Abstract

We reveal that nonlocality can provide a simple physical mechanism for stabilization of multihump optical solitons and present what we believe to be the first example of stable rotating dipole solitons and soliton spiraling, which are known to be unstable in all types of realistic nonlinear media with a local response.

© 2006 Optical Society of America

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  1. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
    [Crossref] [PubMed]
  2. X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
    [Crossref]
  3. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
    [Crossref] [PubMed]
  4. W. Krolikowski and O. Bang, Phys. Rev. E 63, 016610 (2000).
    [Crossref]
  5. W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 64, 016612 (2001).
    [Crossref]
  6. J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
    [Crossref]
  7. O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
    [Crossref]
  8. A. I. Yakimenko, Yu. A. Zaliznyak, and Yu. S. Kivshar, Phys. Rev. E 71, 065603 (2005).
    [Crossref]
  9. D. Briedis, D. E. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
    [Crossref] [PubMed]
  10. M. Soljacic and M. Segev, Phys. Rev. Lett. 86, 420 (2001).
    [Crossref] [PubMed]
  11. A. S. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
    [Crossref] [PubMed]
  12. A. S. Desyatnikov, A. A. Sukhoroukov, and Yu. S. Kivshar, Phys. Rev. Lett. 95, 203904 (2005).
    [Crossref] [PubMed]
  13. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003), p. 540.
  14. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47, p. 291, and references therein.
    [Crossref]
  15. T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
    [Crossref] [PubMed]
  16. V. A. Mironov, A. M. Sergeev, and E. M. Sher, Sov. Phys. Dokl. 26, 861 (1981).
  17. B. A. Malomed, in Progress in Optics, E.Wolf, ed. (North-Holland, 2002), Vol. 43, p. 71.
    [Crossref]

2005 (4)

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

A. I. Yakimenko, Yu. A. Zaliznyak, and Yu. S. Kivshar, Phys. Rev. E 71, 065603 (2005).
[Crossref]

D. Briedis, D. E. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
[Crossref] [PubMed]

A. S. Desyatnikov, A. A. Sukhoroukov, and Yu. S. Kivshar, Phys. Rev. Lett. 95, 203904 (2005).
[Crossref] [PubMed]

2004 (2)

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[Crossref]

2002 (3)

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[Crossref]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[Crossref]

A. S. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
[Crossref] [PubMed]

2001 (3)

W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 64, 016612 (2001).
[Crossref]

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[Crossref] [PubMed]

M. Soljacic and M. Segev, Phys. Rev. Lett. 86, 420 (2001).
[Crossref] [PubMed]

2000 (1)

W. Krolikowski and O. Bang, Phys. Rev. E 63, 016610 (2000).
[Crossref]

1981 (1)

V. A. Mironov, A. M. Sergeev, and E. M. Sher, Sov. Phys. Dokl. 26, 861 (1981).

Adamski, A.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[Crossref]

Agrawal, G. P.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003), p. 540.

Assanto, G.

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

Bang, O.

D. Briedis, D. E. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
[Crossref] [PubMed]

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[Crossref]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[Crossref]

W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 64, 016612 (2001).
[Crossref]

W. Krolikowski and O. Bang, Phys. Rev. E 63, 016610 (2000).
[Crossref]

Briedis, D.

Cambournac, C.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[Crossref]

Carmon, T.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[Crossref] [PubMed]

Cohen, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Conti, C.

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

Desyatnikov, A. S.

A. S. Desyatnikov, A. A. Sukhoroukov, and Yu. S. Kivshar, Phys. Rev. Lett. 95, 203904 (2005).
[Crossref] [PubMed]

A. S. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
[Crossref] [PubMed]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47, p. 291, and references therein.
[Crossref]

Edmundson, D.

Haelterman, M.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[Crossref]

Hutsebaut, X.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[Crossref]

Kivshar, Yu. S.

A. I. Yakimenko, Yu. A. Zaliznyak, and Yu. S. Kivshar, Phys. Rev. E 71, 065603 (2005).
[Crossref]

A. S. Desyatnikov, A. A. Sukhoroukov, and Yu. S. Kivshar, Phys. Rev. Lett. 95, 203904 (2005).
[Crossref] [PubMed]

A. S. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
[Crossref] [PubMed]

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003), p. 540.

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47, p. 291, and references therein.
[Crossref]

Krolikowski, W.

D. Briedis, D. E. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
[Crossref] [PubMed]

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[Crossref]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[Crossref]

W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 64, 016612 (2001).
[Crossref]

W. Krolikowski and O. Bang, Phys. Rev. E 63, 016610 (2000).
[Crossref]

Malomed, B. A.

B. A. Malomed, in Progress in Optics, E.Wolf, ed. (North-Holland, 2002), Vol. 43, p. 71.
[Crossref]

Manela, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Mironov, V. A.

V. A. Mironov, A. M. Sergeev, and E. M. Sher, Sov. Phys. Dokl. 26, 861 (1981).

Musslimani, Z. H.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[Crossref] [PubMed]

Nepomnyashchy, A.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[Crossref] [PubMed]

Neyts, K.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[Crossref]

Peccianti, M.

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

Petersen, D. E.

Pigier, C.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[Crossref] [PubMed]

Rasmussen, J. J.

