Abstract

We report the observation of multi-component dipole and vortex vector solitons composed of eight coexisting four-wave mixing (FWM) signals in two-level atomic system. The formation and stability of the multi-component dipole and vortex vector solitons are observed via changing the experiment parameters, including the frequency detuning, powers, and spatial configuration of the involved beams and the temperature of the medium. The transformation between modulated vortex solitons and rotating dipole solitons is observed at different frequency detunings. The interaction forces between different components of vector solitons are also investigated.

© 2012 OSA

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  1. S. Trillo and W. Torruella, Spatial Solitons (Springer-Verlag, Berlin, 2001).
  2. G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286(5444), 1518–1523 (1999).
    [CrossRef] [PubMed]
  3. V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
    [CrossRef] [PubMed]
  4. A. S. Desyatnikov, Y. S. Kivshar, K. Motzek, F. Kaiser, C. Weilnau, and C. Denz, “Multicomponent dipole-mode spatial solitons,” Opt. Lett. 27(8), 634–636 (2002).
    [CrossRef] [PubMed]
  5. K. Motzek, F. Kaiser, C. Weilnau, C. Denz, G. McCarthy, W. Krolikowski, A. Desyatnikov, and Y. S. Kivshar, “Multi-component vector solitons in photorefractive crystals,” Opt. Commun. 209(4-6), 501–506 (2002).
    [CrossRef]
  6. L. J. Ge, Q. Wang, M. Shen, and J. L. Shi, “Dipole solitons in nonlocal nonlinear media with anisotropy,” Opt. Commun. 284(9), 2351–2356 (2011).
    [CrossRef]
  7. M. Shen, X. Chen, J. L. Shi, Q. Wang, and W. Krolikowski, “Incoherently coupled vector dipole soliton pairs in nonlocal media,” Opt. Commun. 282(24), 4805–4809 (2009).
    [CrossRef]
  8. F. W. Ye, Y. V. Kartashov, and L. Torner, “Stabilization of dipole solitons in nonlocal nonlinear media,” Phys. Rev. A 77(4), 043821 (2008).
    [CrossRef]
  9. C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, “Long-range interactions between optical solitons,” Nature 2, 769–774 (2006).
  10. J. K. Yang, I. Makasyuk, A. Bezryadina, and Z. G. Chen, “Dipole solitons in optically induced two-dimensional photonic lattices,” Opt. Lett. 29(14), 1662–1664 (2004).
    [CrossRef] [PubMed]
  11. N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
    [CrossRef] [PubMed]
  12. Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
    [CrossRef] [PubMed]
  13. A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
    [CrossRef]
  14. A. S. Desyatnikov and Y. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88(5), 053901 (2002).
    [CrossRef] [PubMed]
  15. A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95(20), 203904 (2005).
    [CrossRef] [PubMed]
  16. A. Minovich, D. N. Neshev, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Observation of optical soliton azimuthons,” Opt. Express 17(26), 23610–23616 (2009).
    [CrossRef] [PubMed]
  17. W. J. Firth and D. V. Skryabin, “Optical solitons carrying Orbital angular momentum,” Phys. Rev. Lett. 79(13), 2450–2453 (1997).
    [CrossRef]
  18. J. K. Yang and D. E. Pelinovsky, “Stable vortex and dipole vector solitons in a saturable nonlinear medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(1), 016608 (2003).
    [CrossRef] [PubMed]
  19. A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87(3), 033901 (2001).
    [CrossRef] [PubMed]
  20. J. R. Salgueiro and Y. S. Kivshar, “Single- and double-vortex vector solitons in self-focusing nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(5), 056613 (2004).
    [CrossRef] [PubMed]
  21. A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. M. Pérez-García, “Multipole spatial vector solitons,” Opt. Lett. 26(7), 435–437 (2001).
    [CrossRef] [PubMed]
  22. C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92(4), 043904 (2004).
    [CrossRef] [PubMed]
  23. A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, “Stable counter-rotating vortex pairs in saturable media,” Phys. Lett. A 364(3-4), 231–234 (2007).
    [CrossRef]
  24. Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Multicomponent two-dimensional solitons carrying topological charges,” Opt. Lett. 25(1), 61–63 (2000).
    [CrossRef] [PubMed]
  25. C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85(23), 4888–4891 (2000).
    [CrossRef] [PubMed]
  26. Z. H. Musslimani, M. Soljacić, M. Segev, and D. N. Christodoulides, “Interactions between two-dimensional composite vector solitons carrying topological charges,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(6), 066608 (2001).
    [CrossRef] [PubMed]
  27. C. Pigier, R. Uzdin, T. Carmon, M. Segev, A. Nepomnyaschchy, and Z. H. Musslimani, “Collisions between (2+1)D rotating propeller solitons,” Opt. Lett. 26(20), 1577–1579 (2001).
    [CrossRef] [PubMed]
  28. Y. V. Izdebskaya, J. Rebling, A. S. Desyatnikov, and Y. S. Kivshar, “Observation of vector solitons with hidden vorticity,” Opt. Lett. 37(5), 767–769 (2012).
    [CrossRef] [PubMed]
  29. Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
    [CrossRef] [PubMed]
  30. H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
    [CrossRef] [PubMed]
  31. A. W. Snyder and A. P. Sheppard, “Collisions, steering, and guidance with spatial solitons,” Opt. Lett. 18(7), 482–484 (1993).
    [CrossRef] [PubMed]
  32. Y. P. Zhang, Z. Q. Nie, Y. Zhao, C. B. Li, R. M. Wang, J. H. Si, and M. Xiao, “Modulated vortex solitons of four-wave mixing,” Opt. Express 18(11), 10963–10972 (2010).
    [CrossRef] [PubMed]
  33. Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beamsplitter using four-wave mixing images,” Phys. Rev. A 80(5), 055804 (2009).
    [CrossRef]
  34. M. Marinescu and A. Dalgarno, “Dispersion forces and long-range electronic transition dipole moments of alkali-metal dimer excited states,” Phys. Rev. A 52(1), 311–328 (1995).
    [CrossRef] [PubMed]
  35. K. Singer, J. Stanojevic, M. Weidemüller, and R. Côté, “Long-range interactions between alkali Rydberg atoms pairs correlated to the ns-ns, np-np and nd-nd asymptotes,” J. Phys. At. Mol. Opt. Phys. 38(2), S295–S307 (2005).
    [CrossRef]
  36. S. Lopez-Aguayo, A. S. Desyatnikov, Y. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31(8), 1100–1102 (2006).
    [CrossRef]
  37. Y. V. Izdebskaya, A. S. Desyatnikov, G. Assanto, and Y. S. Kivshar, “Dipole azimuthons and vortex charge flipping in nematic liquid crystals,” Opt. Express 19(22), 21457–21466 (2011).
    [CrossRef] [PubMed]
  38. A. H. Carlsson, J. N. Malmberg, D. Anderson, M. Lisak, E. A. Ostrovskaya, T. J. Alexander, and Y. S. Kivshar, “Linear and nonlinear waveguides induced by optical vortex solitons,” Opt. Lett. 25(9), 660–662 (2000).
    [CrossRef] [PubMed]
  39. A. P. Sheppard and M. Haelterman, “Polarization-domain solitary waves of circular symmetry in Kerr media,” Opt. Lett. 19(12), 859–861 (1994).
    [CrossRef] [PubMed]
  40. C. T. Law, X. Zhang, and G. A. Swartzlander., “Waveguiding properties of optical vortex solitons,” Opt. Lett. 25(1), 55–57 (2000).
    [CrossRef] [PubMed]

