)

R. Guo, Y. Liu, H. Hao, and F. Qi, “Coherently coupled solitons, breathers and rogue waves for polarized optical waves in an isotropic medium,” Nonlinear. Dyn. 80, 1221–1230 (2015).
[Crossref]

Opt. Commun. (2)

A. Barthelemy, S. Maneuf, and C. Froehly, “Propagation soliton et auto-confinement de faisceaux laser par non linearité optique de kerr,” Opt. Commun. 55(3), 201–206 (1985).
[Crossref]

Z. Dai, Z. Yang, X. Ling, S. Zhang, and Z. Pang, “Motion of soliton center of interactional solitons in nonlinear media with an exponential nonlocal response,” Opt. Commun. 367, 305–311 (2016).
[Crossref]

Opt. Express (7)

Opt. Lett. (1)

Phys. Lett. A (1)

Z. Yang, D. Lu, W. Hu, Y. Zheng, X. Gao, and Q. Guo, “Propagation of optical beams in strongly nonlocal nonlinear media,” Phys. Lett. A 374, 4007–4013 (2010).
[Crossref]

Phys. Rev. A (3)

D. Lu and W. Hu, “Theory of multibeam interactions in strongly nonlocal nonlinear media,” Phys. Rev. A 80, 053818 (2009).
[Crossref]

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

B. K. Esbensen, M. Bache, W. Krolikowski, and O. Bang, “Quadratic solitons for negative effective second-harmonic diffraction as nonlocal solitons with periodic nonlocal response function,” Phys. Rev. A 86, 023849 (2012).
[Crossref]

Phys. Rev. E (3)

N. I. Nikolov, D. Neshev, O. Bang, and W. Z. Krolikowski, “Quadratic solitons as nonlocal solitons,” Phys. Rev. E 68, 036614 (2003).
[Crossref]

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

Phys. Rev. Lett. (6)

A. S. Desyatnikov and Y. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88(5), 053901 (2002).
[Crossref] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. D. Porto, E. J. Sharp, and R. R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett. 71(4), 533–536 (1993).
[Crossref] [PubMed]

R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[Crossref]

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, “Experimental observation of discrete modulational instability,” Phys. Rev. Lett. 92(16), 163902 (2004).
[Crossref] [PubMed]

M. Shin, M. Segev, and G. Salamo, “Three-dimensional spiraling of interacting spatial solitons,” Phys. Rev. Lett. 78, 2551 (1997).
[Crossref]

X. Ma, Oleg A. Egorov, and Stefan Schumacher, “Creation and manipulation of stable dark solitons and vortices in microcavity polariton condensates,” Phys. Rev. Lett. 118, 157401 (2017).
[Crossref] [PubMed]

Results. Phys. (1)

Z. J. Yang, Z. F. Yang, J. X. Li, Z. P. Dai, S. M. Zhang, and X. L. Li, “Interaction between anomalous vortex beams in nonlocal media,” Results. Phys. 7, 1485–1486 (2017).
[Crossref]

Science (2)

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science,  2761538–1541 (1997).
[Crossref]

G. I. Stegeman and M. Segve, “Optical spatial solitons and their interactions: universality and diversity,” Science,  2861518–1523 (1999).
[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 (9)

Fig. 1
Fig. 1 Transverse intensity patterns of the Gaussian-shaped soliton clusters in SNN media at different propagation positions shown at the top. Each row is a period for different input powers, and (a): η = 2, (b): η = 1, (c): η = 1/2. Parameters: N = 6, ξ = 0, r = 6w0.
Fig. 2
Fig. 2 The same as Fig. 1 except that the velocity parameter ξ = 1/3.
Fig. 3
Fig. 3 The same as Fig. 1 except that the velocity parameter ξ = 1.
Fig. 4
Fig. 4 The same as Fig. 1 except that the velocity parameter ξ = 3/2.
Fig. 5
Fig. 5 (a) Locations of the interacting solitons at initial position. (b)–(e): The projection trajectories of each interacting soliton on xy plane, and (b): ξ = 0, (c): ξ = 1/3, (d): ξ = 1, (e): ξ = 3/2, respectively. The arrows indicate the direction of motion of the soliton beams. Parameters: N = 6, r = 6w0.
Fig. 6
Fig. 6 (a) The center distance of each constituent soliton varies with the propagation distance. (b) The centrifugal velocity, corresponding to the first row. (a1) and (b1): η = 2; (a2) and (b2): η = 1; (a3) and (b3): η = 1/2. Dashed-dot-dot line: ξ = 0, solid line: ξ = 1/3, dashed line: ξ = 1, dashed-dot line: ξ = 3/2. Parameters: N = 6, r = 6w0.
Fig. 7
Fig. 7 (a) The angular velocity of each constituent soliton varies with the propagation distance. (b) The angular acceleration, corresponding to the first row. (a1) and (b1): η = 2; (a2) and (b2): η = 1; (a3) and (b3): η = 1/2. Dashed-dot-dot line: ξ = 0, solid line: ξ = 1/3, dashed line: ξ = 1, dashed-dot line: ξ = 3/2. Parameters: N = 6, r = 6w0.
Fig. 8
Fig. 8 Variation relationship between the angular velocity and the center distance. Solid line: η = 2, dashed-dot line: η = 1, dashed line: η = 1/2. Three points from top to bottom represent, respectively, η = 2, η = 1 and η = 1/2. Parameters: N = 6, r = 6w0.
Fig. 9
Fig. 9 Transverse intensity patterns of Gaussian-shaped soliton clusters in SNN media at different propagation positions shown at the top. Parameters: (a): N = 6, ξ = 1/3, η = 1, r = 12w0; (b): N = 4, ξ = 1, η = 1, r = 4w0; (c): N = 8, ξ = 1/3, η = 1, r = 6w0.

