Abstract

We investigate, both experimentally and theoretically, the interaction of (2D+1) spatial solitons with the boundaries of a nonlinear medium in the presence of nonlocality. We demonstrate power-dependent nonlinear repulsion at the boundaries, in quantitative agreement with the model predictions.

© 2007 Optical Society of America

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References

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  1. Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).
  2. M. Peccianti and G. Assanto, Opt. Lett. 26, 1690 (2001).
    [CrossRef]
  3. M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, Nature 432, 733 (2004).
    [CrossRef] [PubMed]
  4. C. Conti and G. Assanto, in Encyclopedia of Modern Optics, R.D.Guenther, D.G.Steel, and L.Bayvel, eds. (Elsevier, 2004), Vol. 5, pp. 43-55.
  5. A. B. Aceves, J. V. Moloney, and A. C. Newell, Phys. Rev. A 39, 1809 (1989).
    [CrossRef] [PubMed]
  6. L. Jankovic, H. Kim, G. Stegeman, S. Carrasco, L. Torner, and M. Katz, Opt. Lett. 28, 2103 (2003).
    [CrossRef] [PubMed]
  7. F. Baronio, C. De Angelis, P.-H. Pioger, V. Couderc, and A. Barthelemy, Opt. Lett. 29, 986 (2004).
    [CrossRef] [PubMed]
  8. E. Alvarado-Mendez, R. Rojas-Laguna, J. G. Aviña-Cervantes, M. Torres-Cisneros, J. A. Andrade-Lucio, R. Ramos-Garcia, E. A. Kuzin, J. J. Sánchez-Mondragón, and V. Vysloukh, Opt. Commun. 193, 267 (2001).
    [CrossRef]
  9. C. Rothschild, B. Alfassi, O. Cohen, and M. Segev, Nat. Phys. 2, 769 (2006).
    [CrossRef]
  10. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Opt. Lett. 32, 154 (2007).
    [CrossRef]
  11. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, Nat. Phys. 2, 737 (2006).
    [CrossRef]
  12. M. Peccianti, G. Assanto, A. Dyadyusha, and M. Kaczmarek, Opt. Lett. 32, 271 (2007).
    [CrossRef] [PubMed]
  13. A. W. Snyder and D. J. Mitchell, Science 276, 1538 (1997)
    [CrossRef]
  14. W. Krolikowski and O. Bang, Phys. Rev. E 63, 016610 (2000).
    [CrossRef]
  15. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
    [CrossRef] [PubMed]
  16. M. Peccianti and G. Assanto, Opt. Lett. 26, 1791 (2001).
    [CrossRef]
  17. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 91, 073901 (2003).
    [CrossRef] [PubMed]
  18. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
    [CrossRef] [PubMed]
  19. Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. E 73, 055601 (2006).
    [CrossRef]
  20. G. Assanto, M. Peccianti, and C. Conti, Opt. Photon. News 14(2) 44 (2003).
    [CrossRef]
  21. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. E 72, 066614 (2005).
    [CrossRef]
  22. M. Peccianti and G. Assanto, Opt. Lett. 30, 415 (2005).
    [CrossRef] [PubMed]

2007 (2)

2006 (3)

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

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

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. E 73, 055601 (2006).
[CrossRef]

2005 (3)

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. E 72, 066614 (2005).
[CrossRef]

M. Peccianti and G. Assanto, Opt. Lett. 30, 415 (2005).
[CrossRef] [PubMed]

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

2004 (3)

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

F. Baronio, C. De Angelis, P.-H. Pioger, V. Couderc, and A. Barthelemy, Opt. Lett. 29, 986 (2004).
[CrossRef] [PubMed]

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

2003 (3)

L. Jankovic, H. Kim, G. Stegeman, S. Carrasco, L. Torner, and M. Katz, Opt. Lett. 28, 2103 (2003).
[CrossRef] [PubMed]

G. Assanto, M. Peccianti, and C. Conti, Opt. Photon. News 14(2) 44 (2003).
[CrossRef]

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

2001 (3)

