Abstract

We show that bimodal systems with a spatially nonuniform defocusing cubic nonlinearity, whose strength grows toward the periphery, can support stable two-component solitons. For a sufficiently strong cross-phase-modulation interaction, vector solitons with overlapping components become unstable, while stable families of solitons with spatially separated components emerge. Stable complexes with separated components may be built not only of fundamental solitons, but of multipoles, too.

© 2011 Optical Society of America

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References

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  1. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).
  2. V. A. Brazhnyi and V. V. Konotop, Mod. Phys. Lett. B 18, 627(2004).
    [CrossRef]
  3. Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
    [CrossRef]
  4. O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Opt. Lett. 36, 3088 (2011).
    [CrossRef] [PubMed]
  5. O. V. Borovkova, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 84, 035602 (2011).
    [CrossRef]
  6. E. Timmermans, Phys. Rev. Lett. 81, 5718 (1998).
    [CrossRef]
  7. M. Trippenbach, K. Goral, K. Rzazewski, B. Malomed, and Y. B. Band, J. Phys. B 33, 4017 (2000).
    [CrossRef]
  8. V. S. Shchesnovich, A. M. Kamchatnov, and R. A. Kraenkel, Phys. Rev. A 69, 033601 (2004).
    [CrossRef]
  9. F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
    [CrossRef]
  10. Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 3625 (2009).
    [CrossRef] [PubMed]
  11. J. Belmonte-Beitia, V. M. Perez-Garcia, and V. Brazhnyi, Commun. Nonlinear Sci. Numer. Simul. 16, 158 (2011).
    [CrossRef]
  12. C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010).
    [CrossRef]
  13. J. Hukriede, D. Runde, and D. Kip, J. Phys. D 36, R1 (2003).
    [CrossRef]
  14. K. Peithmann, J. Hukriede, K. Buze, and E. Krätzig, Phys. Rev. B 61, 4615 (2000).
    [CrossRef]
  15. V. Shandarov, Ferroelectrics 201, 185 (1997).
    [CrossRef]

2011

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Opt. Lett. 36, 3088 (2011).
[CrossRef] [PubMed]

O. V. Borovkova, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 84, 035602 (2011).
[CrossRef]

J. Belmonte-Beitia, V. M. Perez-Garcia, and V. Brazhnyi, Commun. Nonlinear Sci. Numer. Simul. 16, 158 (2011).
[CrossRef]

2010

C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010).
[CrossRef]

2009

2008

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
[CrossRef]

2004

V. S. Shchesnovich, A. M. Kamchatnov, and R. A. Kraenkel, Phys. Rev. A 69, 033601 (2004).
[CrossRef]

V. A. Brazhnyi and V. V. Konotop, Mod. Phys. Lett. B 18, 627(2004).
[CrossRef]

2003

J. Hukriede, D. Runde, and D. Kip, J. Phys. D 36, R1 (2003).
[CrossRef]

2000

K. Peithmann, J. Hukriede, K. Buze, and E. Krätzig, Phys. Rev. B 61, 4615 (2000).
[CrossRef]

M. Trippenbach, K. Goral, K. Rzazewski, B. Malomed, and Y. B. Band, J. Phys. B 33, 4017 (2000).
[CrossRef]

1998

E. Timmermans, Phys. Rev. Lett. 81, 5718 (1998).
[CrossRef]

1997

V. Shandarov, Ferroelectrics 201, 185 (1997).
[CrossRef]

Abdullaev, F. K.

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
[CrossRef]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

Band, Y. B.

M. Trippenbach, K. Goral, K. Rzazewski, B. Malomed, and Y. B. Band, J. Phys. B 33, 4017 (2000).
[CrossRef]

Belmonte-Beitia, J.

J. Belmonte-Beitia, V. M. Perez-Garcia, and V. Brazhnyi, Commun. Nonlinear Sci. Numer. Simul. 16, 158 (2011).
[CrossRef]

Borovkova, O. V.

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Opt. Lett. 36, 3088 (2011).
[CrossRef] [PubMed]

O. V. Borovkova, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 84, 035602 (2011).
[CrossRef]

Brazhnyi, V.