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[Crossref]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[Crossref]

W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 64, 016612 (2001).
[Crossref]

Rotschild, C.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Segev, M.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

M. Soljacic and M. Segev, Phys. Rev. Lett. 86, 420 (2001).
[Crossref] [PubMed]

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[Crossref] [PubMed]

Sergeev, A. M.

V. A. Mironov, A. M. Sergeev, and E. M. Sher, Sov. Phys. Dokl. 26, 861 (1981).

Sher, E. M.

V. A. Mironov, A. M. Sergeev, and E. M. Sher, Sov. Phys. Dokl. 26, 861 (1981).

Soljacic, M.

M. Soljacic and M. Segev, Phys. Rev. Lett. 86, 420 (2001).
[Crossref] [PubMed]

Sukhoroukov, A. A.

A. S. Desyatnikov, A. A. Sukhoroukov, and Yu. S. Kivshar, Phys. Rev. Lett. 95, 203904 (2005).
[Crossref] [PubMed]

Torner, L.

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47, p. 291, and references therein.
[Crossref]

Uzdin, R.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[Crossref] [PubMed]

Wyller, J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[Crossref]

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[Crossref]

Yakimenko, A. I.

A. I. Yakimenko, Yu. A. Zaliznyak, and Yu. S. Kivshar, Phys. Rev. E 71, 065603 (2005).
[Crossref]

Zaliznyak, Yu. A.

A. I. Yakimenko, Yu. A. Zaliznyak, and Yu. S. Kivshar, Phys. Rev. E 71, 065603 (2005).
[Crossref]

Opt. Commun. (1)

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[Crossref]

Opt. Express (1)

Phys. Rev. E (5)

W. Krolikowski and O. Bang, Phys. Rev. E 63, 016610 (2000).
[Crossref]

W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 64, 016612 (2001).
[Crossref]

J. Wyller, W. Krolikowski, O. Bang, and J. J. Rasmussen, Phys. Rev. E 66, 066615 (2002).
[Crossref]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, Phys. Rev. E 66, 046619 (2002).
[Crossref]

A. I. Yakimenko, Yu. A. Zaliznyak, and Yu. S. Kivshar, Phys. Rev. E 71, 065603 (2005).
[Crossref]

Phys. Rev. Lett. (6)

M. Soljacic and M. Segev, Phys. Rev. Lett. 86, 420 (2001).
[Crossref] [PubMed]

A. S. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
[Crossref] [PubMed]

A. S. Desyatnikov, A. A. Sukhoroukov, and Yu. S. Kivshar, Phys. Rev. Lett. 95, 203904 (2005).
[Crossref] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, Phys. Rev. Lett. 87, 143901 (2001).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

Sov. Phys. Dokl. (1)

V. A. Mironov, A. M. Sergeev, and E. M. Sher, Sov. Phys. Dokl. 26, 861 (1981).

Other (3)

B. A. Malomed, in Progress in Optics, E.Wolf, ed. (North-Holland, 2002), Vol. 43, p. 71.
[Crossref]

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003), p. 540.

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47, p. 291, and references therein.
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

(Color online) Beam radial intensity U 2 ( r ) (solid curves) and effective nonlinear potential N ( U , r ) (dashed curves) for the dipole soliton ( p = 0 , red) and vortex soliton ( p = 1 , blue) for (a) relatively low nonlocality with k = 1 and (b) high nonlocality with k = 70 . (c) Power versus propagation constant k for the dipole solitons; several lines for different p coincide. (d)–(f) Envelopes of the (top) intensity and (bottom) phase for three characteristic cases with k = 70 and (d) p = 0 , (e) p = 2 1 2 , (f) p = 1 .

Fig. 2
Fig. 2

(Color online) Two different instability scenarios for rotating dipole solitons with p = 0.5 for (a) k = 1 and (b) k = 20 . (c) Stable rotation for p = 0.5 and k = 100 . In all three cases the initial noise is 10%. (d) Stability domain of dipole solitons in the ( p , k ) space. (e) Numerically found relation between the angular velocity Ω of a dipole soliton and its contrast parameter p.

Fig. 3
Fig. 3

(Color online) (a), (b) Evolution of a dipole soliton ( k = 60 , p = 0 ) excited by a strong initial pertubation. Persistent oscillations of both the mode amplitude I max (dashed curve) and the diameter D (a distance between two peaks, solid curve) are observed; these oscillations decay slowly during propagation. (c) Example of the soliton revivals observed in the instability-induced evolution of double-ring single-charge vortex solitons with k = 100 .

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

i z E + 2 E + n ( I , r ) E = 0 ,
n ( I , r ) = R ( r ρ ) I ( ρ ) d ρ ,
R ( r ) = σ 2 π 1 exp ( r 2 σ 2 ) ,
E = π U ( r ) [ cos ( m φ ) + i p sin ( m φ ) ] exp ( i k z ) ,
k U + U r r + r 1 U r m 2 r 2 U + U N ( U 2 , r ) = 0 ,
N ( U 2 , r ) = π ( 1 + p 2 ) e r 2 0 ρ d ρ e ρ 2 U 2 ( ρ ) × { I 0 ( 2 r ρ ) + 1 2 ( 1 p 2 1 + p 2 ) 2 I 2 m ( 2 r ρ ) } ,

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