2012 (1)

2011 (3)

Y. V. Izdebskaya, A. S. Desyatnikov, G. Assanto, and Y. S. Kivshar, “Dipole azimuthons and vortex charge flipping in nematic liquid crystals,” Opt. Express 19(22), 21457–21466 (2011).
[CrossRef] [PubMed]

L. J. Ge, Q. Wang, M. Shen, and J. L. Shi, “Dipole solitons in nonlocal nonlinear media with anisotropy,” Opt. Commun. 284(9), 2351–2356 (2011).
[CrossRef]

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[CrossRef] [PubMed]

2010 (2)

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[CrossRef] [PubMed]

Y. P. Zhang, Z. Q. Nie, Y. Zhao, C. B. Li, R. M. Wang, J. H. Si, and M. Xiao, “Modulated vortex solitons of four-wave mixing,” Opt. Express 18(11), 10963–10972 (2010).
[CrossRef] [PubMed]

2009 (3)

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beamsplitter using four-wave mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[CrossRef]

A. Minovich, D. N. Neshev, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Observation of optical soliton azimuthons,” Opt. Express 17(26), 23610–23616 (2009).
[CrossRef] [PubMed]

M. Shen, X. Chen, J. L. Shi, Q. Wang, and W. Krolikowski, “Incoherently coupled vector dipole soliton pairs in nonlocal media,” Opt. Commun. 282(24), 4805–4809 (2009).
[CrossRef]

2008 (1)

F. W. Ye, Y. V. Kartashov, and L. Torner, “Stabilization of dipole solitons in nonlocal nonlinear media,” Phys. Rev. A 77(4), 043821 (2008).
[CrossRef]

2007 (1)

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, “Stable counter-rotating vortex pairs in saturable media,” Phys. Lett. A 364(3-4), 231–234 (2007).
[CrossRef]

2006 (2)

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

S. Lopez-Aguayo, A. S. Desyatnikov, Y. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31(8), 1100–1102 (2006).
[CrossRef]

2005 (3)

K. Singer, J. Stanojevic, M. Weidemüller, and R. Côté, “Long-range interactions between alkali Rydberg atoms pairs correlated to the ns-ns, np-np and nd-nd asymptotes,” J. Phys. At. Mol. Opt. Phys. 38(2), S295–S307 (2005).
[CrossRef]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95(20), 203904 (2005).
[CrossRef] [PubMed]

2004 (3)

C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92(4), 043904 (2004).
[CrossRef] [PubMed]

J. R. Salgueiro and Y. S. Kivshar, “Single- and double-vortex vector solitons in self-focusing nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(5), 056613 (2004).
[CrossRef] [PubMed]

J. K. Yang, I. Makasyuk, A. Bezryadina, and Z. G. Chen, “Dipole solitons in optically induced two-dimensional photonic lattices,” Opt. Lett. 29(14), 1662–1664 (2004).
[CrossRef] [PubMed]

2003 (2)

J. K. Yang and D. E. Pelinovsky, “Stable vortex and dipole vector solitons in a saturable nonlinear medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(1), 016608 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

2002 (3)

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

K. Motzek, F. Kaiser, C. Weilnau, C. Denz, G. McCarthy, W. Krolikowski, A. Desyatnikov, and Y. S. Kivshar, “Multi-component vector solitons in photorefractive crystals,” Opt. Commun. 209(4-6), 501–506 (2002).
[CrossRef]

