Abstract

We demonstrate the existence of a broad class of higher-order rotating spatial solitons in nonlocal nonlinear media. We employ the generalized Hermite–Laguerre–Gaussian ansatz for constructing multivortex soliton solutions and study numerically their dynamics and stability. We discuss in detail the tripole soliton carrying two spiraling phase dislocations, or self-trapped optical vortices.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, 288 (2004).
    [CrossRef]
  2. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
    [CrossRef] [PubMed]
  3. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
    [CrossRef]
  4. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
    [CrossRef] [PubMed]
  5. C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
    [CrossRef]
  6. A. Dreischuh, D. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
    [CrossRef] [PubMed]
  7. C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
    [CrossRef] [PubMed]
  8. D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
    [CrossRef] [PubMed]
  9. A. I. Yakimenko, Yu. A. Zaliznyak, and Yu. S. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
    [CrossRef]
  10. S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
    [CrossRef]
  11. A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, Phys. Rev. Lett. 95, 203904 (2005).
    [CrossRef] [PubMed]
  12. S. Lopez-Aguayo, A. S. Desyatnikov, and Yu. S. Kivshar, Opt. Express 14, 7903 (2006).
    [CrossRef] [PubMed]
  13. S. Skupin, M. Saffman, and W. Krolikowski, Phys. Rev. Lett. 98, 263902 (2007).
    [CrossRef] [PubMed]
  14. D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 98, 053901 (2007).
    [CrossRef] [PubMed]
  15. A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
    [CrossRef]
  16. S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, Opt. Lett. 31, 1100 (2006).
    [CrossRef] [PubMed]
  17. Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, Opt. Lett. 31, 1483 (2006).
    [CrossRef] [PubMed]
  18. E. G. Abramochkin and V. G. Volostnikov, J. Opt. A, Pure Appl. Opt. 6, S157 (2004).
    [CrossRef]
  19. Yu. S. Kivshar and G. Agrawal, Optical Solitons (Academic, 2003), Sec. 6.5, and references therein.
  20. N. N. Rozanov, Opt. Spectrosc. 96, 405 (2004).
    [CrossRef]
  21. D. Rozas and G. A. Swartzlander, Jr., Opt. Lett. 25, 126 (2000).
    [CrossRef]
  22. D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., Phys. Rev. Lett. 79, 3399 (1997).
    [CrossRef]
  23. A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (Elsevier, 2005), Vol. 47, p. 291, and references therein.
    [CrossRef]
  24. M. R. Dennis, New J. Phys. 5, 134 (2003).
    [CrossRef]
  25. J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
    [CrossRef] [PubMed]

2007 (2)

S. Skupin, M. Saffman, and W. Krolikowski, Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef] [PubMed]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

2006 (9)

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
[CrossRef]

S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, Opt. Lett. 31, 1100 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, Opt. Lett. 31, 1483 (2006).
[CrossRef] [PubMed]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

A. Dreischuh, D. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
[CrossRef] [PubMed]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

S. Lopez-Aguayo, A. S. Desyatnikov, and Yu. S. Kivshar, Opt. Express 14, 7903 (2006).
[CrossRef] [PubMed]

2005 (4)

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

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

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

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

2004 (5)

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, 288 (2004).
[CrossRef]

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

E. G. Abramochkin and V. G. Volostnikov, J. Opt. A, Pure Appl. Opt. 6, S157 (2004).
[CrossRef]

N. N. Rozanov, Opt. Spectrosc. 96, 405 (2004).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef] [PubMed]

2003 (1)

M. R. Dennis, New J. Phys. 5, 134 (2003).
[CrossRef]

2000 (1)

1997 (1)

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

E. G. Abramochkin and V. G. Volostnikov, J. Opt. A, Pure Appl. Opt. 6, S157 (2004).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt. (1)

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, 288 (2004).
[CrossRef]

Nat. Phys. (2)

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
[CrossRef]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
[CrossRef]

Nature (1)

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef] [PubMed]

New J. Phys. (1)

M. R. Dennis, New J. Phys. 5, 134 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Opt. Spectrosc. (1)

N. N. Rozanov, Opt. Spectrosc. 96, 405 (2004).
[CrossRef]

Phys. Rev. E (3)

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
[CrossRef]

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

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

Phys. Rev. Lett. (7)

A. S. Desyatnikov, A. A. Sukhorukov, 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]

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

S. Skupin, M. Saffman, and W. Krolikowski, Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef] [PubMed]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

A. Dreischuh, D. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
[CrossRef] [PubMed]

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

Other (2)

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (Elsevier, 2005), Vol. 47, p. 291, and references therein.
[CrossRef]

Yu. S. Kivshar and G. Agrawal, Optical Solitons (Academic, 2003), Sec. 6.5, and references therein.

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

Family of the tripole-like solitons for power P = 200 versus α. The cross sections of the beam profiles are shown in the top row. The colors for intensity (middle row) are mapped from zero (blue online) to maximal value (red online), while phase (bottom row) is scaled from π to π.

Fig. 2
Fig. 2

(a) Rotation velocity (4) of the tripole solitons. (b) Stability domain in the parameter plane ( α , P ) .

Fig. 3
Fig. 3

Propagation dynamics of the tripole with α = π 8 , k = 89.4 , and P = 200 . The corresponding variational solution predicts Ω = 1.89 , which corresponds to the period of rotation (pitch) 3.33 ; the numerically obtained values are very close, pitch 3.03 and Ω 2.07 .

Fig. 4
Fig. 4

Double helix formed by the braided nodal lines obtained by tracing the spatial locations of the vortex cores during propagation in Fig. 3.

Equations (5)

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

i E z + 2 E x 2 + 2 E y 2 + E R ( r r ) E ( r ) 2 d r = 0 ,
U n m ( x , y ; α ) = A exp ( x 2 2 a x 2 y 2 2 a y 2 ) × j = 0 n + m C n m j ( α ) H n + m j ( x b x ) H j ( y b y ) .
U 20 ( x , y ; α ) = A exp ( ( x 2 + y 2 ) 2 a 2 ) × [ 4 ( x cos α + i y sin α ) 2 b 2 cos 2 α ] .
Ω = Ω ln + A 2 Ω nln ,
R ( r r ) E ( r ) 2 d r ( 1 r 2 σ 2 ) P π σ 2 .

Metrics