Abstract

We study the mutual trapping of two dipole-mode light beams in a medium with a nonlocal anisotropic saturable nonlinearity. It is shown that the incoherent attraction of perpendicularly aligned dipole-mode beams leads to the stabilization of their composite structure. Our numerical analysis gives a stationary solution that is stable only with respect to small amplitude modulations. The coupled solitary structure disintegrates in a well-defined way when the numerical perturbations or the experimental propagation length exceeds a certain limit. In this case a new and more robust, multicomponent solitary transverse light structure consisting of two dipole-mode vector solitons will be generated.

© 2002 Optical Society of America

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  1. For an overview, see G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518–1523 (1999).
    [CrossRef] [PubMed]
  2. P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).
    [CrossRef]
  3. M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett. 80, 4657–4660 (1998).
    [CrossRef]
  4. Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljačic, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000).
    [CrossRef] [PubMed]
  5. Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Multicomponent two-dimensional solitons carrying topological charges,” Opt. Lett. 25, 61–63 (2000).
    [CrossRef]
  6. E. A. Ostrovskaya, Yu. S. Kivshar, D. V. Skryabin, and W. J. Firth, “Stability of multihump optical solitons,” Phys. Rev. Lett. 83, 296–299 (1999).
    [CrossRef]
  7. J. J. García-Ripoll, V. Pérez-García, E. A. Ostrovskaya, and Yu. S. Kivshar, “Dipole-mode vector solitons,” Phys. Rev. Lett. 85, 82–85 (2000).
    [CrossRef] [PubMed]
  8. W. Królikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
    [CrossRef] [PubMed]
  9. T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, and M. Segev, “Observation of two-dimensional multimode solitons,” Opt. Lett. 25, 1113–1115 (2000).
    [CrossRef]
  10. Z. H. Musslimani, M. Soljačic, M. Segev, and D. N. Christodoulides, “Delayed-action interaction and spin-orbit coupling between solitons,” Phys. Rev. Lett. 86, 799–802 (2001).
    [CrossRef] [PubMed]
  11. Z. H. Musslimani, M. Soljačic, M. Segev, and D. N. Christodoulides, “Interactions between two-dimensional composite vector solitons carrying topological charges,” Phys. Rev. E 63, 66608 (2001).
    [CrossRef]
  12. A. S. Desyatnikov, D. Neshev, E. A. Ostrovskaya, Yu. S. Kivshar, W. Królikowski, B. Luther-Davies, J. J. García-Ripoll, and V. Pérez-García, “Multipole spatial vector solitons,” Opt. Lett. 26, 435–437 (2001).
    [CrossRef]
  13. M. Soljačic, S. Sears, and M. Segev, “Self-trapping of ‘necklace’ beams in self-focusing Kerr media,” Phys. Rev. Lett. 81, 4851–4854 (1998).
    [CrossRef]
  14. A. S. Desyatnikov and Yu. S. Kivshar, “Necklace-ring vector solitons,” Phys. Rev. Lett. 87, 033901 (2001).
    [CrossRef] [PubMed]
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    [CrossRef]
  17. T. Taha and M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation,” J. Comput. Phys. 55, 203–230 (1994).
    [CrossRef]
  18. D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
    [CrossRef]
  19. A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
    [CrossRef] [PubMed]
  20. M. Saffman and A. A. Zozulya, “Circular solitons do not exist in photorefractive media,” Opt. Lett. 23, 1579–1581 (1998).
    [CrossRef]
  21. A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
    [CrossRef]

2001

Z. H. Musslimani, M. Soljačic, M. Segev, and D. N. Christodoulides, “Delayed-action interaction and spin-orbit coupling between solitons,” Phys. Rev. Lett. 86, 799–802 (2001).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Soljačic, M. Segev, and D. N. Christodoulides, “Interactions between two-dimensional composite vector solitons carrying topological charges,” Phys. Rev. E 63, 66608 (2001).
[CrossRef]

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

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

2000

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

W. Królikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, and M. Segev, “Observation of two-dimensional multimode solitons,” Opt. Lett. 25, 1113–1115 (2000).
[CrossRef]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljačic, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000).
[CrossRef] [PubMed]

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

1999

E. A. Ostrovskaya, Yu. S. Kivshar, D. V. Skryabin, and W. J. Firth, “Stability of multihump optical solitons,” Phys. Rev. Lett. 83, 296–299 (1999).
[CrossRef]

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

1998

M. Soljačic, S. Sears, and M. Segev, “Self-trapping of ‘necklace’ beams in self-focusing Kerr media,” Phys. Rev. Lett. 81, 4851–4854 (1998).
[CrossRef]

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

M. Saffman and A. A. Zozulya, “Circular solitons do not exist in photorefractive media,” Opt. Lett. 23, 1579–1581 (1998).
[CrossRef]

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

1997

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
[CrossRef]

1996

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

1995

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
[CrossRef] [PubMed]

1994

T. Taha and M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation,” J. Comput. Phys. 55, 203–230 (1994).
[CrossRef]

1965

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).
[CrossRef]

Ablowitz, M. J.