Equations (47)

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

2 i k Φ z + Δ Φ + 2 k 2 Δ n n 0 Φ = 0 ,
Δ n = n 2 R ( | r r c | ) | Φ ( r c , z ) | 2 d 2 r c
R ( r ) = 1 2 π w R 2 exp ( r 2 2 w R 2 )
2 i k Φ z + Δ Φ k 2 γ 2 P 0 r 2 Φ + 2 k 2 n 2 R 0 P 0 n 0 Φ = 0 ,
Φ ( r , z ) = ψ ( r , z ) exp ( i k n 2 R 0 P 0 n 0 z ) ,
2 i k ψ z + ( 2 x 2 + 2 y 2 ) ψ k 2 γ 2 P 0 ( x 2 + y 2 ) ψ = 0 .
ψ ( x , y , z ) = P 0 π w ( z ) exp [ x 2 + y 2 2 w 2 ( z ) + i c ( z ) ( x 2 + y 2 ) + i θ ( z ) ] ,
w ( z ) = w 0 ( cos 2 α + sin 2 α / η ) 1 / 2 ,
c ( z ) = k β ( 1 η ) sin ( 2 α ) 4 ( η cos 2 α + sin 2 α ) ,
θ ( z ) = arctan ( tan α / η ) ,
ψ ± ( r , z ) = ψ ( r ± r 0 ( z ) , z ) exp [ i u ( z ) r + i ϕ ( z ) ]
r 0 ( z ) + β 2 r 0 ( z ) = 0 ,
u ( z ) = k r 0 ( z ) ,
ϕ ( z ) = k 2 [ β 2 r 0 2 ( z ) r 0 2 ( z ) ] .
r 0 ( z ) = r 0 ( 0 ) cos α + r 0 ( 0 ) β sin α .
ψ ( x , y , z ) = G 0 n = 1 N ψ n ( x , y , z ) ( n = 1 , 2 , , N ) ,
ψ n ( x , y , z ) = P 0 π w ( z ) exp [ ( x x 0 n ) 2 + ( y y 0 n ) 2 2 w 2 ( z ) + i θ ( z ) ] × exp { i c ( z ) [ ( x x 0 n ) 2 + ( y y 0 n ) 2 ] + i ( u x n x + u y n y ) + i ϕ n } ,
x 0 n ( z ) = c x n cos α + v x n β sin α ,
y 0 n ( z ) = c y n cos α + v y n β sin α ,
u x n ( z ) = c x n k β sin α + k v x n cos α ,
u y n ( z ) = c y n k β sin α + k v y n cos α ,
ϕ n ( z ) = k 4 [ β ( c x n 2 + c y n 2 ) v x n 2 + v y n 2 β ] sin ( 2 α ) k 2 [ c x n v y n + c y n v x n ] cos ( 2 α ) .
k n = k n x e x + k n y e y + k n z e z = k v x n e x + k v y n e y + k e z ,
c x n = r cos φ n , c y n = r sin φ n ,
v x n = ξ β r sin φ n , v y n = ξ β r cos φ n ,
ψ n ( x , y , 0 ) = P 0 π w 0 exp [ ( x r cos φ n ) 2 + ( y r sin φ n ) 2 2 w 0 2 ] × exp [ i k ξ β r ( sin φ n x cos φ n y ) ] ( n = 1 , 2 , , 6 ) .
ψ ( x , y , 0 ) = G 0 n = 1 6 ψ n ( x , y , 0 ) .
G 0 = { 6 exp [ ( k 2 ξ 2 β 2 ) / w 0 2 ] [ 1 + 2 exp ( 3 r 2 ( w 0 4 k 2 ξ 2 β 2 ) / 4 w 0 2 ) + 2 exp ( r 2 ( w 0 4 k 2 ξ 2 β 2 ) / 4 w 0 2 ) ] / w 0 4 } 1 / 2 .