A. S. Desyatnikov, Y. S. Kivshar, K. Motzek, F. Kaiser, C. Weilnau, and C. Denz, “Multicomponent dipole-mode spatial solitons,” Opt. Lett. 27(8), 634–636 (2002).
[CrossRef] [PubMed]

2001 (5)

Z. H. Musslimani, M. Soljacić, M. Segev, and D. N. Christodoulides, “Interactions between two-dimensional composite vector solitons carrying topological charges,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(6), 066608 (2001).
[CrossRef] [PubMed]

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. M. Pérez-García, “Multipole spatial vector solitons,” Opt. Lett. 26(7), 435–437 (2001).
[CrossRef] [PubMed]

C. Pigier, R. Uzdin, T. Carmon, M. Segev, A. Nepomnyaschchy, and Z. H. Musslimani, “Collisions between (2+1)D rotating propeller solitons,” Opt. Lett. 26(20), 1577–1579 (2001).
[CrossRef] [PubMed]

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
[CrossRef] [PubMed]

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87(3), 033901 (2001).
[CrossRef] [PubMed]

2000 (4)

1999 (1)

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

1997 (1)

W. J. Firth and D. V. Skryabin, “Optical solitons carrying Orbital angular momentum,” Phys. Rev. Lett. 79(13), 2450–2453 (1997).
[CrossRef]

1996 (1)

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

1995 (1)

M. Marinescu and A. Dalgarno, “Dispersion forces and long-range electronic transition dipole moments of alkali-metal dimer excited states,” Phys. Rev. A 52(1), 311–328 (1995).
[CrossRef] [PubMed]

1994 (1)

1993 (1)

Alexander, T. J.

Alfassi, B.

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

Anastassiou, C.

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85(23), 4888–4891 (2000).
[CrossRef] [PubMed]

Anderson, D.

Assanto, G.

Bang, O.

Bezryadina, A.

Carlsson, A. H.

Carmon, T.

Chang, H.

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beamsplitter using four-wave mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[CrossRef]

Chen, H. X.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[CrossRef] [PubMed]

Chen, S.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[CrossRef] [PubMed]

Chen, X.

M. Shen, X. Chen, J. L. Shi, Q. Wang, and W. Krolikowski, “Incoherently coupled vector dipole soliton pairs in nonlocal media,” Opt. Commun. 282(24), 4805–4809 (2009).
[CrossRef]

Chen, Z. G.

Christodoulides, D. N.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Soljacić, M. Segev, and D. N. Christodoulides, “Interactions between two-dimensional composite vector solitons carrying topological charges,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(6), 066608 (2001).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85(23), 4888–4891 (2000).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Multicomponent two-dimensional solitons carrying topological charges,” Opt. Lett. 25(1), 61–63 (2000).
[CrossRef] [PubMed]

Christou, J.

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

Cohen, O.

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

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

Côté, R.

K. Singer, J. Stanojevic, M. Weidemüller, and R. Côté, “Long-range interactions between alkali Rydberg atoms pairs correlated to the ns-ns, np-np and nd-nd asymptotes,” J. Phys. At. Mol. Opt. Phys. 38(2), S295–S307 (2005).
[CrossRef]

Dalgarno, A.

M. Marinescu and A. Dalgarno, “Dispersion forces and long-range electronic transition dipole moments of alkali-metal dimer excited states,” Phys. Rev. A 52(1), 311–328 (1995).
[CrossRef] [PubMed]

Denz, C.

A. S. Desyatnikov, Y. S. Kivshar, K. Motzek, F. Kaiser, C. Weilnau, and C. Denz, “Multicomponent dipole-mode spatial solitons,” Opt. Lett. 27(8), 634–636 (2002).
[CrossRef] [PubMed]

K. Motzek, F. Kaiser, C. Weilnau, C. Denz, G. McCarthy, W. Krolikowski, A. Desyatnikov, and Y. S. Kivshar, “Multi-component vector solitons in photorefractive crystals,” Opt. Commun. 209(4-6), 501–506 (2002).
[CrossRef]

Desyatnikov, A.

K. Motzek, F. Kaiser, C. Weilnau, C. Denz, G. McCarthy, W. Krolikowski, A. Desyatnikov, and Y. S. Kivshar, “Multi-component vector solitons in photorefractive crystals,” Opt. Commun. 209(4-6), 501–506 (2002).
[CrossRef]

Desyatnikov, A. S.

Y. V. Izdebskaya, J. Rebling, A. S. Desyatnikov, and Y. S. Kivshar, “Observation of vector solitons with hidden vorticity,” Opt. Lett. 37(5), 767–769 (2012).
[CrossRef] [PubMed]

Y. V. Izdebskaya, A. S. Desyatnikov, G. Assanto, and Y. S. Kivshar, “Dipole azimuthons and vortex charge flipping in nematic liquid crystals,” Opt. Express 19(22), 21457–21466 (2011).
[CrossRef] [PubMed]

A. Minovich, D. N. Neshev, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Observation of optical soliton azimuthons,” Opt. Express 17(26), 23610–23616 (2009).
[CrossRef] [PubMed]

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, “Stable counter-rotating vortex pairs in saturable media,” Phys. Lett. A 364(3-4), 231–234 (2007).
[CrossRef]

S. Lopez-Aguayo, A. S. Desyatnikov, Y. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31(8), 1100–1102 (2006).
[CrossRef]

A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95(20), 203904 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

A. S. Desyatnikov, Y. S. Kivshar, K. Motzek, F. Kaiser, C. Weilnau, and C. Denz, “Multicomponent dipole-mode spatial solitons,” Opt. Lett. 27(8), 634–636 (2002).
[CrossRef] [PubMed]

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

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. M. Pérez-García, “Multipole spatial vector solitons,” Opt. Lett. 26(7), 435–437 (2001).
[CrossRef] [PubMed]

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87(3), 033901 (2001).
[CrossRef] [PubMed]

Durand, M.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[CrossRef] [PubMed]

Efremidis, N. K.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

Eugenieva, E. D.

