Abstract

We describe a physical mechanism for creating multisoliton bound states by which optical solitons are glued together by attraction between the nonsoliton beams that they guide, solitonic gluons. We verify the concept of the solitonic gluons experimentally, observing a suppression of the repulsion between dark solitons owing to an attractive force acting between out-of-phase bright guided beams.

© 1999 Optical Society of America

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References

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  1. M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
    [CrossRef]
  2. Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
    [CrossRef]
  3. S. V. Manakov, Sov. Phys. JETP 38, 248 (1974)Y. Silberberg and Y. Barad, Opt. Lett. 20, 246 (1995).
    [CrossRef] [PubMed]
  4. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 53 (1988)M. V. Tratnik and J. E. Sipe, Phys. Rev. A 38, 2001 (1988)A. W. Snyder, S. J. Hewlett, and D. J. Mitchell, Phys. Rev. Lett. 72, 1012 (1994).
    [CrossRef] [PubMed]
  5. Y. Inoue, J. Plasma Phys. 16, 439 (1976)D. N. Christodoulides, Phys. Lett. A 132, 451 (1988)S. Trillo, S. Wabnitz, E. M. Wright, and G. Stegeman, Opt. Lett. 13, 871 (1988)V. V. Afanasjev, Yu. S. Kivshar, V. V. Konotop, and V. N. Serkin, Opt. Lett. 14, 805 (1989)M. Shalaby and A. J. Barthelemy, IEEE J. Quantum Electron. 28, 2736 (1992)A. P. Sheppard and Yu. Kivshar, Phys. Rev. E 55, 4773 (1997).
    [CrossRef] [PubMed]
  6. D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, Appl. Phys. Lett. 68, 1763 (1996).
    [CrossRef]
  7. M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
    [CrossRef]
  8. See, e.g., M. Haelterman, A. P. Sheppard, and A. W. Snyder, Opt. Lett. 18, 1406 (1993)M. Haelterman and A. P. Sheppard, Phys. Rev. E 49, 3376 (1994).
    [CrossRef] [PubMed]
  9. See, e.g., F. J. Ynduráin, Quantum Chromodynamics:?An Introduction to the Theory of Quarks and Gluons (Springer-Verlag, New York, 1983).
    [CrossRef]
  10. Of course, this analogy is not complete because dark solitons can exist on their own.
  11. E. A. Ostrovskaya and Yu. S. Kivshar, Opt. Lett. 23, 1268 (1998).
    [CrossRef]
  12. Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, Yu. S. Kivshar, and V. V. Afanasjev, Opt. Lett. 21, 1821 (1996)J. Opt. Soc. Am. B 14, 3066 (1997).
    [CrossRef] [PubMed]
  13. Z. Chen, M. Mitchell, and M. Segev, Opt. Lett. 21, 716 (1996).
    [CrossRef] [PubMed]
  14. E. A. Ostrovskaya and Yu. S. Kivshar, “Multi-hump optical solitons in a saturable medium,” J. Opt. B (to be published).

1998 (4)

M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
[CrossRef]

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

E. A. Ostrovskaya and Yu. S. Kivshar, Opt. Lett. 23, 1268 (1998).
[CrossRef]

1996 (3)

1993 (1)

1988 (1)

1976 (1)

Y. Inoue, J. Plasma Phys. 16, 439 (1976)D. N. Christodoulides, Phys. Lett. A 132, 451 (1988)S. Trillo, S. Wabnitz, E. M. Wright, and G. Stegeman, Opt. Lett. 13, 871 (1988)V. V. Afanasjev, Yu. S. Kivshar, V. V. Konotop, and V. N. Serkin, Opt. Lett. 14, 805 (1989)M. Shalaby and A. J. Barthelemy, IEEE J. Quantum Electron. 28, 2736 (1992)A. P. Sheppard and Yu. Kivshar, Phys. Rev. E 55, 4773 (1997).
[CrossRef] [PubMed]

1974 (1)

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974)Y. Silberberg and Y. Barad, Opt. Lett. 20, 246 (1995).
[CrossRef] [PubMed]

Afanasjev, V. V.

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.

Coskun, T. H.

Haelterman, M.

Inoue, Y.

Y. Inoue, J. Plasma Phys. 16, 439 (1976)D. N. Christodoulides, Phys. Lett. A 132, 451 (1988)S. Trillo, S. Wabnitz, E. M. Wright, and G. Stegeman, Opt. Lett. 13, 871 (1988)V. V. Afanasjev, Yu. S. Kivshar, V. V. Konotop, and V. N. Serkin, Opt. Lett. 14, 805 (1989)M. Shalaby and A. J. Barthelemy, IEEE J. Quantum Electron. 28, 2736 (1992)A. P. Sheppard and Yu. Kivshar, Phys. Rev. E 55, 4773 (1997).
[CrossRef] [PubMed]

Joseph, R. I.