J. Belmonte-Beitia, V. M. Perez-Garcia, and V. Brazhnyi, Commun. Nonlinear Sci. Numer. Simul. 16, 158 (2011).
[CrossRef]

Brazhnyi, V. A.

V. A. Brazhnyi and V. V. Konotop, Mod. Phys. Lett. B 18, 627(2004).
[CrossRef]

Buze, K.

K. Peithmann, J. Hukriede, K. Buze, and E. Krätzig, Phys. Rev. B 61, 4615 (2000).
[CrossRef]

Chin, C.

C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010).
[CrossRef]

Gammal, A.

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
[CrossRef]

Goral, K.

M. Trippenbach, K. Goral, K. Rzazewski, B. Malomed, and Y. B. Band, J. Phys. B 33, 4017 (2000).
[CrossRef]

Grimm, R.

C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010).
[CrossRef]

Hukriede, J.

J. Hukriede, D. Runde, and D. Kip, J. Phys. D 36, R1 (2003).
[CrossRef]

K. Peithmann, J. Hukriede, K. Buze, and E. Krätzig, Phys. Rev. B 61, 4615 (2000).
[CrossRef]

Julienne, P.

C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010).
[CrossRef]

Kamchatnov, A. M.

V. S. Shchesnovich, A. M. Kamchatnov, and R. A. Kraenkel, Phys. Rev. A 69, 033601 (2004).
[CrossRef]

Kartashov, Y. V.

O. V. Borovkova, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 84, 035602 (2011).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Opt. Lett. 36, 3088 (2011).
[CrossRef] [PubMed]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 3625 (2009).
[CrossRef] [PubMed]

Kip, D.

J. Hukriede, D. Runde, and D. Kip, J. Phys. D 36, R1 (2003).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

Konotop, V. V.

V. A. Brazhnyi and V. V. Konotop, Mod. Phys. Lett. B 18, 627(2004).
[CrossRef]

Kraenkel, R. A.

V. S. Shchesnovich, A. M. Kamchatnov, and R. A. Kraenkel, Phys. Rev. A 69, 033601 (2004).
[CrossRef]

Krätzig, E.

K. Peithmann, J. Hukriede, K. Buze, and E. Krätzig, Phys. Rev. B 61, 4615 (2000).
[CrossRef]

Malomed, B.

M. Trippenbach, K. Goral, K. Rzazewski, B. Malomed, and Y. B. Band, J. Phys. B 33, 4017 (2000).
[CrossRef]

Malomed, B. A.

O. V. Borovkova, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 84, 035602 (2011).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Opt. Lett. 36, 3088 (2011).
[CrossRef] [PubMed]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 3625 (2009).
[CrossRef] [PubMed]

Peithmann, K.

K. Peithmann, J. Hukriede, K. Buze, and E. Krätzig, Phys. Rev. B 61, 4615 (2000).
[CrossRef]

Perez-Garcia, V. M.

J. Belmonte-Beitia, V. M. Perez-Garcia, and V. Brazhnyi, Commun. Nonlinear Sci. Numer. Simul. 16, 158 (2011).
[CrossRef]

Runde, D.

J. Hukriede, D. Runde, and D. Kip, J. Phys. D 36, R1 (2003).
[CrossRef]

Rzazewski, K.

M. Trippenbach, K. Goral, K. Rzazewski, B. Malomed, and Y. B. Band, J. Phys. B 33, 4017 (2000).
[CrossRef]

Salerno, M.

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
[CrossRef]

Shandarov, V.

V. Shandarov, Ferroelectrics 201, 185 (1997).
[CrossRef]

Shchesnovich, V. S.

V. S. Shchesnovich, A. M. Kamchatnov, and R. A. Kraenkel, Phys. Rev. A 69, 033601 (2004).
[CrossRef]

Tiesinga, E.

C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010).
[CrossRef]

Timmermans, E.

E. Timmermans, Phys. Rev. Lett. 81, 5718 (1998).
[CrossRef]

Tomio, L.

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
[CrossRef]

Torner, L.