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85(23), 4888–4891 (2000).
[CrossRef] [PubMed]

Firth, W. J.

W. J. Firth and D. V. Skryabin, “Optical solitons carrying Orbital angular momentum,” Phys. Rev. Lett. 79(13), 2450–2453 (1997).
[CrossRef]

Fleischer, J. W.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

Forestier, B.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[CrossRef] [PubMed]

García-Ripoll, J. J.

Ge, L. J.

L. J. Ge, Q. Wang, M. Shen, and J. L. Shi, “Dipole solitons in nonlocal nonlinear media with anisotropy,” Opt. Commun. 284(9), 2351–2356 (2011).
[CrossRef]

Goorskey, D.

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
[CrossRef] [PubMed]

Haelterman, M.

Houard, A.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[CrossRef] [PubMed]

Hudock, J.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

Izdebskaya, Y. V.

Jeng, C. C.

C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92(4), 043904 (2004).
[CrossRef] [PubMed]

Kaiser, F.

K. Motzek, F. Kaiser, C. Weilnau, C. Denz, G. McCarthy, W. Krolikowski, A. Desyatnikov, and Y. S. Kivshar, “Multi-component vector solitons in photorefractive crystals,” Opt. Commun. 209(4-6), 501–506 (2002).
[CrossRef]

A. S. Desyatnikov, Y. S. Kivshar, K. Motzek, F. Kaiser, C. Weilnau, and C. Denz, “Multicomponent dipole-mode spatial solitons,” Opt. Lett. 27(8), 634–636 (2002).
[CrossRef] [PubMed]

Kartashov, Y. V.

F. W. Ye, Y. V. Kartashov, and L. Torner, “Stabilization of dipole solitons in nonlocal nonlinear media,” Phys. Rev. A 77(4), 043821 (2008).
[CrossRef]

Kip, D.

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85(23), 4888–4891 (2000).
[CrossRef] [PubMed]

Kivshar, Y.

C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92(4), 043904 (2004).
[CrossRef] [PubMed]

Kivshar, Y. S.

Y. V. Izdebskaya, J. Rebling, A. S. Desyatnikov, and Y. S. Kivshar, “Observation of vector solitons with hidden vorticity,” Opt. Lett. 37(5), 767–769 (2012).
[CrossRef] [PubMed]

Y. V. Izdebskaya, A. S. Desyatnikov, G. Assanto, and Y. S. Kivshar, “Dipole azimuthons and vortex charge flipping in nematic liquid crystals,” Opt. Express 19(22), 21457–21466 (2011).
[CrossRef] [PubMed]

A. Minovich, D. N. Neshev, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, “Observation of optical soliton azimuthons,” Opt. Express 17(26), 23610–23616 (2009).
[CrossRef] [PubMed]

S. Lopez-Aguayo, A. S. Desyatnikov, Y. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31(8), 1100–1102 (2006).
[CrossRef]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95(20), 203904 (2005).
[CrossRef] [PubMed]

J. R. Salgueiro and Y. S. Kivshar, “Single- and double-vortex vector solitons in self-focusing nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(5), 056613 (2004).
[CrossRef] [PubMed]

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

A. S. Desyatnikov, Y. S. Kivshar, K. Motzek, F. Kaiser, C. Weilnau, and C. Denz, “Multicomponent dipole-mode spatial solitons,” Opt. Lett. 27(8), 634–636 (2002).
[CrossRef] [PubMed]

K. Motzek, F. Kaiser, C. Weilnau, C. Denz, G. McCarthy, W. Krolikowski, A. Desyatnikov, and Y. S. Kivshar, “Multi-component vector solitons in photorefractive crystals,” Opt. Commun. 209(4-6), 501–506 (2002).
[CrossRef]

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87(3), 033901 (2001).
[CrossRef] [PubMed]

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. M. Pérez-García, “Multipole spatial vector solitons,” Opt. Lett. 26(7), 435–437 (2001).
[CrossRef] [PubMed]

A. H. Carlsson, J. N. Malmberg, D. Anderson, M. Lisak, E. A. Ostrovskaya, T. J. Alexander, and Y. S. Kivshar, “Linear and nonlinear waveguides induced by optical vortex solitons,” Opt. Lett. 25(9), 660–662 (2000).
[CrossRef] [PubMed]

Krolikowski, W.

Law, C. T.

Lederer, F.

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, “Stable counter-rotating vortex pairs in saturable media,” Phys. Lett. A 364(3-4), 231–234 (2007).
[CrossRef]

Li, C. B.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[CrossRef] [PubMed]

Y. P. Zhang, Z. Q. Nie, Y. Zhao, C. B. Li, R. M. Wang, J. H. Si, and M. Xiao, “Modulated vortex solitons of four-wave mixing,” Opt. Express 18(11), 10963–10972 (2010).
[CrossRef] [PubMed]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beamsplitter using four-wave mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[CrossRef]

Lisak, M.

