Abstract

We introduce a type of (2+1)D surface soliton in virtue of the cooperation of nonlocal and local nonlinearities. Furthermore, taking advantage of diffusion and drift nonlinearity this type of surface soliton is demonstrated theoretically and experimentally in a storintium barium nitrate crystal. The dynamics behavior of the excitation and propagation of this type of surface soliton are studied using the beam-propagation method and the nonlinear equation of light rays.

© 2009 Optical Society of America

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  1. I. I. Smolyaninov, C. H. Lee, and C. C. Davis, Phys. Rev. Lett. 83, 2429 (1999).
    [CrossRef]
  2. D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).
  3. P. Varatharajah, A. B. Aceves, J. V. Moloney, and E. M. Wright, J. Opt. Soc. Am. B 7, 220 (1990).
    [CrossRef]
  4. P. Varatharajah, A. Aceves, J. V. Moloney, D. R. Heatley, and E. M. Wright, Opt. Lett. 13, 690 (1988).
    [CrossRef] [PubMed]
  5. G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
    [CrossRef] [PubMed]
  6. M. Cronin-Golomb, Opt. Lett. 20, 2075 (1995).
    [CrossRef] [PubMed]
  7. T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
    [CrossRef]
  8. V. A. Aleshkevich, V. A. Vysloukh, and Y. V. Kartashev, Quantum Electron. 30, 905 (2000).
    [CrossRef]
  9. V. A. Aleshkevich, V. A. Vysloukh, A. A. Egorov, and Y. V. Kartashev, Quantum Electron. 31, 713 (2001).
    [CrossRef]
  10. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 98, 213901 (2007).
    [CrossRef] [PubMed]
  11. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, Opt. Lett. 30, 2466 (2005).
    [CrossRef] [PubMed]
  12. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef] [PubMed]
  13. A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
    [CrossRef]
  14. X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
    [CrossRef] [PubMed]

2007 (4)

T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
[CrossRef]

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

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

2006 (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

2005 (1)

2001 (1)

V. A. Aleshkevich, V. A. Vysloukh, A. A. Egorov, and Y. V. Kartashev, Quantum Electron. 31, 713 (2001).
[CrossRef]

2000 (1)

V. A. Aleshkevich, V. A. Vysloukh, and Y. V. Kartashev, Quantum Electron. 30, 905 (2000).
[CrossRef]

1999 (1)

I. I. Smolyaninov, C. H. Lee, and C. C. Davis, Phys. Rev. Lett. 83, 2429 (1999).
[CrossRef]

1995 (2)

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

M. Cronin-Golomb, Opt. Lett. 20, 2075 (1995).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).

1988 (1)

Aceves, A.

Aceves, A. B.

Aleshkevich, V. A.

V. A. Aleshkevich, V. A. Vysloukh, A. A. Egorov, and Y. V. Kartashev, Quantum Electron. 31, 713 (2001).
[CrossRef]

V. A. Aleshkevich, V. A. Vysloukh, and Y. V. Kartashev, Quantum Electron. 30, 905 (2000).
[CrossRef]

Alfassi, B.

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

Bertolotti, M.

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).

Bezryadina, A.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Chen, Z.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Christodoulides, D. N.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

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

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, Opt. Lett. 30, 2466 (2005).
[CrossRef] [PubMed]

Cronin-Golomb, M.

Davis, C. C.

I. I. Smolyaninov, C. H. Lee, and C. C. Davis, Phys. Rev. Lett. 83, 2429 (1999).
[CrossRef]

Dreisow, F.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Egorov, A. A.

V. A. Aleshkevich, V. A. Vysloukh, A. A. Egorov, and Y. V. Kartashev, Quantum Electron. 31, 713 (2001).
[CrossRef]

Feng, L.

T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
[CrossRef]

Garcia Quirino, G. S.

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Hache, A.

Heatley, D. R.

Hu, Z. J.

T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
[CrossRef]

Kang, H. Z.

T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
[CrossRef]

Kartashev, Y. V.

V. A. Aleshkevich, V. A. Vysloukh, A. A. Egorov, and Y. V. Kartashev, Quantum Electron. 31, 713 (2001).
[CrossRef]

V. A. Aleshkevich, V. A. Vysloukh, and Y. V. Kartashev, Quantum Electron. 30, 905 (2000).
[CrossRef]

Kartashov, Y. V.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

Lee, C. H.

I. I. Smolyaninov, C. H. Lee, and C. C. Davis, Phys. Rev. Lett. 83, 2429 (1999).
[CrossRef]

Lou, C. B.

T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
[CrossRef]

Makris, K. G.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, Opt. Lett. 30, 2466 (2005).
[CrossRef] [PubMed]

Manela, O.

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

Mihalache, D.

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).

