Abstract

We report experimental observation of bound states formed by two well-separated vector spatial solitons as the result of a force balance between vector-soliton components. We also demonstrate a link between such soliton bound states and two-hump, two-mode solitons, along with the induced coherence effect observed for incoherently interacting solitons.

© 2000 Optical Society of America

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  1. See, e.g., S. Lan, E. DelRe, Z. Chen, M. Shih, and M. Segev, Opt. Lett. 24, 475 (1999).
    [CrossRef]
  2. M. Segev and G. Stegeman, Phys. Today 51(8), 42 (1998); Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
    [CrossRef]
  3. D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
    [CrossRef]
  4. Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulies, Opt. Lett. 21, 1436 (1996); J. Opt. Soc. Am. B 14, 3066 (1997).
    [CrossRef] [PubMed]
  5. A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
    [CrossRef] [PubMed]
  6. M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
    [CrossRef]
  7. J. P. Gordon, Opt. Lett. 8, 596 (1983).
    [CrossRef] [PubMed]
  8. D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1985).
    [CrossRef] [PubMed]
  9. E. A. Ostrovskaya, Yu. S. Kivshar, Z. Chen, and M. Segev, Opt. Lett. 24, 327 (1999).
    [CrossRef]
  10. C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
    [CrossRef]
  11. M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996); M. Mitchell and M. Segev, Nature 387, 880 (1997); Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
    [CrossRef] [PubMed]
  12. M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Lett. 18, 1406 (1993).
    [CrossRef] [PubMed]
  13. E. A. Ostrovskaya, Yu. S. Kivshar, D. K. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999); J. Opt. B 1, 77 (1999).
    [CrossRef]
  14. P. Kockaert and M. Haelterman, J. Opt. Soc. Am. B 16, 732 (1999).
    [CrossRef]
  15. M. Haelterman and A. P. Sheppard, Phys. Rev. E 49, 3376 (1994).
    [CrossRef]
  16. A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
    [CrossRef]

1999 (6)

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

E. A. Ostrovskaya, Yu. S. Kivshar, D. K. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999); J. Opt. B 1, 77 (1999).
[CrossRef]

P. Kockaert and M. Haelterman, J. Opt. Soc. Am. B 16, 732 (1999).
[CrossRef]

E. A. Ostrovskaya, Yu. S. Kivshar, Z. Chen, and M. Segev, Opt. Lett. 24, 327 (1999).
[CrossRef]

See, e.g., S. Lan, E. DelRe, Z. Chen, M. Shih, and M. Segev, Opt. Lett. 24, 475 (1999).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

1998 (2)

M. Segev and G. Stegeman, Phys. Today 51(8), 42 (1998); Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

1996 (3)

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996); M. Mitchell and M. Segev, Nature 387, 880 (1997); Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulies, Opt. Lett. 21, 1436 (1996); J. Opt. Soc. Am. B 14, 3066 (1997).
[CrossRef] [PubMed]

1994 (2)

M. Haelterman and A. P. Sheppard, Phys. Rev. E 49, 3376 (1994).
[CrossRef]

A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

1993 (1)

1985 (1)

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1985).
[CrossRef] [PubMed]

1983 (1)

Anastassiou, C.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

Anderson, D.

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1985).
[CrossRef] [PubMed]

Buryak, A. V.

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

Carvalho, M. I.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

Chen, Z.

Christodoulides, D. N.

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

Christodoulies, D. N.

Coskun, T. H.

DelRe, E.

Firth, W. J.

E. A. Ostrovskaya, Yu. S. Kivshar, D. K. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999); J. Opt. B 1, 77 (1999).
[CrossRef]

Giordmaine, J. A.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

Gordon, J. P.

Haelterman, M.

Hewlett, S. J.

A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

Kivshar, Yu. S.

E. A. Ostrovskaya, Yu. S. Kivshar, Z. Chen, and M. Segev, Opt. Lett. 24, 327 (1999).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

E. A. Ostrovskaya, Yu. S. Kivshar, D. K. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999); J. Opt. B 1, 77 (1999).
[CrossRef]

Kockaert, P.