Liu, Y.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[CrossRef] [PubMed]

Lopez-Aguayo, S.

Lu, K. Q.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[CrossRef] [PubMed]

Luther-Davies, B.

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. M. Pérez-García, “Multipole spatial vector solitons,” Opt. Lett. 26(7), 435–437 (2001).
[CrossRef] [PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

Makasyuk, I.

Malmberg, J. N.

Malomed, B. A.

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, “Stable counter-rotating vortex pairs in saturable media,” Phys. Lett. A 364(3-4), 231–234 (2007).
[CrossRef]

Marinescu, M.

M. Marinescu and A. Dalgarno, “Dispersion forces and long-range electronic transition dipole moments of alkali-metal dimer excited states,” Phys. Rev. A 52(1), 311–328 (1995).
[CrossRef] [PubMed]

Mazilu, D.

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, “Stable counter-rotating vortex pairs in saturable media,” Phys. Lett. A 364(3-4), 231–234 (2007).
[CrossRef]

McCarthy, G.

K. Motzek, F. Kaiser, C. Weilnau, C. Denz, G. McCarthy, W. Krolikowski, A. Desyatnikov, and Y. S. Kivshar, “Multi-component vector solitons in photorefractive crystals,” Opt. Commun. 209(4-6), 501–506 (2002).
[CrossRef]

Mihalache, D.

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, “Stable counter-rotating vortex pairs in saturable media,” Phys. Lett. A 364(3-4), 231–234 (2007).
[CrossRef]

Minovich, A.

Motzek, K.

C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92(4), 043904 (2004).
[CrossRef] [PubMed]

K. Motzek, F. Kaiser, C. Weilnau, C. Denz, G. McCarthy, W. Krolikowski, A. Desyatnikov, and Y. S. Kivshar, “Multi-component vector solitons in photorefractive crystals,” Opt. Commun. 209(4-6), 501–506 (2002).
[CrossRef]

A. S. Desyatnikov, Y. S. Kivshar, K. Motzek, F. Kaiser, C. Weilnau, and C. Denz, “Multicomponent dipole-mode spatial solitons,” Opt. Lett. 27(8), 634–636 (2002).
[CrossRef] [PubMed]

Musslimani, Z. H.

Z. H. Musslimani, M. Soljacić, M. Segev, and D. N. Christodoulides, “Interactions between two-dimensional composite vector solitons carrying topological charges,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(6), 066608 (2001).
[CrossRef] [PubMed]

C. Pigier, R. Uzdin, T. Carmon, M. Segev, A. Nepomnyaschchy, and Z. H. Musslimani, “Collisions between (2+1)D rotating propeller solitons,” Opt. Lett. 26(20), 1577–1579 (2001).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Multicomponent two-dimensional solitons carrying topological charges,” Opt. Lett. 25(1), 61–63 (2000).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85(23), 4888–4891 (2000).
[CrossRef] [PubMed]

Mysyrowicz, A.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[CrossRef] [PubMed]

Nepomnyaschchy, A.

Neshev, D.

Neshev, D. N.

Nie, Z. Q.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[CrossRef] [PubMed]

Y. P. Zhang, Z. Q. Nie, Y. Zhao, C. B. Li, R. M. Wang, J. H. Si, and M. Xiao, “Modulated vortex solitons of four-wave mixing,” Opt. Express 18(11), 10963–10972 (2010).
[CrossRef] [PubMed]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beamsplitter using four-wave mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[CrossRef]

Ostrovskaya, E. A.

Pelinovsky, D. E.

J. K. Yang and D. E. Pelinovsky, “Stable vortex and dipole vector solitons in a saturable nonlinear medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(1), 016608 (2003).
[CrossRef] [PubMed]

Pérez-García, V. M.

Pigier, C.

Prade, B.

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[CrossRef] [PubMed]

Rebling, J.

Rotschild, C.

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

Salgueiro, J. R.

J. R. Salgueiro and Y. S. Kivshar, “Single- and double-vortex vector solitons in self-focusing nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(5), 056613 (2004).
[CrossRef] [PubMed]

Segev, M.

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

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Soljacić, M. Segev, and D. N. Christodoulides, “Interactions between two-dimensional composite vector solitons carrying topological charges,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(6), 066608 (2001).
[CrossRef] [PubMed]

C. Pigier, R. Uzdin, T. Carmon, M. Segev, A. Nepomnyaschchy, and Z. H. Musslimani, “Collisions between (2+1)D rotating propeller solitons,” Opt. Lett. 26(20), 1577–1579 (2001).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85(23), 4888–4891 (2000).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Multicomponent two-dimensional solitons carrying topological charges,” Opt. Lett. 25(1), 61–63 (2000).
[CrossRef] [PubMed]

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

Shen, M.

L. J. Ge, Q. Wang, M. Shen, and J. L. Shi, “Dipole solitons in nonlocal nonlinear media with anisotropy,” Opt. Commun. 284(9), 2351–2356 (2011).
[CrossRef]

M. Shen, X. Chen, J. L. Shi, Q. Wang, and W. Krolikowski, “Incoherently coupled vector dipole soliton pairs in nonlocal media,” Opt. Commun. 282(24), 4805–4809 (2009).
[CrossRef]

Sheppard, A. P.

Shi, J. L.