Kivshar, Yu. S.

Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
[CrossRef]

E. A. Ostrovskaya and Yu. S. Kivshar, Opt. Lett. 23, 1268 (1998).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, Yu. S. Kivshar, and V. V. Afanasjev, Opt. Lett. 21, 1821 (1996)J. Opt. Soc. Am. B 14, 3066 (1997).
[CrossRef] [PubMed]

E. A. Ostrovskaya and Yu. S. Kivshar, “Multi-hump optical solitons in a saturable medium,” J. Opt. B (to be published).

Luther-Davies, B.

Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
[CrossRef]

Manakov, S. V.

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974)Y. Silberberg and Y. Barad, Opt. Lett. 20, 246 (1995).
[CrossRef] [PubMed]

Mitchell, M.

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

Z. Chen, M. Mitchell, and M. Segev, Opt. Lett. 21, 716 (1996).
[CrossRef] [PubMed]

Ostrovskaya, E. A.

E. A. Ostrovskaya and Yu. S. Kivshar, Opt. Lett. 23, 1268 (1998).
[CrossRef]

E. A. Ostrovskaya and Yu. S. Kivshar, “Multi-hump optical solitons in a saturable medium,” J. Opt. B (to be published).

Segev, M.

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

M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, D. N. Christodoulides, Yu. S. Kivshar, and V. V. Afanasjev, Opt. Lett. 21, 1821 (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]

Z. Chen, M. Mitchell, and M. Segev, Opt. Lett. 21, 716 (1996).
[CrossRef] [PubMed]

Sheppard, A. P.

Singh, S. R.

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

Snyder, A. W.

Stegeman, G. I.

M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

Ynduráin, F. J.

See, e.g., F. J. Ynduráin, Quantum Chromodynamics:?An Introduction to the Theory of Quarks and Gluons (Springer-Verlag, New York, 1983).
[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. Plasma Phys. (1)

Y. Inoue, J. Plasma Phys. 16, 439 (1976)D. N. Christodoulides, Phys. Lett. A 132, 451 (1988)S. Trillo, S. Wabnitz, E. M. Wright, and G. Stegeman, Opt. Lett. 13, 871 (1988)V. V. Afanasjev, Yu. S. Kivshar, V. V. Konotop, and V. N. Serkin, Opt. Lett. 14, 805 (1989)M. Shalaby and A. J. Barthelemy, IEEE J. Quantum Electron. 28, 2736 (1992)A. P. Sheppard and Yu. Kivshar, Phys. Rev. E 55, 4773 (1997).
[CrossRef] [PubMed]

Opt. Lett. (5)

Phys. Rep. (1)

Yu. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998), and references therein.
[CrossRef]

Phys. Rev. Lett. (1)

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

Phys. Today (1)

M. Segev and G. I. Stegeman, Phys. Today 51(8), 42 (1998).
[CrossRef]

Sov. Phys. JETP (1)

S. V. Manakov, Sov. Phys. JETP 38, 248 (1974)Y. Silberberg and Y. Barad, Opt. Lett. 20, 246 (1995).
[CrossRef] [PubMed]

Other (3)

See, e.g., F. J. Ynduráin, Quantum Chromodynamics:?An Introduction to the Theory of Quarks and Gluons (Springer-Verlag, New York, 1983).
[CrossRef]

Of course, this analogy is not complete because dark solitons can exist on their own.

E. A. Ostrovskaya and Yu. S. Kivshar, “Multi-hump optical solitons in a saturable medium,” J. Opt. B (to be published).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic representation of the force balance between two-component solitons; ϕ is a relative phase between the bright guided beams. Propagation of two dark solitons for s=0.43, λ=0.563: (b) without and (c) with a bright component.

Fig. 2
Fig. 2

Generation of a pair of dark solitons from a localized boxlike input in the model [Eqs.  (1)] for s=0.5, λ=0.8: (a) with no bright component introduced, (b) in the presence of an antisymmetric bright component. Bottom row, corresponding input beam profiles.

Fig. 3
Fig. 3

Observation of the effect of the solitonic gluons through coupling of dark (top) and bright (bottom) incoherently interacting beams. Photographs were taken on (a) the input and (b)–(c)(d) the output faces of the crystal for (b) normal linear diffraction, (c) coupled dark and bright beams, (d) uncoupled dark and bright beams (see discussion in text).

Fig. 4
Fig. 4

Bound states of bright vector solitons in the model [Eqs.  (1)] at σ=-1 with the solitonic gluons in the shape of (a) the first and (b) the second guided modes. (c), (d) Interaction of two bright solitons from (a) for s=0.8 and λ=0.63, without and with the gluon component, respectively.

Equations (1)

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iuz+122ux2-σu2+w2u1+su2+w2+u=0,iwz+122wx2-σu2+w2w1+su2+w2+λw=0,

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