Abstract

We demonstrate that spatially inhomogeneous defocusing nonlinear landscapes with the nonlinearity coefficient growing toward the periphery as (1+|r|α) support one- and two-dimensional fundamental and higher-order bright solitons, as well as vortex solitons, with algebraically decaying tails. The energy flow of the solitons converges as long as nonlinearity growth rate exceeds the dimensionality, i.e., α>D. Fundamental solitons are always stable, while multipoles and vortices are stable if the nonlinearity growth rate is large enough.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
    [CrossRef]
  2. Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
    [CrossRef]
  3. H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
    [CrossRef]
  4. F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).
  5. G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
    [CrossRef]
  6. G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
    [CrossRef]
  7. J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
    [CrossRef] [PubMed]
  8. Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616(2006).
    [CrossRef]
  9. Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. Jones, J. Phys. A 40, 14151 (2007).
    [CrossRef]
  10. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1747 (2008).
    [CrossRef] [PubMed]
  11. Y. Kominis and K. Hizanidis, Opt. Express 16, 12124 (2008).
    [CrossRef] [PubMed]
  12. H. Sakaguchi and B. A. Malomed, Phys. Rev. A 81, 013624(2010).
    [CrossRef]
  13. A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. E 65, 036609 (2002).
    [CrossRef]
  14. Y. Kominis, Phys. Rev. E 73, 066619 (2006).
    [CrossRef]
  15. H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
    [CrossRef]
  16. Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
    [CrossRef] [PubMed]
  17. Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 770 (2009).
    [CrossRef] [PubMed]
  18. Y. S. Kivshar, W. Krolikowski, and O. A. Chubykalo, Phys. Rev. E 50, 5020 (1994).
    [CrossRef]
  19. Y. Kominis and K. Hizanidis, Opt. Lett. 31, 2888 (2006).
    [CrossRef] [PubMed]
  20. V. Perez-Garcia and R. Pardo, Physica D 238, 1352 (2009).
    [CrossRef]
  21. R. W. Micallef, V. V. Afanasjev, Y. S. Kivshar, and D. J. Love, Phys. Rev. E 54, 2936 (1996).
    [CrossRef]
  22. R. Pardo and V. M. Perez-Garcia, Phys. Rev. Lett. 97, 254101 (2006).
    [CrossRef]
  23. A. Alexandrescu and V. M. Perez-Garcia, Phys. Rev. A 73, 053610 (2006).
    [CrossRef]
  24. J. Hukriede, D. Runde, and D. Kip, J. Phys. D 36, R1 (2003).
    [CrossRef]
  25. I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008).
    [CrossRef]

2011 (1)

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

2010 (1)

H. Sakaguchi and B. A. Malomed, Phys. Rev. A 81, 013624(2010).
[CrossRef]

2009 (2)

2008 (3)

2007 (2)

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

2006 (8)

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616(2006).
[CrossRef]

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

R. Pardo and V. M. Perez-Garcia, Phys. Rev. Lett. 97, 254101 (2006).
[CrossRef]

A. Alexandrescu and V. M. Perez-Garcia, Phys. Rev. A 73, 053610 (2006).
[CrossRef]

Y. Kominis, Phys. Rev. E 73, 066619 (2006).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
[CrossRef]

Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

Y. Kominis and K. Hizanidis, Opt. Lett. 31, 2888 (2006).
[CrossRef] [PubMed]

2005 (3)

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
[CrossRef]

F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).

G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
[CrossRef]

2004 (1)

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
[CrossRef]

2003 (1)

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

2002 (1)

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. E 65, 036609 (2002).
[CrossRef]

1996 (1)

R. W. Micallef, V. V. Afanasjev, Y. S. Kivshar, and D. J. Love, Phys. Rev. E 54, 2936 (1996).
[CrossRef]

1994 (1)

Y. S. Kivshar, W. Krolikowski, and O. A. Chubykalo, Phys. Rev. E 50, 5020 (1994).
[CrossRef]

Abdullaev, F. K.

F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).

Afanasjev, V. V.

R. W. Micallef, V. V. Afanasjev, Y. S. Kivshar, and D. J. Love, Phys. Rev. E 54, 2936 (1996).
[CrossRef]

Alexandrescu, A.

A. Alexandrescu and V. M. Perez-Garcia, Phys. Rev. A 73, 053610 (2006).
[CrossRef]

Belmonte-Beitia, J.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Bloch, I.

I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008).
[CrossRef]

Bludov, Y. V.

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616(2006).
[CrossRef]

Chubykalo, O. A.

Y. S. Kivshar, W. Krolikowski, and O. A. Chubykalo, Phys. Rev. E 50, 5020 (1994).
[CrossRef]

Dalibard, J.

I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008).
[CrossRef]

Fibich, G.

Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

Frantzeskakis, D. J.

G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
[CrossRef]

Garnier, J.

F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).

Hizanidis, K.

Hukriede, J.

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

Jones, C.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

Kartashov, Y. V.

Kevrekidis, P. G.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
[CrossRef]

Kip, D.

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

Kivshar, Y. S.

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. E 65, 036609 (2002).
[CrossRef]

R. W. Micallef, V. V. Afanasjev, Y. S. Kivshar, and D. J. Love, Phys. Rev. E 54, 2936 (1996).
[CrossRef]

Y. S. Kivshar, W. Krolikowski, and O. A. Chubykalo, Phys. Rev. E 50, 5020 (1994).
[CrossRef]

Kominis, Y.