L. J. Ge, Q. Wang, M. Shen, and J. L. Shi, “Dipole solitons in nonlocal nonlinear media with anisotropy,” Opt. Commun. 284(9), 2351–2356 (2011).
[CrossRef]

M. Shen, X. Chen, J. L. Shi, Q. Wang, and W. Krolikowski, “Incoherently coupled vector dipole soliton pairs in nonlocal media,” Opt. Commun. 282(24), 4805–4809 (2009).
[CrossRef]

Shih, M. F.

C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92(4), 043904 (2004).
[CrossRef] [PubMed]

Si, J. H.

Singer, K.

K. Singer, J. Stanojevic, M. Weidemüller, and R. Côté, “Long-range interactions between alkali Rydberg atoms pairs correlated to the ns-ns, np-np and nd-nd asymptotes,” J. Phys. At. Mol. Opt. Phys. 38(2), S295–S307 (2005).
[CrossRef]

Skryabin, D. V.

W. J. Firth and D. V. Skryabin, “Optical solitons carrying Orbital angular momentum,” Phys. Rev. Lett. 79(13), 2450–2453 (1997).
[CrossRef]

Skupin, S.

Snyder, A. W.

Soljacic, M.

Z. H. Musslimani, M. Soljacić, M. Segev, and D. N. Christodoulides, “Interactions between two-dimensional composite vector solitons carrying topological charges,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(6), 066608 (2001).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85(23), 4888–4891 (2000).
[CrossRef] [PubMed]

Song, J. P.

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beamsplitter using four-wave mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[CrossRef]

Stanojevic, J.

K. Singer, J. Stanojevic, M. Weidemüller, and R. Côté, “Long-range interactions between alkali Rydberg atoms pairs correlated to the ns-ns, np-np and nd-nd asymptotes,” J. Phys. At. Mol. Opt. Phys. 38(2), S295–S307 (2005).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

Sukhorukov, A. A.

A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95(20), 203904 (2005).
[CrossRef] [PubMed]

Swartzlander, G. A.

Tikhonenko, V.

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

Torner, L.

F. W. Ye, Y. V. Kartashov, and L. Torner, “Stabilization of dipole solitons in nonlocal nonlinear media,” Phys. Rev. A 77(4), 043821 (2008).
[CrossRef]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

Torres, J. P.

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85(23), 4888–4891 (2000).
[CrossRef] [PubMed]

Uzdin, R.

Wang, H.

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
[CrossRef] [PubMed]

Wang, Q.

L. J. Ge, Q. Wang, M. Shen, and J. L. Shi, “Dipole solitons in nonlocal nonlinear media with anisotropy,” Opt. Commun. 284(9), 2351–2356 (2011).
[CrossRef]

M. Shen, X. Chen, J. L. Shi, Q. Wang, and W. Krolikowski, “Incoherently coupled vector dipole soliton pairs in nonlocal media,” Opt. Commun. 282(24), 4805–4809 (2009).
[CrossRef]

Wang, R. M.

Wang, Z. G.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[CrossRef] [PubMed]

Weidemüller, M.

K. Singer, J. Stanojevic, M. Weidemüller, and R. Côté, “Long-range interactions between alkali Rydberg atoms pairs correlated to the ns-ns, np-np and nd-nd asymptotes,” J. Phys. At. Mol. Opt. Phys. 38(2), S295–S307 (2005).
[CrossRef]

Weilnau, C.

K. Motzek, F. Kaiser, C. Weilnau, C. Denz, G. McCarthy, W. Krolikowski, A. Desyatnikov, and Y. S. Kivshar, “Multi-component vector solitons in photorefractive crystals,” Opt. Commun. 209(4-6), 501–506 (2002).
[CrossRef]

A. S. Desyatnikov, Y. S. Kivshar, K. Motzek, F. Kaiser, C. Weilnau, and C. Denz, “Multicomponent dipole-mode spatial solitons,” Opt. Lett. 27(8), 634–636 (2002).
[CrossRef] [PubMed]

Xiao, M.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[CrossRef] [PubMed]

Y. P. Zhang, Z. Q. Nie, Y. Zhao, C. B. Li, R. M. Wang, J. H. Si, and M. Xiao, “Modulated vortex solitons of four-wave mixing,” Opt. Express 18(11), 10963–10972 (2010).
[CrossRef] [PubMed]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beamsplitter using four-wave mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[CrossRef]

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
[CrossRef] [PubMed]

Yang, J. K.

J. K. Yang, I. Makasyuk, A. Bezryadina, and Z. G. Chen, “Dipole solitons in optically induced two-dimensional photonic lattices,” Opt. Lett. 29(14), 1662–1664 (2004).
[CrossRef] [PubMed]

J. K. Yang and D. E. Pelinovsky, “Stable vortex and dipole vector solitons in a saturable nonlinear medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(1), 016608 (2003).
[CrossRef] [PubMed]

Ye, F. W.

F. W. Ye, Y. V. Kartashov, and L. Torner, “Stabilization of dipole solitons in nonlocal nonlinear media,” Phys. Rev. A 77(4), 043821 (2008).
[CrossRef]

Zhang, X.

Zhang, Y. P.

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[CrossRef] [PubMed]

Y. P. Zhang, Z. Q. Nie, Y. Zhao, C. B. Li, R. M. Wang, J. H. Si, and M. Xiao, “Modulated vortex solitons of four-wave mixing,” Opt. Express 18(11), 10963–10972 (2010).
[CrossRef] [PubMed]

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beamsplitter using four-wave mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[CrossRef]

Zhao, Y.

