Abstract

We have introduced a novel class of higher-order spatial optical Ince–Gaussian solitons (IGSs) that constitute the third complete family of exact and orthogonal soliton solutions of the Snyder–Mitchell model. The transverse structure of the IGSs is characterized by the Ince polynomials and has an inherent elliptical symmetry. The IGSs form the exact and continuous transition modes between Hermite–Gaussian solitons and Laguerre–Gaussian solitons.

© 2007 Optical Society of America

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  1. A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
    [CrossRef]
  2. A. W. Snyder and Y. Kivshar, J. Opt. Soc. Am. B 11, 3025 (1997).
    [CrossRef]
  3. W. Krolikowski and O. Bang, Phys. Rev. E 63, 016610 (2000).
    [CrossRef]
  4. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
    [CrossRef] [PubMed]
  5. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
    [CrossRef] [PubMed]
  6. D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 98, 053901 (2007).
    [CrossRef] [PubMed]
  7. D. M. Deng, X. Zhao, Q. Guo, and S. Lan, J. Opt. Soc. Am. B 24, 2537 (2007).
    [CrossRef]
  8. D. M. Deng and Q. Guo, "Propagation of Laguerre-Gaussian beams in nonlocal nonlinear media," J. Opt. Soc. Am. B (in preparation).
  9. Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, Phys. Rev. E 69, 016602 (2004).
    [CrossRef]
  10. Q. Guo, Proc. SPIE 5281, 581 (2004).
    [CrossRef]
  11. Y. Xie and Q. Guo, Opt. Quantum Electron. 36, 1335 (2004).
    [CrossRef]
  12. M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, Opt. Lett. 27, 1460 (2002).
    [CrossRef]
  13. M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Appl. Phys. Lett. 81, 3335 (2002).
    [CrossRef]
  14. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
    [CrossRef] [PubMed]
  15. X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
    [CrossRef]
  16. Z. Xu, Y. V. Kartashov, and L. Torner, Opt. Lett. 30, 3171 (2005).
    [CrossRef] [PubMed]
  17. S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
    [CrossRef]
  18. N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
    [CrossRef] [PubMed]
  19. A. Dreischuh, D. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
    [CrossRef] [PubMed]
  20. C. Rotschild, M. Segev, Z. Y. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
    [CrossRef] [PubMed]
  21. S. G. Ouyang, Q. Guo, and W. Hu, Phys. Rev. E 74, 036622 (2006).
    [CrossRef]
  22. P. D. Rasmussen, O. Bang, and W. Królikowski, Phys. Rev. E 72, 066611 (2005).
    [CrossRef]
  23. W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, Appl. Phys. Lett. 89, 071111 (2006).
    [CrossRef]
  24. A. I. Yakimenko, Y. A. Zaliznyak, and Y. Kivshar, Phys. Rev. E 71, 065603 (2005).
    [CrossRef]
  25. D. Briedis, D. E. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, Opt. Express 13, 435 (2005).
    [CrossRef] [PubMed]
  26. A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
    [CrossRef]
  27. Y. R. Shen, Science 276, 1520 (1997).
    [CrossRef]
  28. F. M. Arscott, Periodic Differential Equations (Pergamon, 1964).
  29. M. A. Bandres and J. C. Gutiérrez-Vega, Opt. Lett. 29, 144 (2004).
    [CrossRef] [PubMed]
  30. M. A. Bandres and J. C. Gutiérrez-Vega, Opt. Lett. 30, 540 (2005).
    [CrossRef] [PubMed]

2007

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

D. M. Deng, X. Zhao, Q. Guo, and S. Lan, J. Opt. Soc. Am. B 24, 2537 (2007).
[CrossRef]

2006

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

S. G. Ouyang, Q. Guo, and W. Hu, Phys. Rev. E 74, 036622 (2006).
[CrossRef]

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

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

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

2005

M. A. Bandres and J. C. Gutiérrez-Vega, Opt. Lett. 30, 540 (2005).
[CrossRef] [PubMed]

A. I. Yakimenko, Y. A. Zaliznyak, and Y. 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]

P. D. Rasmussen, O. Bang, and W. Królikowski, Phys. Rev. E 72, 066611 (2005).
[CrossRef]

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

Z. Xu, Y. V. Kartashov, and L. Torner, Opt. Lett. 30, 3171 (2005).
[CrossRef] [PubMed]

2004

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

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, Phys. Rev. E 69, 016602 (2004).
[CrossRef]

Q. Guo, Proc. SPIE 5281, 581 (2004).
[CrossRef]

Y. Xie and Q. Guo, Opt. Quantum Electron. 36, 1335 (2004).
[CrossRef]

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

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

M. A. Bandres and J. C. Gutiérrez-Vega, Opt. Lett. 29, 144 (2004).
[CrossRef] [PubMed]

2003

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

2002

M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, Opt. Lett. 27, 1460 (2002).
[CrossRef]

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Appl. Phys. Lett. 81, 3335 (2002).
[CrossRef]

2000

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

1997

A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
[CrossRef]

A. W. Snyder and Y. Kivshar, J. Opt. Soc. Am. B 11, 3025 (1997).
[CrossRef]

Y. R. Shen, Science 276, 1520 (1997).
[CrossRef]

1964

F. M. Arscott, Periodic Differential Equations (Pergamon, 1964).

Adamski, A.