Moloney, J. V.

Nolte, S.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Pertsch, T.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Ren, X. K.

T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
[CrossRef]

Rotschild, C.

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

Sanchez-Mondragon, J. J.

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Segev, M.

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

Shao, W. W.

T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
[CrossRef]

Sibilia, C.

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).

Smolyaninov, I. I.

I. I. Smolyaninov, C. H. Lee, and C. C. Davis, Phys. Rev. Lett. 83, 2429 (1999).
[CrossRef]

Stegeman, G. I.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Hache, Opt. Lett. 30, 2466 (2005).
[CrossRef] [PubMed]

Stepanov, S.

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Suntsov, S.

Szameit, A.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Torner, L.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

Tünnermann, A.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Varatharajah, P.

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

V. A. Aleshkevich, V. A. Vysloukh, A. A. Egorov, and Y. V. Kartashev, Quantum Electron. 31, 713 (2001).
[CrossRef]

V. A. Aleshkevich, V. A. Vysloukh, and Y. V. Kartashev, Quantum Electron. 30, 905 (2000).
[CrossRef]

Wang, B. H.

T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
[CrossRef]

Wang, X.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Wright, E. M.

Xu, J. J.

T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
[CrossRef]

Xu, Y. H.

T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
[CrossRef]

Yang, D. P.

T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
[CrossRef]

Yang, J.

T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
[CrossRef]

Zhang, T. H.

T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
[CrossRef]

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

Opt. Lett. (3)

Phys. Rev. A (2)

T. H. Zhang, X. K. Ren, B. H. Wang, C. B. Lou, Z. J. Hu, W. W. Shao, Y. H. Xu, H. Z. Kang, J. Yang, D. P. Yang, L. Feng, and J. J. Xu, Phys. Rev. A 76, 013827 (2007).
[CrossRef]

G. S. Garcia Quirino, J. J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

I. I. Smolyaninov, C. H. Lee, and C. C. Davis, Phys. Rev. Lett. 83, 2429 (1999).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

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

Prog. Opt. (1)

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).

Quantum Electron. (2)

V. A. Aleshkevich, V. A. Vysloukh, and Y. V. Kartashev, Quantum Electron. 30, 905 (2000).
[CrossRef]

V. A. Aleshkevich, V. A. Vysloukh, A. A. Egorov, and Y. V. Kartashev, Quantum Electron. 31, 713 (2001).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Sketch of a 2D surface soliton, (b) trajectories of the incident beam with the beam center coordinates x = 200 μ m for one-time reflection, (c) x = 22 μ m for five-times reflection, (d) x = 16.75 μ m for steadily propagated PR surface soliton. The applied external electric field is E 0 = 4000 V cm . The FWHMs of the incident beam at z = 0 cm are all 10 μ m . The crystal surface is located at x = 0 μ m .

Fig. 2
Fig. 2

Self-bending of PR screening soliton. The incident beam is converged and self-bended and reaches the steady state at 45 s .

Fig. 3
Fig. 3

One-time reflection of a PR screening soliton at the boundary with x = 85 μ m : (a) input image; (b) output image at 0 s . (c), (d) Incident beam is converged and (e) self-bended to the interface at the 8 s , then (f) reflected to the bulk and (g) reaches the steady state at the 45 s ; (h) steady output image at 95 s .

Fig. 4
Fig. 4

Two-times reflection of PR screening soliton at the boundary with x = 35 μ m : (a) the input image; (b) output image at 0 s . (c) Incident beam is converged and self-bended to the interface for the first time at 2.33 s , then (d) reflected to the bulk and (e) self-bended to the interface again at 7.67 s then (f) reflected for the second time; it (g) reaches the steady state at the 45 s and (h) steady output image in at 95 s .

Fig. 5
Fig. 5

Formation of the PR surface soliton when the incident beam was launched very closed to the c boundary with x = 15 μ m ; (a) the input image; (b) output image at 0 s . (c) Incident beam is converged and (d) self-bended to the interface at the 4 s then (e) confined near the interface, and (f) the image at the output face reaches the steady state at the 17 s , and the (g), (h) steady output image at 45 s and 95 s , respectively.

Equations (4)

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

2 E ( x , y , z ) + k 2 E ( x , y , z ) = 0 ,
E SC ( x , y ) = k B T e ln [ I ( x , y ) + I d + I b ] + E 0 ( I d + I b ) I ( x , y ) + I d + I b ,
d 2 x d z 2 + 1 n ( x ) d n ( x ) d x d x 2 d z 2 1 n ( x ) d n ( x ) d x = 0 ,
d n ( x ) d x = d d x { 1 2 n 3 r eff { E 0 A 2 ( x ) + 1 + k B T e d d x [ ln ( A 2 ( x ) + 1 ) ] } } .

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