Zheng, H. B.

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beamsplitter using four-wave mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[CrossRef]

Zuo, C. C.

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beamsplitter using four-wave mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[CrossRef]

J. Phys. At. Mol. Opt. Phys. (1)

K. Singer, J. Stanojevic, M. Weidemüller, and R. Côté, “Long-range interactions between alkali Rydberg atoms pairs correlated to the ns-ns, np-np and nd-nd asymptotes,” J. Phys. At. Mol. Opt. Phys. 38(2), S295–S307 (2005).
[CrossRef]

Nature (1)

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

Opt. Commun. (3)

K. Motzek, F. Kaiser, C. Weilnau, C. Denz, G. McCarthy, W. Krolikowski, A. Desyatnikov, and Y. S. Kivshar, “Multi-component vector solitons in photorefractive crystals,” Opt. Commun. 209(4-6), 501–506 (2002).
[CrossRef]

L. J. Ge, Q. Wang, M. Shen, and J. L. Shi, “Dipole solitons in nonlocal nonlinear media with anisotropy,” Opt. Commun. 284(9), 2351–2356 (2011).
[CrossRef]

M. Shen, X. Chen, J. L. Shi, Q. Wang, and W. Krolikowski, “Incoherently coupled vector dipole soliton pairs in nonlocal media,” Opt. Commun. 282(24), 4805–4809 (2009).
[CrossRef]

Opt. Express (3)

Opt. Lett. (11)

Y. V. Izdebskaya, J. Rebling, A. S. Desyatnikov, and Y. S. Kivshar, “Observation of vector solitons with hidden vorticity,” Opt. Lett. 37(5), 767–769 (2012).
[CrossRef] [PubMed]

C. T. Law, X. Zhang, and G. A. Swartzlander., “Waveguiding properties of optical vortex solitons,” Opt. Lett. 25(1), 55–57 (2000).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Multicomponent two-dimensional solitons carrying topological charges,” Opt. Lett. 25(1), 61–63 (2000).
[CrossRef] [PubMed]

A. H. Carlsson, J. N. Malmberg, D. Anderson, M. Lisak, E. A. Ostrovskaya, T. J. Alexander, and Y. S. Kivshar, “Linear and nonlinear waveguides induced by optical vortex solitons,” Opt. Lett. 25(9), 660–662 (2000).
[CrossRef] [PubMed]

A. W. Snyder and A. P. Sheppard, “Collisions, steering, and guidance with spatial solitons,” Opt. Lett. 18(7), 482–484 (1993).
[CrossRef] [PubMed]

A. P. Sheppard and M. Haelterman, “Polarization-domain solitary waves of circular symmetry in Kerr media,” Opt. Lett. 19(12), 859–861 (1994).
[CrossRef] [PubMed]

A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Y. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. M. Pérez-García, “Multipole spatial vector solitons,” Opt. Lett. 26(7), 435–437 (2001).
[CrossRef] [PubMed]

C. Pigier, R. Uzdin, T. Carmon, M. Segev, A. Nepomnyaschchy, and Z. H. Musslimani, “Collisions between (2+1)D rotating propeller solitons,” Opt. Lett. 26(20), 1577–1579 (2001).
[CrossRef] [PubMed]

A. S. Desyatnikov, Y. S. Kivshar, K. Motzek, F. Kaiser, C. Weilnau, and C. Denz, “Multicomponent dipole-mode spatial solitons,” Opt. Lett. 27(8), 634–636 (2002).
[CrossRef] [PubMed]

J. K. Yang, I. Makasyuk, A. Bezryadina, and Z. G. Chen, “Dipole solitons in optically induced two-dimensional photonic lattices,” Opt. Lett. 29(14), 1662–1664 (2004).
[CrossRef] [PubMed]

S. Lopez-Aguayo, A. S. Desyatnikov, Y. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31(8), 1100–1102 (2006).
[CrossRef]

Phys. Lett. A (1)

A. S. Desyatnikov, D. Mihalache, D. Mazilu, B. A. Malomed, and F. Lederer, “Stable counter-rotating vortex pairs in saturable media,” Phys. Lett. A 364(3-4), 231–234 (2007).
[CrossRef]

Phys. Rev. A (3)

Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, “Controlled spatial beamsplitter using four-wave mixing images,” Phys. Rev. A 80(5), 055804 (2009).
[CrossRef]

M. Marinescu and A. Dalgarno, “Dispersion forces and long-range electronic transition dipole moments of alkali-metal dimer excited states,” Phys. Rev. A 52(1), 311–328 (1995).
[CrossRef] [PubMed]

F. W. Ye, Y. V. Kartashov, and L. Torner, “Stabilization of dipole solitons in nonlocal nonlinear media,” Phys. Rev. A 77(4), 043821 (2008).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (3)

J. K. Yang and D. E. Pelinovsky, “Stable vortex and dipole vector solitons in a saturable nonlinear medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(1), 016608 (2003).
[CrossRef] [PubMed]

J. R. Salgueiro and Y. S. Kivshar, “Single- and double-vortex vector solitons in self-focusing nonlinear media,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(5), 056613 (2004).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Soljacić, M. Segev, and D. N. Christodoulides, “Interactions between two-dimensional composite vector solitons carrying topological charges,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 63(6), 066608 (2001).
[CrossRef] [PubMed]

Phys. Rev. Lett. (11)