O. V. Borovkova, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 84, 035602 (2011).
[CrossRef]

O. V. Borovkova, Y. V. Kartashov, B. A. Malomed, and L. Torner, Opt. Lett. 36, 3088 (2011).
[CrossRef] [PubMed]

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 3625 (2009).
[CrossRef] [PubMed]

Trippenbach, M.

M. Trippenbach, K. Goral, K. Rzazewski, B. Malomed, and Y. B. Band, J. Phys. B 33, 4017 (2000).
[CrossRef]

Vysloukh, V. A.

Commun. Nonlinear Sci. Numer. Simul.

J. Belmonte-Beitia, V. M. Perez-Garcia, and V. Brazhnyi, Commun. Nonlinear Sci. Numer. Simul. 16, 158 (2011).
[CrossRef]

Ferroelectrics

V. Shandarov, Ferroelectrics 201, 185 (1997).
[CrossRef]

J. Phys. B

M. Trippenbach, K. Goral, K. Rzazewski, B. Malomed, and Y. B. Band, J. Phys. B 33, 4017 (2000).
[CrossRef]

J. Phys. D

J. Hukriede, D. Runde, and D. Kip, J. Phys. D 36, R1 (2003).
[CrossRef]

Mod. Phys. Lett. B

V. A. Brazhnyi and V. V. Konotop, Mod. Phys. Lett. B 18, 627(2004).
[CrossRef]

Opt. Lett.

Phys. Rev. A

V. S. Shchesnovich, A. M. Kamchatnov, and R. A. Kraenkel, Phys. Rev. A 69, 033601 (2004).
[CrossRef]

F. K. Abdullaev, A. Gammal, M. Salerno, and L. Tomio, Phys. Rev. A 77, 023615 (2008).
[CrossRef]

Phys. Rev. B

K. Peithmann, J. Hukriede, K. Buze, and E. Krätzig, Phys. Rev. B 61, 4615 (2000).
[CrossRef]

Phys. Rev. E

O. V. Borovkova, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 84, 035602 (2011).
[CrossRef]

Phys. Rev. Lett.

E. Timmermans, Phys. Rev. Lett. 81, 5718 (1998).
[CrossRef]

Rev. Mod. Phys.

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Rev. Mod. Phys. 82, 1225 (2010).
[CrossRef]

Other

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

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Figures (4)

Fig. 1
Fig. 1

Fundamental vector solitons with overlapping components, for (a)  b 2 = 8 and (b)  b 2 = 3.1 , and with separated ones for (c)  b 2 = 5 and (d)  b 2 = 7.2 . In all the cases, b 1 = 5 and C = 2 . The soliton in (a) is unstable, while the ones in (b)–(d) are stable.

Fig. 2
Fig. 2

(a) Energy-sharing ratio and (b) coordinates of centers of the two components, versus b 2 at b 1 = 5 and C = 2 . Circles correspond to the solitons in Figs. 1c, 1d. (c) Existence domains in the plane of (C, b 2 ) for vector solitons with overlapping and separated components (left black and right red curves, respectively) at b 1 = 5 . (d) Existence domains of vector solitons with separated components in the ( b 1 , b 2 ) plane at C = 2 .

Fig. 3
Fig. 3

Dipole solitons with separated components at (a)  b 1 = 5 , b 2 = 5 and (b)  b 1 = 5 , b 2 = 7.4 for C = 3 . (c) Tripole soliton with separated components at b 1 = 5 , b 2 = 6.5 , C = 3 . The solitons in (a) and (b) are stable, while the one in (c) is unstable.

Fig. 4
Fig. 4

(a) Energy-sharing ratio versus b 2 at b 1 = 5 , C = 3 . Circles correspond to solitons in Figs. 3a, 3b. The existence domains of dipoles with separated components in the plane of (b) (C, b 2 ) at b 1 = 5 , and (c) in the plane of ( b 1 , b 2 ) at C = 2 . (d) Real part of the perturbation growth rate versus b 2 at b 1 = 5 , C = 2.2 for the dipole soliton with separated components.

Equations (1)

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i q 1 , 2 ξ = 1 2 2 q 1 , 2 η 2 + σ ( η ) q 1 , 2 ( | q 1 , 2 | 2 + C | q 2 , 1 | 2 ) .

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