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

Arscott, F. M.

F. M. Arscott, Periodic Differential Equations (Pergamon, 1964).

Assanto, G.

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

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Appl. Phys. Lett. 81, 3335 (2002).
[CrossRef]

M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, Opt. Lett. 27, 1460 (2002).
[CrossRef]

Bandres, M. A.

Bang, O.

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

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

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

P. D. Rasmussen, O. Bang, and W. Królikowski, Phys. Rev. E 72, 066611 (2005).
[CrossRef]

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

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

Briedis, D.

Brzdakiewicz, K. A.

Buccoliero, D.

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

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]

Chi, S.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, Phys. Rev. E 69, 016602 (2004).
[CrossRef]

Christiansen, P. L.

Cohen, O.

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

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]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Appl. Phys. Lett. 81, 3335 (2002).
[CrossRef]

Deng, D. M.

D. M. Deng, X. Zhao, Q. Guo, and S. Lan, J. Opt. Soc. Am. B 24, 2537 (2007).
[CrossRef]

D. M. Deng and Q. Guo, "Propagation of Laguerre-Gaussian beams in nonlocal nonlinear media," J. Opt. Soc. Am. B (in preparation).

Desyatnikov, A. S.

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

Dreischuh, A.

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

Edmundson, D.

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

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

Guo, Q.

D. M. Deng, X. Zhao, Q. Guo, and S. Lan, J. Opt. Soc. Am. B 24, 2537 (2007).
[CrossRef]

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

S. G. Ouyang, Q. Guo, and W. Hu, Phys. Rev. E 74, 036622 (2006).
[CrossRef]

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, Phys. Rev. E 69, 016602 (2004).
[CrossRef]

Q. Guo, Proc. SPIE 5281, 581 (2004).
[CrossRef]

Y. Xie and Q. Guo, Opt. Quantum Electron. 36, 1335 (2004).
[CrossRef]

D. M. Deng and Q. Guo, "Propagation of Laguerre-Gaussian beams in nonlocal nonlinear media," J. Opt. Soc. Am. B (in preparation).

Gutiérrez-Vega, J. C.

Haelterman, M.

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

Hu, W.

S. G. Ouyang, Q. Guo, and W. Hu, Phys. Rev. E 74, 036622 (2006).
[CrossRef]

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

Hutsebaut, X.

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

Kartashov, Y. V.

Kivshar, Y.

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

A. W. Snyder and Y. Kivshar, J. Opt. Soc. Am. B 11, 3025 (1997).
[CrossRef]

Kivshar, Y. S.

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

Krolikowski, W.

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

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

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

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

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

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

Królikowski, W.

P. D. Rasmussen, O. Bang, and W. Królikowski, Phys. Rev. E 72, 066611 (2005).
[CrossRef]

Lan, S.

D. M. Deng, X. Zhao, Q. Guo, and S. Lan, J. Opt. Soc. Am. B 24, 2537 (2007).
[CrossRef]

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

Lashkin, V. M.

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

Luca, A. D.

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Appl. Phys. Lett. 81, 3335 (2002).
[CrossRef]

Luo, B.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, Phys. Rev. E 69, 016602 (2004).
[CrossRef]

Manela, O.

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

Mitchell, D. J.

A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
[CrossRef]

Neshev, D.

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

N. I. Nikolov, D. Neshev, W. Krolikowski, O. Bang, J. J. Rasmussen, and P. L. Christiansen, Opt. Lett. 29, 286 (2004).
[CrossRef] [PubMed]

Neyts, K.

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

Nikolov, N. I.

Ouyang, S. G.

S. G. Ouyang, Q. Guo, and W. Hu, Phys. Rev. E 74, 036622 (2006).
[CrossRef]

Peccianti, M.

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

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Appl. Phys. Lett. 81, 3335 (2002).
[CrossRef]

M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, Opt. Lett. 27, 1460 (2002).
[CrossRef]

Petersen, D. E.

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

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

Prikhodko, O. O.

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

Rasmussen, J. J.

Rasmussen, P. D.

P. D. Rasmussen, O. Bang, and W. Królikowski, Phys. Rev. E 72, 066611 (2005).
[CrossRef]

Rotschild, C.

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

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

Segev, M.

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

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

Shen, Y. R.

Y. R. Shen, Science 276, 1520 (1997).
[CrossRef]

Skupin, S.

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

Snyder, A. W.