Y. Liu, M. Durand, S. Chen, A. Houard, B. Prade, B. Forestier, and A. Mysyrowicz, “Energy exchange between femtosecond laser filaments in air,” Phys. Rev. Lett. 105(5), 055003 (2010).
[CrossRef] [PubMed]

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
[CrossRef] [PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76(15), 2698–2701 (1996).
[CrossRef] [PubMed]

C. C. Jeng, M. F. Shih, K. Motzek, and Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92(4), 043904 (2004).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljačić, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J. P. Torres, “Eliminating the transverse instabilities of Kerr solitons,” Phys. Rev. Lett. 85(23), 4888–4891 (2000).
[CrossRef] [PubMed]

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87(3), 033901 (2001).
[CrossRef] [PubMed]

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

A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, “Azimuthons: spatially modulated vortex solitons,” Phys. Rev. Lett. 95(20), 203904 (2005).
[CrossRef] [PubMed]

W. J. Firth and D. V. Skryabin, “Optical solitons carrying Orbital angular momentum,” Phys. Rev. Lett. 79(13), 2450–2453 (1997).
[CrossRef]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91(21), 213906 (2003).
[CrossRef] [PubMed]

Y. P. Zhang, Z. G. Wang, Z. Q. Nie, C. B. Li, H. X. Chen, K. Q. Lu, and M. Xiao, “Four-wave mixing dipole soliton in laser-induced atomic gratings,” Phys. Rev. Lett. 106(9), 093904 (2011).
[CrossRef] [PubMed]

Prog. Opt. (1)

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical vortices and vortex solitons,” Prog. Opt. 47, 291–391 (2005).
[CrossRef]

Science (1)

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286(5444), 1518–1523 (1999).
[CrossRef] [PubMed]

Other (1)

S. Trillo and W. Torruella, Spatial Solitons (Springer-Verlag, Berlin, 2001).

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Figures (6)

Fig. 1
Fig. 1

(a) Two-level system with six laser beams tuned to the same transition. (b) Spatial beam geometry used in the experiment. (c) and (d) The horizontally- and vertically-aligned EIG1 and EIG2, respectively.

Fig. 2
Fig. 2

(a) Images (left) and horizontal-sizes (right) of FWM signals E F1,2,5,6 at different detuning Δ 2 , E F1 (squares), E F2 (circles), E F5 (triangles) and E F6 (reverse triangles). (b) Images (left) and vertical-sizes (right) of FWM signals E F3,4,7,8 at different detuning Δ 2 , E F3 (squares), E F4 (circles), E F7 (triangles) and E F8 (reverse triangles).

Fig. 3
Fig. 3

(a1,2) Images of E F7 at different powers of (a1) E 1 , (a2) E 2 . (a3) Images of E F1 for different spatial configuration of E 1 and E 1 . From left to right, the intersection position of E 1 and E 1 is adjusted to change from the front to the back of the heat-pipe oven. (b) Beam vertical-size of E F7 versus P 1 (Squares) and P 2 (circles). (c) Beam vertical-size (triangles) and horizontal-size (asterisks) of E F1 versus the intersection position of E 1 and E 1 . Here the distance between the intersection position and the oven centre is denoted as l. (d) Nonlinear refractive index n 2 of E F4 . (e) Images of the pure FWM signal E F4 and coexisting signals E F4 + E F3 , E F4 + E F8 , E F1 + E F2 and E F1 + E F5 , respectively.

Fig. 4
Fig. 4

(a) Images of the four-component dipole-mode soliton i E Fi and j E Fj at different Δ 2 with and without dressing field E 2 and E 1 , respectively. (b) Experimental (left) and numerical (right) results of ten-component dipole-mode soliton with the propagation length Z=0, 15.9mm at Δ 2 =15GHZ

Fig. 5
Fig. 5

Images (the five top rows) of the pure FWM signals E F1,2,5,6 and E 2 dressed signal E F6 versus Δ 1 . The two bottom rows give the numerical results of E F6 with and without dressed field E 2 , respectively

Fig. 6
Fig. 6

Images of the superposition vortex signals at different Δ 1 . (a) Two-component vortex solitons E F1 + E F5 and E F1 + E F2 , respectively. The two bottom rows give the numerical results of E F1 + E F2 and E 2 dressed E F1 + E F2 . (b) Four-component vortex solitons i E Fi and j E Fj .

Equations (4)

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p=1,2,5,6 E Fp z i 2 E Fp 2 k Fp = p=1,2,5,6 i k Fp n 1 ( n 2 Sp | E Fp | 2 +2 n 2 Fp ) E Fp + η 1 E 1 ( E 1 ) * q=3,4,7,8 E Fq
q=3,4,7,8 E Fq z i 2 E Fq 2 k Fq = q=3,4,7,8 i k Fq n 1 ( n 2 Sq | E Fq | 2 +2 n 2 Fq ) E Fq + η 2 E 2 ( E 2 ) * p=1,2,5,6 E Fp
p=1,2,5,6 E Fp z i 2 k Fp ( 1 r E Fp r + 2 E Fp r 2 + 1 r 2 2 E Fp φ 2 )= p=1,2,5,6 i k Fp n 1 ( n 2 Sp | E Fp | 2 +2 n 2 Fp ) E Fp
q=3,4,7,8 E Fq z i 2 k Fq ( 1 r E Fq r + 2 E Fq r 2 + 1 r 2 2 E Fq φ 2 )= q=3,4,7,8 i k Fq n 1 ( n 2 Sq | E Fq | 2 +2 n 2 Fq ) E Fq

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