ψ ( x , y , z ) = G 0 P 0 exp ( i α ) π w 0 × { exp [ [ x r ( cos α 3 ξ sin α ) / 2 ] 2 + [ y r ( 3 cos α ξ sin α ) / 2 ] 2 2 w 0 2 + i k β r 2 [ ( sin α 3 ξ cos α ) x + ( 3 sin α + ξ cos α ) y ] i k β r 2 ( ξ 2 1 ) 4 sin ( 2 α ) ] + exp [ [ x r ( cos α 3 ξ sin α ) / 2 ] 2 + [ y r ( 3 cos α + ξ sin α ) / 2 ] 2 2 w 0 2 + i k β r 2 [ ( sin α 3 ξ cos α ) x + ( 3 sin α ξ cos α ) y ] i k β r 2 ( ξ 2 1 ) 4 sin ( 2 α ) ] + exp [ ( x + r cos α ) 2 + ( y + ξ r sin α ) 2 2 w 0 2 + i k β r ( sin α x ξ cos α y ) i k β r 2 ( ξ 2 1 ) 4 sin ( 2 α ) ] + exp [ [ x r ( cos α + 3 ξ sin α ) / 2 ] 2 + [ y r ( 3 cos α ξ sin α ) / 2 ] 2 2 w 0 2 + i k β r 2 [ ( sin α + 3 ξ cos α ) x + ( 3 sin α ξ cos α ) y ] i k β r 2 ( ξ 2 1 ) 4 sin ( 2 α ) ] + exp [ [ x r ( cos α + 3 ξ sin α ) / 2 ] 2 + [ y r ( 3 cos α + ξ sin α ) / 2 ] 2 2 w 0 2 + i k β r 2 [ ( sin α + 3 ξ cos α ) x + ( 3 sin α + ξ cos α ) y ] i k β r 2 ( ξ 2 1 ) 4 sin ( 2 α ) ] + exp [ ( x r cos α ) 2 + ( y r sin α ) 2 2 w 0 2 i k β r ( sin α x ξ cos α y ) i k β r 2 ( ξ 2 1 ) 4 sin ( 2 α ) ] } .
z p = 1 β = 1 γ 2 P 0 .
M n = i 2 k ( ψ n ψ n * ψ n * ψ n ) d x d y ,
M n = ξ β r P 0 ( sin φ n e x + cos φ n e y ) .
M n / P 0 = v x n e x + v y n e y = ( k n x e x + k n y e y ) / k = [ u x n ( 0 ) e x + u y n ( 0 ) e y ] / k = u n ( 0 ) / k = r 0 n ( 0 ) ,
( v y n x v x n y ) 2 + β 2 ( c y n x c x n y ) 2 = ( c x n v y n v y n v x n ) 2 .
c y n x c x n y = 0 .
( ξ 2 cos 2 φ n + sin 2 φ n ) x 2 ( ξ 2 sin 2 φ n + cos 2 φ n ) y 2 + [ ( ξ 2 1 ) sin ( 2 φ n ) ] x y = ξ 2 r 2 ,
d n ( z ) = ( c x n cos α + v x n β sin α ) 2 + ( c y n cos α + v y n β sin α ) 2 .
d n ( z ) = r cos 2 α + ξ 2 sin 2 α .
Δ d n ( z ) = d n ( z ) z = ( ξ 2 1 ) β r ( sin 2 α ) 2 ξ 2 + 1 ( ξ 2 1 ) cos ( 2 α ) .
z p = z R / η ,
Ω n ( z ) = arctan ( β c y n cos α + v y n sin α β c x n cos α + v x n sin α ) .
ω n ( z ) = Ω n ( z ) z = β 2 ( c x n v y n c y n v x n ) ( β c x n cos α + v x n sin α ) 2 + ( β c y n cos α + v y n sin α ) 2 .
ω n ( z ) = ξ β cos 2 α + ξ 2 sin 2 α .
Δ ω n ( z ) = ω n ( z ) x = ξ β 2 ( 1 ξ 2 ) sin ( 2 α ) ( cos 2 α + ξ 2 sin 2 α ) 2 .
β = η / z R ,
ω n ( z ) = ξ β r 2 d n 2 ( z ) ( ξ 0 ) ,
r 2 w 0 ξ sin ( π / N ) .

Metrics