T. Taha and M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation,” J. Comput. Phys. 55, 203–230 (1994).
[CrossRef]

Anastassiou, C.

Anderson, D. Z.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
[CrossRef]

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
[CrossRef] [PubMed]

Carmon, T.

Carvalho, M. I.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

Christodoulides, D. N.

Z. H. Musslimani, M. Soljačic, M. Segev, and D. N. Christodoulides, “Delayed-action interaction and spin-orbit coupling between solitons,” Phys. Rev. Lett. 86, 799–802 (2001).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Soljačic, M. Segev, and D. N. Christodoulides, “Interactions between two-dimensional composite vector solitons carrying topological charges,” Phys. Rev. E 63, 66608 (2001).
[CrossRef]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljačic, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000).
[CrossRef] [PubMed]

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

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

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

Denz, C.

W. Królikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

Desyatnikov, A. S.

Firth, W. J.

E. A. Ostrovskaya, Yu. S. Kivshar, D. V. Skryabin, and W. J. Firth, “Stability of multihump optical solitons,” Phys. Rev. Lett. 83, 296–299 (1999).
[CrossRef]

García-Ripoll, J. J.

Geisser, M.

W. Królikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

Kelley, P. L.

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).
[CrossRef]

Kip, D.

Kivshar, Yu. S.

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

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

W. Królikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

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

E. A. Ostrovskaya, Yu. S. Kivshar, D. V. Skryabin, and W. J. Firth, “Stability of multihump optical solitons,” Phys. Rev. Lett. 83, 296–299 (1999).
[CrossRef]

Królikowski, W.

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

W. Królikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

Lan, S.

Luther-Davies, B.

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

W. Królikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

Mamaev, A. V.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
[CrossRef]

McCarthy, G.

W. Królikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

Mezentsev, V. K.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
[CrossRef]

Mitchell, M.

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

Musslimani, Z. H.

Z. H. Musslimani, M. Soljačic, M. Segev, and D. N. Christodoulides, “Delayed-action interaction and spin-orbit coupling between solitons,” Phys. Rev. Lett. 86, 799–802 (2001).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Soljačic, M. Segev, and D. N. Christodoulides, “Interactions between two-dimensional composite vector solitons carrying topological charges,” Phys. Rev. E 63, 66608 (2001).
[CrossRef]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, and M. Segev, “Observation of two-dimensional multimode solitons,” Opt. Lett. 25, 1113–1115 (2000).
[CrossRef]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljačic, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000).
[CrossRef] [PubMed]

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

Neshev, D.

Ostrovskaya, E. A.

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

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

W. Królikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

E. A. Ostrovskaya, Yu. S. Kivshar, D. V. Skryabin, and W. J. Firth, “Stability of multihump optical solitons,” Phys. Rev. Lett. 83, 296–299 (1999).
[CrossRef]

Pérez-García, V.

Saffman, M.

M. Saffman and A. A. Zozulya, “Circular solitons do not exist in photorefractive media,” Opt. Lett. 23, 1579–1581 (1998).
[CrossRef]

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
[CrossRef]

Sears, S.

M. Soljačic, S. Sears, and M. Segev, “Self-trapping of ‘necklace’ beams in self-focusing Kerr media,” Phys. Rev. Lett. 81, 4851–4854 (1998).
[CrossRef]

Segev, M.

Z. H. Musslimani, M. Soljačic, M. Segev, and D. N. Christodoulides, “Delayed-action interaction and spin-orbit coupling between solitons,” Phys. Rev. Lett. 86, 799–802 (2001).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Soljačic, M. Segev, and D. N. Christodoulides, “Interactions between two-dimensional composite vector solitons carrying topological charges,” Phys. Rev. E 63, 66608 (2001).
[CrossRef]

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

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljačic, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000).
[CrossRef] [PubMed]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, and M. Segev, “Observation of two-dimensional multimode solitons,” Opt. Lett. 25, 1113–1115 (2000).
[CrossRef]

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

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

M. Soljačic, S. Sears, and M. Segev, “Self-trapping of ‘necklace’ beams in self-focusing Kerr media,” Phys. Rev. Lett. 81, 4851–4854 (1998).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

Singh, S. R.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

Skryabin, D. V.

E. A. Ostrovskaya, Yu. S. Kivshar, D. V. Skryabin, and W. J. Firth, “Stability of multihump optical solitons,” Phys. Rev. Lett. 83, 296–299 (1999).
[CrossRef]

Soljacic, M.

Z. H. Musslimani, M. Soljačic, M. Segev, and D. N. Christodoulides, “Delayed-action interaction and spin-orbit coupling between solitons,” Phys. Rev. Lett. 86, 799–802 (2001).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Soljačic, M. Segev, and D. N. Christodoulides, “Interactions between two-dimensional composite vector solitons carrying topological charges,” Phys. Rev. E 63, 66608 (2001).
[CrossRef]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljačic, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000).
[CrossRef] [PubMed]

M. Soljačic, S. Sears, and M. Segev, “Self-trapping of ‘necklace’ beams in self-focusing Kerr media,” Phys. Rev. Lett. 81, 4851–4854 (1998).
[CrossRef]

Stegeman, G. I.