Konotop, V. V.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616(2006).
[CrossRef]

Krolikowski, W.

Y. S. Kivshar, W. Krolikowski, and O. A. Chubykalo, Phys. Rev. E 50, 5020 (1994).
[CrossRef]

Love, D. J.

R. W. Micallef, V. V. Afanasjev, Y. S. Kivshar, and D. J. Love, Phys. Rev. E 54, 2936 (1996).
[CrossRef]

Malomed, B. A.

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

H. Sakaguchi and B. A. Malomed, Phys. Rev. A 81, 013624(2010).
[CrossRef]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Opt. Lett. 34, 770 (2009).
[CrossRef] [PubMed]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
[CrossRef]

Micallef, R. W.

R. W. Micallef, V. V. Afanasjev, Y. S. Kivshar, and D. J. Love, Phys. Rev. E 54, 2936 (1996).
[CrossRef]

Pardo, R.

V. Perez-Garcia and R. Pardo, Physica D 238, 1352 (2009).
[CrossRef]

R. Pardo and V. M. Perez-Garcia, Phys. Rev. Lett. 97, 254101 (2006).
[CrossRef]

Pelinovsky, D. E.

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
[CrossRef]

Perez-Garcia, V.

V. Perez-Garcia and R. Pardo, Physica D 238, 1352 (2009).
[CrossRef]

Perez-Garcia, V. M.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

R. Pardo and V. M. Perez-Garcia, Phys. Rev. Lett. 97, 254101 (2006).
[CrossRef]

A. Alexandrescu and V. M. Perez-Garcia, Phys. Rev. A 73, 053610 (2006).
[CrossRef]

Rapti, Z.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

Runde, D.

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

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, Phys. Rev. A 81, 013624(2010).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
[CrossRef]

Schmelcher, P.

G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
[CrossRef]

Sivan, Y.

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

Sukhorukov, A. A.

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. E 65, 036609 (2002).
[CrossRef]

Theocharis, G.

G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
[CrossRef]

Torner, L.

Torres, P. J.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Vekslerchik, V.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Vysloukh, V. A.

Weinstein, M. I.

Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

Zwerger, W.

I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008).
[CrossRef]

J. Phys. A (1)

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

J. Phys. D (1)

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

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (5)

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616(2006).
[CrossRef]

A. Alexandrescu and V. M. Perez-Garcia, Phys. Rev. A 73, 053610 (2006).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. A 81, 013624(2010).
[CrossRef]

F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).

G. Theocharis, P. Schmelcher, P. G. Kevrekidis, and D. J. Frantzeskakis, Phys. Rev. A 72, 033614 (2005).
[CrossRef]

Phys. Rev. E (7)

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
[CrossRef]

A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. E 65, 036609 (2002).
[CrossRef]

Y. Kominis, Phys. Rev. E 73, 066619 (2006).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
[CrossRef]

R. W. Micallef, V. V. Afanasjev, Y. S. Kivshar, and D. J. Love, Phys. Rev. E 54, 2936 (1996).
[CrossRef]

Y. S. Kivshar, W. Krolikowski, and O. A. Chubykalo, Phys. Rev. E 50, 5020 (1994).
[CrossRef]

Phys. Rev. Lett. (3)

R. Pardo and V. M. Perez-Garcia, Phys. Rev. Lett. 97, 254101 (2006).
[CrossRef]

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

Physica D (2)

V. Perez-Garcia and R. Pardo, Physica D 238, 1352 (2009).
[CrossRef]

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

Rev. Mod. Phys. (2)

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

I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) Profiles of 2D solitons with different topological charges corresponding to b = 10 , α = 5 . (b) Vortices with m = 1 corresponding to b = 5 , 10 , 20 (curves 1, 2, 3). (c) 1D solitons with different numbers of nodes corresponding to b = 10 , α = 5 . In each panel, the nonlinearity profile is shown by the red curve.

Fig. 2
Fig. 2

The energy flow versus the propagation constant, b, for 2D solitons at α = 5 (a), and versus α for 2D (b) and 1D (c) solitons at b = 10 . Red curves in (b) and (c) show the prediction of the TF approximation.

Fig. 3
Fig. 3

(a) The real part of the perturbation growth rate versus b at α = 3.5 , 4, and 5 (curves 1, 2, and 3) for vortices with m = 1 and perturbation index n = 1 . (b) The largest perturbation growth rate for the vortex with m = 1 versus α.

Fig. 4
Fig. 4

(a) Decay of unstable vortex with m = 1 , b = 3 , α = 3.5 . (b) Decay of unstable vortex with m = 2 , b = 20 , α = 4 . (c) Stable propagation of vortex with m = 1 , b = 30 , α = 5 (left, center) and vortex with m = 2 , b = 15 , α = 10 (right). In all cases, white noise was added to input field distributions.

Equations (2)

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

i q ξ = 1 2 2 q + σ ( r ) | q | 2 q ,
i δ u = 1 2 ( d 2 d r 2 + 1 r d d r ( m + n ) 2 r 2 ) u + b u + σ w 2 ( v + 2 u ) , i δ v = + 1 2 ( d 2 d r 2 + 1 r d d r ( m n ) 2 r 2 ) v b v σ w 2 ( u + 2 v ) .

Metrics