Abstract

We reveal that lattice interfaces imprinted in nonlocal nonlinear media support surface solitons that do not exist in other similar settings, including interfaces of local and nonlocal uniform materials. We show the impact of nonlocality on the domains of existence and stability of the surface solitons, focusing on new types of dipole solitons residing partially inside the optical lattice. We find that such solitons feature strongly asymmetric shapes and that they are stable in large parts of their existence domain.

© 2006 Optical Society of America

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References

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  1. H.E.Ponath and G.I.Stegeman, eds., Nonlinear Surface Electromagnetic Phenomena (North-Holland, 1991).
  2. D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).
  3. A. A. Maradudin, in Optical and Acoustic Waves in Solids: Modern Topics, M.Borissov, ed. (World Scientific, 1983), p. 72.
  4. K. G. Makris, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, Opt. Lett. 30, 2466 (2005).
    [CrossRef] [PubMed]
  5. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
    [CrossRef] [PubMed]
  6. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef] [PubMed]
  7. C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, http://arxiv.org/abs/physics/0603202.
  8. M. Peccianti, C. Conti, and G. Assanto, Opt. Lett. 30, 415 (2005).
    [CrossRef] [PubMed]
  9. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, Opt. Lett. 29, 1530 (2004).
    [CrossRef] [PubMed]
  10. A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
    [CrossRef]
  11. W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
    [CrossRef]
  12. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
    [CrossRef] [PubMed]
  13. I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, Pis'ma Zh. Eksp. Teor. Fiz. 31, 333 (1980) I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev,[JETP Lett. 31, 304 (1980)].
  14. Z. Xu, Y. V. Kartashov, and L. Torner, Opt. Lett. 30, 3171 (2005).
    [CrossRef] [PubMed]
  15. A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 96, 043901 (2006).
    [CrossRef] [PubMed]
  16. S. Lopez-Aguayo, A. S. Desyatnikov, Y. 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. P. Varatharajah, A. Aceves, J. V. Moloney, D. R. Heatley, and E. M. Wright, Opt. Lett. 13, 690 (1988).
    [CrossRef] [PubMed]
  19. D. R. Andersen, Phys. Rev. A 37, 189 (1988).
    [CrossRef] [PubMed]

2006 (5)

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

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

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

S. Lopez-Aguayo, A. S. Desyatnikov, Y. 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]

2005 (4)

2004 (2)

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, Opt. Lett. 29, 1530 (2004).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

1997 (1)

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
[CrossRef]

1989 (1)

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

1988 (2)

1980 (1)

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, Pis'ma Zh. Eksp. Teor. Fiz. 31, 333 (1980) I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev,[JETP Lett. 31, 304 (1980)].

Aceves, A.

Andersen, D. R.

D. R. Andersen, Phys. Rev. A 37, 189 (1988).
[CrossRef] [PubMed]

Anderson, D. Z.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
[CrossRef]

Assanto, G.

Bang, O.

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

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

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

Bertolotti, M.

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

Brzdakiewicz, K. A.

Carmon, T.

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

Christodoulides, D. N.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

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

Cohen, O.

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

Conti, C.

Desyatnikov, A. S.

Dreischuh, A.

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

Edmundson, D.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

Fratalocchi, A.

Hache, A.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Heatley, D. R.

Karpierz, M. A.

Kartashov, Y. V.

Kivshar, Y. S.

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

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, http://arxiv.org/abs/physics/0603202.

Kolchugina, I. A.

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, Pis'ma Zh. Eksp. Teor. Fiz. 31, 333 (1980) I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev,[JETP Lett. 31, 304 (1980)].

Krolikowski, W.

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

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

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, http://arxiv.org/abs/physics/0603202.

Lopez-Aguayo, S.

Makris, K. G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

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

Mamaev, A. V.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
[CrossRef]

Manela, O.

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

Maradudin, A. A.

A. A. Maradudin, in Optical and Acoustic Waves in Solids: Modern Topics, M.Borissov, ed. (World Scientific, 1983), p. 72.

Mezentsev, V. K.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
[CrossRef]

Mihalache, D.

Mironov, V. A.

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, Pis'ma Zh. Eksp. Teor. Fiz. 31, 333 (1980) I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev,[JETP Lett. 31, 304 (1980)].

