Abstract

We numerically study soliton dynamics at the interface between media with uniform and periodically modulated self-focusing nonlinearities. We find that the soliton can spontaneously laterally drift if its power is large enough. The drift direction can be controlled by changing the sign of the nonlinear modulation coefficient. We also study the dynamics of soliton launched with a tilt angle toward the nonlinear interface and reveal unique features, such as soliton rebound, penetration, and trapping.

© 2010 Optical Society of America

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  1. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1747 (2008).
    [CrossRef] [PubMed]
  2. Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Phys. Rev. A 80, 053816 (2009).
    [CrossRef]
  3. H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601(2006).
    [CrossRef]
  4. Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
    [CrossRef] [PubMed]
  5. F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, Opt. Express 17, 11328 (2009).
    [CrossRef] [PubMed]
  6. W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
    [CrossRef] [PubMed]
  7. D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
    [CrossRef] [PubMed]
  8. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef] [PubMed]
  9. C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
    [CrossRef] [PubMed]
  10. K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774(2006).
    [CrossRef] [PubMed]
  11. E. Smirnov, M. Stepić, C. E. Rüter, D. Kip, and V. Shandarov, Opt. Lett. 31, 2338 (2006).
    [CrossRef] [PubMed]
  12. M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 31, 2332 (2006).
    [CrossRef] [PubMed]
  13. X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
    [CrossRef] [PubMed]
  14. Y. J. He, W. H. Chen, H. Z. Wang, and B. A. Malomed, Opt. Lett. 32, 1390 (2007).
    [CrossRef] [PubMed]
  15. Y. Kominis, A. Papadopoulos, and K. Hizanidis, Opt. Express 15, 10041 (2007).
    [CrossRef] [PubMed]
  16. Y. Kominis and K. Hizanidis, Phys. Rev. Lett. 102, 133903(2009).
    [CrossRef] [PubMed]
  17. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
    [CrossRef]
  18. D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, Opt. Lett. 32, 3173 (2007).
    [CrossRef] [PubMed]
  19. D. Blömer, A. Szameit, F. Dreisow, T. Schreiber, S. Nolte, and A. Tünnermann, Opt. Express 14, 2151 (2006).
    [CrossRef] [PubMed]

2009 (3)

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Phys. Rev. A 80, 053816 (2009).
[CrossRef]

F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, Opt. Express 17, 11328 (2009).
[CrossRef] [PubMed]

Y. Kominis and K. Hizanidis, Phys. Rev. Lett. 102, 133903(2009).
[CrossRef] [PubMed]

2008 (2)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1747 (2008).
[CrossRef] [PubMed]

2007 (4)

2006 (8)

2005 (1)

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef] [PubMed]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Artigas, D.

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef] [PubMed]

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

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]

Blömer, D.

Chen, W. H.

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.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[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]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774(2006).
[CrossRef] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Dreisow, F.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Fibich, G.

Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

Garanovich, I. L.

He, Y. J.

Hizanidis, K.

Y. Kominis and K. Hizanidis, Phys. Rev. Lett. 102, 133903(2009).
[CrossRef] [PubMed]

Hizanidis, K.

Hu, B.

Hudock, J.

Kartashov, Y. V.

F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, Opt. Express 17, 11328 (2009).
[CrossRef] [PubMed]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Phys. Rev. A 80, 053816 (2009).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1747 (2008).
[CrossRef] [PubMed]

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

Kip, D.

Kivshar, Y. S.

Kominis, Y.

Krolikowski, W.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Lederer, F.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, Opt. Lett. 32, 3173 (2007).
[CrossRef] [PubMed]

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, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774(2006).
[CrossRef] [PubMed]

Malomed, B. A.

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Phys. Rev. A 80, 053816 (2009).
[CrossRef]

Y. J. He, W. H. Chen, H. Z. Wang, and B. A. Malomed, Opt. Lett. 32, 1390 (2007).
[CrossRef] [PubMed]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601(2006).
[CrossRef]

Manela, O.

Mazilu, D.

Mihalache, D.

