Abstract

We investigate the propagation of spatial solitons in cylindrical strongly nonlocal media by a method of image beam of light. The dynamic force of the soliton steering resulting from the boundary effect is equivalent to the force between the soliton beam and the image beam. The trajectory of the soliton is analytically studied, which is in good agreement with the experimental results.

© 2009 Optical Society of America

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References

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  1. A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997).
    [CrossRef]
  2. C. Rotschild, M. Segev, Z. Y. Xu, Y. V. Kartashov, and L. Torner, Opt. Lett. 31, 3312 (2006).
    [CrossRef] [PubMed]
  3. C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
    [CrossRef]
  4. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007).
    [CrossRef] [PubMed]
  5. C. Rotschild, O. Cohen, O. Manela, and M. Segev, Phys. Rev. Lett. 95, 213904 (2005).
    [CrossRef] [PubMed]
  6. B. Alfassi, C. Rotschild, O. Manela, and M. Segev, Opt. Lett. 32, 154 (2007).
    [CrossRef]
  7. A. Alberucci, M. Peccianti, and G. Assanto, Opt. Lett. 32, 2795 (2007).
    [CrossRef] [PubMed]
  8. A. Alberucci and G. Assanto, J. Opt. Soc. Am. B 24, 2314 (2007).
    [CrossRef]
  9. M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
    [CrossRef]
  10. M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, Opt. Lett. 27, 1460 (2002).
    [CrossRef]
  11. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
    [CrossRef] [PubMed]
  12. M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, Nature 432, 733 (2004).
    [CrossRef] [PubMed]
  13. Q. Guo, B. Luo, F. H. Yi, S. Chi, and Y. Q. Xie, Phys. Rev. E 69, 016602 (2004).
    [CrossRef]
  14. W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, Appl. Phys. Lett. 89, 071111 (2006).
    [CrossRef]
  15. Z. P. Dai, Y. Q. Wang, and Q. Guo, Phys. Rev. A 77, 063834 (2008).
    [CrossRef]
  16. D. M. Deng and Q. Guo, Opt. Lett. 32, 3206 (2007).
    [CrossRef] [PubMed]
  17. A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
    [CrossRef] [PubMed]
  18. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  19. Y. B. Liang, Y. J. Zheng, P. B. Yang, L. G. Cao, D. Q. Lu, W. Hu, and Q. Guo, Acta Phys. Sin. 57, 5690 (2008).

2008 (2)

Z. P. Dai, Y. Q. Wang, and Q. Guo, Phys. Rev. A 77, 063834 (2008).
[CrossRef]

Y. B. Liang, Y. J. Zheng, P. B. Yang, L. G. Cao, D. Q. Lu, W. Hu, and Q. Guo, Acta Phys. Sin. 57, 5690 (2008).

2007 (5)

2006 (3)

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

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

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

2005 (1)

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

2004 (2)

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

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

2003 (1)

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

2002 (1)

2000 (1)

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

1997 (1)

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

1989 (1)

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef] [PubMed]

Aceves, A. B.

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef] [PubMed]

Alberucci, A.

Alfassi, B.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

B. Alfassi, C. Rotschild, O. Manela, and M. Segev, Opt. Lett. 32, 154 (2007).
[CrossRef]

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

Assanto, G.

A. Alberucci, M. Peccianti, and G. Assanto, Opt. Lett. 32, 2795 (2007).
[CrossRef] [PubMed]

A. Alberucci and G. Assanto, J. Opt. Soc. Am. B 24, 2314 (2007).
[CrossRef]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

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

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

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Brzdakiewicz, K. A.

Cao, L. G.

Y. B. Liang, Y. J. Zheng, P. B. Yang, L. G. Cao, D. Q. Lu, W. Hu, and Q. Guo, Acta Phys. Sin. 57, 5690 (2008).

Chi, S.

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

Christodoulides, D. N.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

Cohen, O.

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

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

Conti, C.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

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

Dai, Z. P.

Z. P. Dai, Y. Q. Wang, and Q. Guo, Phys. Rev. A 77, 063834 (2008).
[CrossRef]

De Luca, A.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

De Rossi, A.

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Deng, D. M.

Guo, Q.

Z. P. Dai, Y. Q. Wang, and Q. Guo, Phys. Rev. A 77, 063834 (2008).
[CrossRef]

Y. B. Liang, Y. J. Zheng, P. B. Yang, L. G. Cao, D. Q. Lu, W. Hu, and Q. Guo, Acta Phys. Sin. 57, 5690 (2008).

D. M. Deng and Q. Guo, Opt. Lett. 32, 3206 (2007).
[CrossRef] [PubMed]

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

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

Hu, W.

Y. B. Liang, Y. J. Zheng, P. B. Yang, L. G. Cao, D. Q. Lu, W. Hu, and Q. Guo, Acta Phys. Sin. 57, 5690 (2008).

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

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Kartashov, Y. V.

Khoo, I. C.

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Lan, S.

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

Liang, Y. B.

Y. B. Liang, Y. J. Zheng, P. B. Yang, L. G. Cao, D. Q. Lu, W. Hu, and Q. Guo, Acta Phys. Sin. 57, 5690 (2008).

Lu, D. Q.