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

Taha, T.

T. Taha and M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation,” J. Comput. Phys. 55, 203–230 (1994).
[CrossRef]

Weilnau, C.

W. Królikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

Zozulya, A. A.

M. Saffman and A. A. Zozulya, “Circular solitons do not exist in photorefractive media,” Opt. Lett. 23, 1579–1581 (1998).
[CrossRef]

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
[CrossRef]

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
[CrossRef] [PubMed]

Appl. Phys. Lett.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

J. Comput. Phys.

T. Taha and M. J. Ablowitz, “Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation,” J. Comput. Phys. 55, 203–230 (1994).
[CrossRef]

Opt. Lett.

Phys. Rev. A

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, “Bound dipole solitary solutions in anisotropic nonlocal self-focusing media,” Phys. Rev. A 56, R1110–R1113 (1997).
[CrossRef]

A. A. Zozulya and D. Z. Anderson, “Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric field,” Phys. Rev. A 51, 1520–1531 (1995).
[CrossRef] [PubMed]

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

Phys. Rev. E

Z. H. Musslimani, M. Soljačic, M. Segev, and D. N. Christodoulides, “Interactions between two-dimensional composite vector solitons carrying topological charges,” Phys. Rev. E 63, 66608 (2001).
[CrossRef]

Phys. Rev. Lett.

M. Soljačic, S. Sears, and M. Segev, “Self-trapping of ‘necklace’ beams in self-focusing Kerr media,” Phys. Rev. Lett. 81, 4851–4854 (1998).
[CrossRef]

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

Z. H. Musslimani, M. Soljačic, M. Segev, and D. N. Christodoulides, “Delayed-action interaction and spin-orbit coupling between solitons,” Phys. Rev. Lett. 86, 799–802 (2001).
[CrossRef] [PubMed]

P. L. Kelley, “Self-focusing of optical beams,” Phys. Rev. Lett. 15, 1005–1008 (1965).
[CrossRef]

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

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljačic, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000).
[CrossRef] [PubMed]

E. A. Ostrovskaya, Yu. S. Kivshar, D. V. Skryabin, and W. J. Firth, “Stability of multihump optical solitons,” Phys. Rev. Lett. 83, 296–299 (1999).
[CrossRef]

J. J. García-Ripoll, V. Pérez-García, E. A. Ostrovskaya, and Yu. S. Kivshar, “Dipole-mode vector solitons,” Phys. Rev. Lett. 85, 82–85 (2000).
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W. Królikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

Science

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

Other

I. V. Petviashvili, “On the equation of a nonuniform soliton,” Fiz. Plazmy 2, 469–472 (1976) [ Sov. J. Plasma Phys. 2, 257–260 (1976)].

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Figures (5)

Fig. 1
Fig. 1

(a) Initial intensity distribution and (b) the numerical exact solution of two perpendicularly aligned dipole mode beams given by the Petviashvili routine. (c) The same components after they have propagated separately in the nonlinear medium (ξ=4.5).

Fig. 2
Fig. 2

Numerical simulation at several stages of propagation for simultaneous propagation of both components u and v. Top, |u|2+|v|2; middle, |u|2; bottom, |v|2. (a) ξ=0, (b) ξ=9.5, (c) ξ=16.

Fig. 3
Fig. 3

Experimental results: (a) input intensity distribution, (b) beam profiles after 13.5-mm separate propagation.

Fig. 4
Fig. 4

Experimental results: (a) input intensity distribution; (b), (c) beam evolution after 5- and 13.5-mm propagation, respectively. The three rows depict the total intensity |u|2+|v|2 and the single constituents |u|2 and |v|2.

Fig. 5
Fig. 5

The same sequence of frames as in Fig. 2 but with 10% initial perturbation for (a) ξ=2.5, (b) ξ=4.5, (c) ξ=10.

Equations (12)

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iUξ+122U=-γϕxU,
iVξ+122V=-γϕxV,
2ϕ+ϕ ln(1+I)=E0xln(1+I).
U(x, y, ξ)=u(x, y)exp(iβ1ξ),
V(x, y, ξ)=v(x, y)exp(iβ2ξ),
(β1-1/22)u(x, y)=γxϕ(x, y)u(x, y),
(β2-1/22)v(x, y)=γxϕ(x, y)v(x, y),
u(k)=Fˆ[γxϕu(x, y)](k)β1+k2/2,
v(k)=Fˆ[γxϕv(x, y)](k)β2+k2/2,
Mj= dkFˆ[γxϕsj(x, y)](k)sj*(k) dk(βj+k2/2)|sj(k)|2,
un+1(k)=|M1|-3/2un(k),
vn+1(k)=|M1|-3/2vn(k),

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