Mitchell, A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Molina, M. I.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

M. I. Molina, I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 31, 2332 (2006).
[CrossRef] [PubMed]

Neshev, D. N.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Nolte, S.

Papadopoulos, A.

Rosberg, C. R.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Rüter, C. E.

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601(2006).
[CrossRef]

Schreiber, T.

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[CrossRef]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774(2006).
[CrossRef] [PubMed]

Shandarov, V.

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[CrossRef]

Sivan, Y.

Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

Smirnov, E.

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[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]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774(2006).
[CrossRef] [PubMed]

Stepic, M.

Sukhorukov, A. A.

Szameit, A.

Torner, L.

F. Ye, Y. V. Kartashov, B. Hu, and L. Torner, Opt. Express 17, 11328 (2009).
[CrossRef] [PubMed]

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Phys. Rev. A 80, 053816 (2009).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1747 (2008).
[CrossRef] [PubMed]

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

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef] [PubMed]

Tünnermann, A.

Vicencio, R. A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Vysloukh, V. A.

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Phys. Rev. A 80, 053816 (2009).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Opt. Lett. 33, 1747 (2008).
[CrossRef] [PubMed]

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

Wang, H. Z.

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]

Weinstein, M. I.

Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

Ye, F.

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (6)

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1(2008).
[CrossRef]

Phys. Rev. A (1)

Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, Phys. Rev. A 80, 053816 (2009).
[CrossRef]

Phys. Rev. E (1)

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601(2006).
[CrossRef]

Phys. Rev. Lett. (6)

Y. Sivan, G. Fibich, and M. I. Weinstein, Phys. Rev. Lett. 97, 193902 (2006).
[CrossRef] [PubMed]

D. Artigas and L. Torner, Phys. Rev. Lett. 94, 013901 (2005).
[CrossRef] [PubMed]

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

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

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

Y. Kominis and K. Hizanidis, Phys. Rev. Lett. 102, 133903(2009).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) Soliton power U versus propagation constant μ. (b), (c) Soliton trapping at the nonlinear interface for U = 0.9 , p = 0.1 , and μ = 0.1 . (b) Soliton profile. (c) Soliton propagation.

Fig. 2
Fig. 2

Soliton lateral drift: (a), (b) left drift for p = 0.5 , U = 2.1 , and μ = 0.3 ; (c), (d) right drift for p = 0.5 , U = 1.3 , and μ = 0.3 . (e), (f) left drift for p = 0.1 , U = 3.8 , and μ = 1.7 ; (g), (h) right drift for p = 0.1 , U = 2.6 , and μ = 0.9 .

Fig. 3
Fig. 3

(a), (b) Surface soliton swing (zig-zag) motion between the edges of two semi-infinite nonlinear lattices for μ = 1.5 and p = 0.5 . (c), (d) Surface soliton swing motion followed by penetration into one of the nonlinear lattices for μ = 1.7 and p = 0.1 .

Fig. 4
Fig. 4

Dynamics of a soliton inputted with a tilt angle α toward the nonlinear lattice for p = 0.5 . (a) Input profile for μ = 6 . (b) Dependence α = α ( μ ) for p = 0.5 : upper white region, soliton penetration regime; gray region, soliton trapping regime; bottom white region, soliton rebound regime. (c) Soliton rebounds from the interface for α = 1.2 . Soliton is trapped by the lattice for (d) α = 1.6 and (e) α = 1.9 , and penetrates the lattice for (f) α = 2.2 .

Fig. 5
Fig. 5

Same as Fig. 4 but for p = 0.1 . (a) Input profile for μ = 6 . Soliton rebound for (b) α = 0.4 and (c) α = 0.8 . (d) Soliton penetration for α = 0.9 . (e) Dependence α = α ( μ ) for p = 0.1 : upper region, soliton penetration regime; bottom region, soliton rebound regime.

Equations (2)

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i q z = 1 2 2 q x 2 [ 1 p R ( x ) ] | q | 2 q ,
1 2 d 2 f d x 2 μ f + [ 1 p R ( x ) ] f 3 = 0.

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