Y. B. Liang, Y. J. Zheng, P. B. Yang, L. G. Cao, D. Q. Lu, W. Hu, and Q. Guo, Acta Phys. Sin. 57, 5690 (2008).

Luo, B.

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

Manela, O.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

B. Alfassi, C. Rotschild, O. Manela, and M. Segev, Opt. Lett. 32, 154 (2007).
[CrossRef]

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

Mitchell, D. J.

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

Moloney, J. V.

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef] [PubMed]

Newell, A. C.

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef] [PubMed]

Peccianti, M.

A. Alberucci, M. Peccianti, and G. Assanto, Opt. Lett. 32, 2795 (2007).
[CrossRef] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

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

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

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Rotschild, C.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

B. Alfassi, C. Rotschild, O. Manela, and M. Segev, Opt. Lett. 32, 154 (2007).
[CrossRef]

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

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

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

Segev, M.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

B. Alfassi, C. Rotschild, O. Manela, and M. Segev, Opt. Lett. 32, 154 (2007).
[CrossRef]

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

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

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

Snyder, A. W.

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

Torner, L.

Umeton, C.

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

Wang, Y. Q.

Z. P. Dai, Y. Q. Wang, and Q. Guo, Phys. Rev. A 77, 063834 (2008).
[CrossRef]

Xie, Y. Q.

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

Xu, Z. Y.

Xuan, L.

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

Yang, P. B.

Y. B. Liang, Y. J. Zheng, P. B. Yang, L. G. Cao, D. Q. Lu, W. Hu, and Q. Guo, Acta Phys. Sin. 57, 5690 (2008).

Yi, F. H.

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

Zhang, T.

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

Zheng, Y. J.

Y. B. Liang, Y. J. Zheng, P. B. Yang, L. G. Cao, D. Q. Lu, W. Hu, and Q. Guo, Acta Phys. Sin. 57, 5690 (2008).

Acta Phys. Sin. (1)

Y. B. Liang, Y. J. Zheng, P. B. Yang, L. G. Cao, D. Q. Lu, W. Hu, and Q. Guo, Acta Phys. Sin. 57, 5690 (2008).

Appl. Phys. Lett. (2)

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

M. Peccianti, A. De Rossi, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, Appl. Phys. Lett. 77, 7 (2000).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nat. Phys. (1)

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

Nature (1)

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, Nature 432, 733 (2004).
[CrossRef] [PubMed]

Opt. Lett. (5)

Phys. Rev. A (2)

Z. P. Dai, Y. Q. Wang, and Q. Guo, Phys. Rev. A 77, 063834 (2008).
[CrossRef]

A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
[CrossRef] [PubMed]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (3)

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

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007).
[CrossRef] [PubMed]

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

Science (1)

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

Other (1)

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

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Figures (3)

Fig. 1
Fig. 1

(a) Diagrammatic layout of a soliton launched at an offset of x 0 in a circular cross section of the sample with radius R. (b) Sketch map of the normalized refractive indexes respectively induced by the soliton beam and the image beam.

Fig. 2
Fig. 2

(a) Oscillation period of the soliton trajectory verses the input offset. The dashed-dotted line, the dashed curve, and the solid curve are the analytical results under the first-order approximation, the third-order approximation, and the fifth-order approximation, respectively. The circles are the numerical results. (b) Beam oscillation at the input offset of 0.4 R versus the propagation distance. The comparison is between the analytical result under the fifth-order approximation (solid curve) and the numerical result (circles). The oscillation period in Fig. 2a and the propagation distance in Fig. 2b are normalized by the Rayleigh distance with w 0 = 1 / 30 R .

Fig. 3
Fig. 3

Net steering relative to the input offset verses the input offset. Squares, experimental result; dashed-dotted curve, first approximation solution x c 0 x c ( 1 ) ; dashed curve, third approximation solution x c 0 x c ( 3 ) ; solid curve, fifth approximation solution x c 0 x c ( 5 ) .

Equations (13)

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

2 T ( X , Y ) = α κ I ( X , Y ) ,
T ( X , Y ) X 2 + Y 2 = R 2 = T 0 ,
2 A + 2 i k A z + 2 k 2 Δ n n 0 A = 0 ,
i z φ + 1 2 2 φ + N φ = 0 ,
2 N ( x , y ) = | φ | 2 ,
N ( x , y ) x 2 + y 2 = 1 = 0 ,
G = 1 2 π ( ln 1 | r r | ln r | r r | ) = G 1 + G 2 ,
f = d 2 x c d z 2 p 1 / x c x c ,
N = ( G 1 + G 2 ) | φ ( x x c , y ) | 2 d x d y = N 1 + N 2 .
N 2 = 1 2 π ln r | r r | | φ ( x x c , y ) | 2 d x d y = p 2 π ln 1 / x c ( x 1 / x c ) 2 + y 2 .
d 2 x c d z 2 = | d N 2 d x | x = x c , y = 0 = p 2 π 1 1 / x c x c .
d 2 x c d z 2 = p 2 π ( x c + x c 3 + x c 5 ) .
x c ( z ) = x c 0   cos ( p π z ) ,

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