A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
[CrossRef]

A. W. Snyder and Y. Kivshar, J. Opt. Soc. Am. B 11, 3025 (1997).
[CrossRef]

Torner, L.

Umeton, C.

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Appl. Phys. Lett. 81, 3335 (2002).
[CrossRef]

Xie, Y.

Y. Xie and Q. Guo, Opt. Quantum Electron. 36, 1335 (2004).
[CrossRef]

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, Phys. Rev. E 69, 016602 (2004).
[CrossRef]

Xu, Z.

Xu, Z. Y.

Xuan, L.

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

Yakimenko, A. I.

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

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

Yi, F.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, Phys. Rev. E 69, 016602 (2004).
[CrossRef]

Zaliznyak, Y. A.

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

Zhang, T.

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

Zhao, X.

Appl. Phys. Lett.

M. Peccianti, C. Conti, G. Assanto, A. D. Luca, and C. Umeton, Appl. Phys. Lett. 81, 3335 (2002).
[CrossRef]

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, Appl. Phys. Lett. 89, 071111 (2006).
[CrossRef]

J. Opt. Soc. Am. B

A. W. Snyder and Y. Kivshar, J. Opt. Soc. Am. B 11, 3025 (1997).
[CrossRef]

D. M. Deng, X. Zhao, Q. Guo, and S. Lan, J. Opt. Soc. Am. B 24, 2537 (2007).
[CrossRef]

Opt. Commun.

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

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

Y. Xie and Q. Guo, Opt. Quantum Electron. 36, 1335 (2004).
[CrossRef]

Phys. Rev. E

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

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, Phys. Rev. E 69, 016602 (2004).
[CrossRef]

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

S. G. Ouyang, Q. Guo, and W. Hu, Phys. Rev. E 74, 036622 (2006).
[CrossRef]

P. D. Rasmussen, O. Bang, and W. Królikowski, Phys. Rev. E 72, 066611 (2005).
[CrossRef]

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

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

Phys. Rev. Lett.

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

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

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. 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]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
[CrossRef] [PubMed]

Proc. SPIE

Q. Guo, Proc. SPIE 5281, 581 (2004).
[CrossRef]

Science

A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
[CrossRef]

Y. R. Shen, Science 276, 1520 (1997).
[CrossRef]

Other

F. M. Arscott, Periodic Differential Equations (Pergamon, 1964).

D. M. Deng and Q. Guo, "Propagation of Laguerre-Gaussian beams in nonlocal nonlinear media," J. Opt. Soc. Am. B (in preparation).

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Figures (4)

Fig. 1
Fig. 1

Propagation dynamics of the even IG soliton in the Gaussian-shaped response material. (a)–(d) Transverse normalized intensity distributions from the analytical solution, (e)–(h) Distributions from the numerical simulation ( α = 0.1 ) , (i)–(l) distributions from the numerical simulation ( α = 0.3 ) , (m)–(p) normalized intensity distributions at y w 0 = 0 . The different columns represent the different propagation distances given at the top of the figure. In (m)–(p), the solid, dotted, and dashed curves are the analytical solutions and the numerical solutions for α = 0.1 and α = 0.3 , respectively; the solid and dotted curves are only a little bit different and cannot be distinguished by one’s eyes. The parameters are chosen as p = 3 , m = 3 , P 0 P c = 1 , ϵ = 2 , and z R = k w 0 2 is the Rayleigh range.

Fig. 2
Fig. 2

Propagation dynamics of the odd IG soliton in the Gaussian-shaped response material. All are the same as in Fig. 1, except y w 0 = 0.25 .

Fig. 3
Fig. 3

Propagation dynamics of the even IG soliton in the Gaussian-shaped response material. All are the same as in Fig. 1, except ϵ .

Fig. 4
Fig. 4

Propagation dynamics of the even IG soliton in the Gaussian-shaped response material. All are the same as in Fig. 1, except ϵ = 0 .

Equations (8)

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i Φ z + μ Φ + k Δ n n 0 Φ = 0 ,
i Φ z + μ Φ n 2 2 n 0 k γ P 0 r 2 Φ = 0 ,
Φ F = F ( ξ ) N ( ζ ) exp [ i θ ( z ) ] ϕ G ( r ) ,
d 2 F d ξ 2 ϵ sinh 2 ξ d F d ξ ( a p ϵ cosh 2 ξ ) F = 0 ,
d 2 N d ζ 2 + ϵ sin 2 ζ d N d ζ + ( a p ϵ cos 2 ζ ) N = 0 ,
w 0 2 2 μ d θ d z = p ,
Φ p m e = c p m e w 0 C p m ( i ξ , ϵ ) C p m ( ζ , ϵ ) exp ( r 2 2 w 0 2 i β p z ) ,
Φ p m o = s p m o w 0 S p m ( i ξ , ϵ ) S p m ( ζ , ϵ ) exp ( r 2 2 w 0 2 i β p z ) ,

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