E. Alvarado-Mendez, R. Rojas-Laguna, J. G. Aviña-Cervantes, M. Torres-Cisneros, J. A. Andrade-Lucio, R. Ramos-Garcia, E. A. Kuzin, J. J. Sánchez-Mondragón, and V. Vysloukh, Opt. Commun. 193, 267 (2001).
[CrossRef]

M. Peccianti and G. Assanto, Opt. Lett. 26, 1690 (2001).
[CrossRef]

M. Peccianti and G. Assanto, Opt. Lett. 26, 1791 (2001).
[CrossRef]

2000 (1)

W. Krolikowski and O. Bang, Phys. Rev. E 63, 016610 (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]

Nat. Phys. (2)

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

C. Rothschild, 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. Commun. (1)

E. Alvarado-Mendez, R. Rojas-Laguna, J. G. Aviña-Cervantes, M. Torres-Cisneros, J. A. Andrade-Lucio, R. Ramos-Garcia, E. A. Kuzin, J. J. Sánchez-Mondragón, and V. Vysloukh, Opt. Commun. 193, 267 (2001).
[CrossRef]

Opt. Lett. (7)

Opt. Photon. News (1)

G. Assanto, M. Peccianti, and C. Conti, Opt. Photon. News 14(2) 44 (2003).
[CrossRef]

Phys. Rev. A (1)

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

Phys. Rev. E (3)

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

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. E 72, 066614 (2005).
[CrossRef]

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. E 73, 055601 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

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. 91, 073901 (2003).
[CrossRef] [PubMed]

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

Science (1)

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

Other (2)

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic, 2003).

C. Conti and G. Assanto, in Encyclopedia of Modern Optics, R.D.Guenther, D.G.Steel, and L.Bayvel, eds. (Elsevier, 2004), Vol. 5, pp. 43-55.

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Figures (3)

Fig. 1
Fig. 1

(a) Boundary force W 0 versus beam position x for P = 1 2 (squares), 2 2 (solid curve) and 3 2 mW (dotted curve) in E7 and cell thickness a = 100 μ m . (b) Corresponding oscillation period Λ versus x for zero initial momentum (i.e., k x ̂ = 0 ). (c) Calculated trajectories of a 2 mW nematicon versus propagation s for various input positions x .

Fig. 2
Fig. 2

(a) 3D sketch of the experimental configuration: the molecular director lies in the cell plane s t z y and the transverse dynamics takes place in x s . (b) Side view: spatial solitons are excited with an input elevation ξ and propagate along s (gray curve) in the plane x s ; as power increases, so does the repulsive force, and the nematicon is pushed away from the (lower) boundary (trajectory in black).

Fig. 3
Fig. 3

(a) Calculated soliton trajectories for the experimental conditions used in (b) and input powers P = 1.5 , 3, 6 mW . (b) Collected and superimposed photographs of SS profiles at the cell output for various powers; the squares correspond to the powers indicated in (c). (c) Experimental (squares) and calculated (curve) output SS positions versus input power. For the fits we used a coupling coefficient factor of 0.7.

Equations (7)

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2 i k A s + T 2 A + 2 n 0 k V 2 Δ n ( A 2 ) A = 0 ,
m d 2 r d s 2 = φ 2 V d x d t ,
m d 2 x d s 2 = X ( x , s ) V e q x ( x , s ) x d x ,
g 1 ( x , t ) = G ( x , t , ζ , η ) A ( ζ , η ) 2 d ζ d η ,
g 2 ( x , t ) = G ( x , t , ζ , η ) A ( ξ , η ) 2 g 1 ( ζ , η ) d ζ d η ,
G ( x , t , ζ , η ) = n = 1 1 π n sin ( π n a ζ ) e π n a t η sin ( π n a x )
W 0 = k 0 ε a 2 n 0 { W 0 ψ sin ( 2 Θ ) + W 0 ψ 2 cos ( 2 Θ ) } ,

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