Abstract

We find the key behind the existence traits of asymptotic saturated nonlinear optical solitons in the emergence of linear wave segments. These traits, produced by the progressive relegation of nonlinear dynamics to wave tails, allow a direct and versatile analytical prediction of self-trapping existence conditions and simple soliton scaling laws, which we confirm experimentally in saturated-Kerr self-trapping observed in photorefractives. This approach provides the means to correctly evaluate beam tails in the saturated regime, which is instrumental in the prediction of soliton interaction forces.

© 2003 Optical Society of America

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References

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  1. S. Trillo and W. Torruellas, eds., Spatial Solitons (Springer-Verlag, Berlin, 2002).
  2. G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  5. D. N. Christodoulides and M. I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995).
    [CrossRef]
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    [CrossRef]
  7. M. Soljacic, M. Segev, and C. R. Menyuk, Phys. Rev. E 61, R1048 (2000).
    [CrossRef]
  8. V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
    [CrossRef] [PubMed]
  9. G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920 (1993).
    [CrossRef] [PubMed]
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    [CrossRef]
  11. E. DelRe, B. Crosignani, M. Tamburrini, M. Segev, M. Mitchell, E. Refaeli, and A. J. Agranat, Opt. Lett. 23, 421 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  17. K. Kos, G. Salamo, and M. Segev, Opt. Lett. 23, 1001 (1998).
    [CrossRef]
  18. One can appreciate the difference between the Taylor expansion approach and ours by comparing our Fig. 2(a) and Fig. 1 of Ref. 7.

2002 (1)

E. DelRe and A. J. Agranat, Phys. Rev. A 65, 53814 (2002).
[CrossRef]

2000 (1)

M. Soljacic, M. Segev, and C. R. Menyuk, Phys. Rev. E 61, R1048 (2000).
[CrossRef]

1999 (1)

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

1998 (3)

1997 (1)

1996 (3)

M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef]

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

1995 (2)

1994 (1)

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

1993 (1)

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

1991 (1)

1983 (1)

Agranat, A. J.

Anderson, D.

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1995).
[CrossRef]

Carvalho, M. I.

Christodoulides, D. N.

Christou, J.

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Crosignani, B.

E. DelRe, B. Crosignani, M. Tamburrini, M. Segev, M. Mitchell, E. Refaeli, and A. J. Agranat, Opt. Lett. 23, 421 (1998).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Degasperis, A.

A. Degasperis, Am. J. Phys. 66, 486 (1998).
[CrossRef]

DelRe, E.

Di Porto, P.

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Gibbs, H. M.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

Gordon, J. P.

Ikegami, T.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

Iwamura, H.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

Kawamura, Y.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

Khitrova, G.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

Kos, K.

K. Kos, G. Salamo, and M. Segev, Opt. Lett. 23, 1001 (1998).
[CrossRef]

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Ladouceur, F.

Lisak, M.

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1995).
[CrossRef]

Luther-Davies, B.

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Meng, H.

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Menyuk, C. R.

M. Soljacic, M. Segev, and C. R. Menyuk, Phys. Rev. E 61, R1048 (2000).
[CrossRef]

Ming, L.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

Mitchell, D. J.

Mitchell, M.

Poladian, L.

Refaeli, E.

Salamo, G.

K. Kos, G. Salamo, and M. Segev, Opt. Lett. 23, 1001 (1998).
[CrossRef]

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Segev, M.

M. Soljacic, M. Segev, and C. R. Menyuk, Phys. Rev. E 61, R1048 (2000).
[CrossRef]

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

E. DelRe, B. Crosignani, M. Tamburrini, M. Segev, M. Mitchell, E. Refaeli, and A. J. Agranat, Opt. Lett. 23, 421 (1998).
[CrossRef]

K. Kos, G. Salamo, and M. Segev, Opt. Lett. 23, 1001 (1998).
[CrossRef]

M. Segev and A. J. Agranat, Opt. Lett. 22, 1299 (1997).
[CrossRef]

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Shih, M.

M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef]

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Sipe, J. E.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

Snyder, A. W.

Soljacic, M.

M. Soljacic, M. Segev, and C. R. Menyuk, Phys. Rev. E 61, R1048 (2000).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Tamburrini, M.

Tikhonenko, V.

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

Valley, G. C.

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

M. Segev, M. Shih, and G. C. Valley, J. Opt. Soc. Am. B 13, 706 (1996).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Am. J. Phys. (1)

A. Degasperis, Am. J. Phys. 66, 486 (1998).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Lett. (5)

Phys. Rev. A (2)

D. Anderson and M. Lisak, Phys. Rev. A 32, 2270 (1995).
[CrossRef]

E. DelRe and A. J. Agranat, Phys. Rev. A 65, 53814 (2002).
[CrossRef]

Phys. Rev. E (2)

M. Soljacic, M. Segev, and C. R. Menyuk, Phys. Rev. E 61, R1048 (2000).
[CrossRef]

K. Kos, H. Meng, G. Salamo, M. Shih, M. Segev, and G. C. Valley, Phys. Rev. E 53, R4330 (1996).
[CrossRef]

Phys. Rev. Lett. (3)

V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76, 2698 (1996).
[CrossRef] [PubMed]

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920 (1993).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

Science (1)

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Other (2)

S. Trillo and W. Torruellas, eds., Spatial Solitons (Springer-Verlag, Berlin, 2002).

One can appreciate the difference between the Taylor expansion approach and ours by comparing our Fig. 2(a) and Fig. 1 of Ref. 7.

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Figures (2)

Fig. 1
Fig. 1

Segmented wave harmonic theory (solid line and curve) of centrosymmetric screening solitons, numerical integration of Eq. (1) (plus symbols), and experiments in a sample of potassium lithium tantalate niobate (circles and squares). The line is the basic segmentation prediction Δξ=π/2u0; the curve is the prediction Δ that adheres more closely to the result of Δξ=π/21+u02/u0 (see text). There are no free parameters.

Fig. 2
Fig. 2

Segmented wave harmonic theory (curves) of (a) conventional screening solitons and (b) high-intensity solitons. Plus symbols, numerical integration of Eq. (1); squares, experiments in strontium barium niobate.10,17 In (a) the bottom curve is the basic segmentation prediction Δξ=π/2u0lnu02+1-1/2; the top curve is the more adherent prediction Δξ=π/2u0lnu02+1-u02/1+u02-1/2. There are no free parameters.

Equations (3)

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uξ=-δuξ+fu2uξ,
uξ+δuξ=0.
Δξ=π/2δ-1/2.

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