Mitchell, A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, http://arxiv.org/abs/physics/0603202.

Molina, M. I.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, http://arxiv.org/abs/physics/0603202.

Moloney, J. V.

Morandotti, R.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Neshev, D.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

Neshev, D. N.

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

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, http://arxiv.org/abs/physics/0603202.

Nikolov, N. I.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

Peccianti, M.

Petersen, D. E.

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

Rasmussen, J. J.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

Rosberg, C. R.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, http://arxiv.org/abs/physics/0603202.

Rotschild, C.

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

Saffman, M.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
[CrossRef]

Salamo, G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Segev, M.

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

Sergeev, A. M.

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, Pis'ma Zh. Eksp. Teor. Fiz. 31, 333 (1980) I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev,[JETP Lett. 31, 304 (1980)].

Sibilia, C.

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

Skupin, S.

Sorel, M.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Stegeman, G. I.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

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

Suntsov, S.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

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

Torner, L.

Varatharajah, P.

Vicencio, R. A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, http://arxiv.org/abs/physics/0603202.

Vysloukh, V. A.

Wright, E. M.

Wyller, J.

W. Krolikowski, O. Bang, N. I. Nikolov, D. Neshev, J. Wyller, J. J. Rasmussen, and D. Edmundson, J. Opt. B: Quantum Semiclassical Opt. 6, S288 (2004).
[CrossRef]

Xu, Z.

Yang, H.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Zozulya, A. A.

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
[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, S288 (2004).
[CrossRef]

Opt. Lett. (7)

Phys. Rev. A (2)

A. V. Mamaev, A. A. Zozulya, V. K. Mezentsev, D. Z. Anderson, and M. Saffman, Phys. Rev. A 56, R1110 (1997).
[CrossRef]

D. R. Andersen, Phys. Rev. A 37, 189 (1988).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

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

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

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

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

Pis'ma Zh. Eksp. Teor. Fiz. (1)

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, Pis'ma Zh. Eksp. Teor. Fiz. 31, 333 (1980) I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev,[JETP Lett. 31, 304 (1980)].

Prog. Opt. (1)

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

Other (3)

A. A. Maradudin, in Optical and Acoustic Waves in Solids: Modern Topics, M.Borissov, ed. (World Scientific, 1983), p. 72.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, http://arxiv.org/abs/physics/0603202.

H.E.Ponath and G.I.Stegeman, eds., Nonlinear Surface Electromagnetic Phenomena (North-Holland, 1991).

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Figures (3)

Fig. 1
Fig. 1

Profiles of single surface solitons with (a) b = 1.34 and (b) b = 2 at p = 1 , d = 5 . Profiles of dipole surface solitons with (c) b = 1.3 and (d) b = 3.2 at p = 1 , d = 3 . Black curves show the field distribution, red curves show the refractive index profile. In the gray regions R ( η ) 1 , while in the white regions R ( η ) < 1 .

Fig. 2
Fig. 2

(a) Energy flow versus propagation constant for the single surface solitons at p = 1 . (b) Domain of existence for single surface solitons on the ( b , p ) plane at d = 1 . (c) Energy flow versus propagation constant for dipole surface solitons at p = 1 . Domains of existence and stability for dipole surface solitons on the ( b , p ) plane at (d) d = 1 and on the ( b , d ) plane at (e) p = 1 . (f) Real part of perturbation growth rate versus propagation constant for dipole surface soliton at p = 1.25 and d = 1 . Points marked by circles in (a) and (c) correspond to the solitons shown in Figs. 1a, 1b, 1c, 1d.

Fig. 3
Fig. 3

Propagation dynamics of a single surface soliton at (a) b = 1.4 , p = 1 , d = 5 and a dipole surface soliton at (b) b = 1.6 , p = 1 , d = 3 . The field modulus is shown. In both cases white noise with variance σ noise 2 = 0.01 was added to the input field distributions.

Equations (4)

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

i q ξ = 1 2 2 q η 2 q n p R q ,
n d 2 n η 2 = q 2 ,
δ u = 1 2 d 2 v d η 2 + b v n v p R v ,
δ v = 1 2 d 2 u d η 2 b u + n u + w Δ n + p R u ,

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