Lan, S.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

See, e.g., S. Lan, E. DelRe, Z. Chen, M. Shih, and M. Segev, Opt. Lett. 24, 475 (1999).
[CrossRef]

Lisak, M.

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1985).
[CrossRef] [PubMed]

Martin, J.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

Mitchell, D. J.

A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

Mitchell, M.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996); M. Mitchell and M. Segev, Nature 387, 880 (1997); Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

Ostrovskaya, E. A.

E. A. Ostrovskaya, Yu. S. Kivshar, D. K. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999); J. Opt. B 1, 77 (1999).
[CrossRef]

E. A. Ostrovskaya, Yu. S. Kivshar, Z. Chen, and M. Segev, Opt. Lett. 24, 327 (1999).
[CrossRef]

Segev, M.

E. A. Ostrovskaya, Yu. S. Kivshar, Z. Chen, and M. Segev, Opt. Lett. 24, 327 (1999).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

See, e.g., S. Lan, E. DelRe, Z. Chen, M. Shih, and M. Segev, Opt. Lett. 24, 475 (1999).
[CrossRef]

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

M. Segev and G. Stegeman, Phys. Today 51(8), 42 (1998); Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996); M. Mitchell and M. Segev, Nature 387, 880 (1997); Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulies, Opt. Lett. 21, 1436 (1996); J. Opt. Soc. Am. B 14, 3066 (1997).
[CrossRef] [PubMed]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

Sheppard, A. P.

Shih, M.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

See, e.g., S. Lan, E. DelRe, Z. Chen, M. Shih, and M. Segev, Opt. Lett. 24, 475 (1999).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996); M. Mitchell and M. Segev, Nature 387, 880 (1997); Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

Singh, S. R.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

Skryabin, D. K.

E. A. Ostrovskaya, Yu. S. Kivshar, D. K. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999); J. Opt. B 1, 77 (1999).
[CrossRef]

Snyder, A. W.

A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Lett. 18, 1406 (1993).
[CrossRef] [PubMed]

Stegeman, G.

M. Segev and G. Stegeman, Phys. Today 51(8), 42 (1998); Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

Steiglitz, K.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
[CrossRef]

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

Opt. Lett. (5)

Phys. Rev. A (1)

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1985).
[CrossRef] [PubMed]

Phys. Rev. E (1)

M. Haelterman and A. P. Sheppard, Phys. Rev. E 49, 3376 (1994).
[CrossRef]

Phys. Rev. Lett. (6)

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, Phys. Rev. Lett. 82, 81 (1999).
[CrossRef]

A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
[CrossRef] [PubMed]

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[CrossRef]

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, Phys. Rev. Lett. 77, 490 (1996); M. Mitchell and M. Segev, Nature 387, 880 (1997); Z. Chen, M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, Science 280, 889 (1998).
[CrossRef] [PubMed]

E. A. Ostrovskaya, Yu. S. Kivshar, D. K. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999); J. Opt. B 1, 77 (1999).
[CrossRef]

Phys. Today (1)

M. Segev and G. Stegeman, Phys. Today 51(8), 42 (1998); Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Numerical results demonstrating the soliton bound states. Top: nonlinear beam propagation of (a) attracting in-phase beams, (b) repelling out-of-phase beams, and (c) parallel vector solitons of coupled beams. Bottom: amplitude profiles at the crystal input z=0.

Fig. 2
Fig. 2

Experimental observation of bound states of vector solitons by incoherently coupling in-phase (top) and out-of-phase (bottom) beams. Photographs were taken at the input (a) and output (b)–(d) faces of the crystal. (a) Input, (b) linear diffraction, (c) coupled, (d) decoupled.

Fig. 3
Fig. 3

Formation of a two-hump soliton through incoherent interaction of in-phase (top) and out-of-phase (bottom) beams at close proximity. (a) Input, (b) coupled output, (c) combined output at steady state.

Fig. 4
Fig. 4

Induced coherence observed for interaction between two mutually incoherent solitons. (a) Combined intensity of two close beams (left and right, mutually incoherent) at input. (b)–(d) Decoupled intensity of each beam at output for (b) t=0.25 s, (c) t=1 s, (d) t=2min (steady state).

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