Abstract

We address the formation and propagation of vector solitons in optical lattices in the presence of anisotropy-induced walk-off between ordinary and extraordinary polarized field components. Stable vector solitons trapped by the lattice form above a threshold power, while decreasing the lattice depth below a critical value results in the abrupt release of the caged solitons that then move across the lattice and may get trapped in a desired lattice channel.

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  1. V. Manakov, Sov. Phys. JETP 38, 248 (1974).
  2. C. R. Menyuk, J. Opt. Soc. Am. B 5, 392 (1987).
    [Crossref]
  3. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 53 (1988).
    [Crossref] [PubMed]
  4. J. M. Soto-Crespo and N. N. Akhmediev, Phys. Rev. E 51, 3547 (1995).
    [Crossref]
  5. J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
    [Crossref] [PubMed]
  6. E. A. Ostrovskaya, N. N. Akhmediev, G. I. Stegeman, J. U. Kang, and J. S. Aitchison, J. Opt. Soc. Am. B 14, 880 (1997).
    [Crossref]
  7. L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, Opt. Commun. 138, 105 (1997).
    [Crossref]
  8. D. Mihalache, D. Mazilu, and L. Torner, Phys. Rev. Lett. 81, 4353 (1998).
    [Crossref]
  9. D. Mihalache, D. Mazilu, and L.-C. Crasovan, Phys. Rev. E 60, 7504 (1999).
    [Crossref]
  10. M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
    [Crossref]
  11. E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
    [Crossref]
  12. L. Berge, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 84, 3302 (2000).
    [Crossref] [PubMed]
  13. S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
    [Crossref]
  14. J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
    [Crossref]
  15. J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
    [Crossref] [PubMed]
  16. Z. Chen, A. Bezryadina, I. Makasyuk, and J. Yang, Opt. Lett. 29, 1656 (2004).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  19. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
    [Crossref]
  20. Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 766 (2004).
    [Crossref] [PubMed]
  21. R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Opt. Lett. 29, 2905 (2004).
    [Crossref]
  22. Y. S. Kivshar and D. K. Campbell, Phys. Rev. E 48, 3077 (1993).
    [Crossref]
  23. J. Gomez-Gardenes, L. M. Floria, M. Peyrard, and A. R. Bishop, Chaos 14, 1130 (2004).
    [Crossref] [PubMed]
  24. L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
    [Crossref] [PubMed]

2004 (5)

2003 (2)

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[Crossref]

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[Crossref] [PubMed]

2000 (1)

L. Berge, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 84, 3302 (2000).
[Crossref] [PubMed]

1999 (3)

D. Mihalache, D. Mazilu, and L.-C. Crasovan, Phys. Rev. E 60, 7504 (1999).
[Crossref]

E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[Crossref]

1998 (3)

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[Crossref]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[Crossref]

D. Mihalache, D. Mazilu, and L. Torner, Phys. Rev. Lett. 81, 4353 (1998).
[Crossref]

1997 (2)

1996 (2)

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[Crossref] [PubMed]

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[Crossref] [PubMed]

1995 (1)

J. M. Soto-Crespo and N. N. Akhmediev, Phys. Rev. E 51, 3547 (1995).
[Crossref]

1994 (1)

1993 (1)

Y. S. Kivshar and D. K. Campbell, Phys. Rev. E 48, 3077 (1993).
[Crossref]

1988 (1)

1987 (1)

1974 (1)

V. Manakov, Sov. Phys. JETP 38, 248 (1974).

Aceves, A. B.

Aitchison, J. S.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[Crossref]

E. A. Ostrovskaya, N. N. Akhmediev, G. I. Stegeman, J. U. Kang, and J. S. Aitchison, J. Opt. Soc. Am. B 14, 880 (1997).
[Crossref]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[Crossref] [PubMed]

Akhmediev, N.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[Crossref] [PubMed]

Akhmediev, N. N.

E. A. Ostrovskaya, N. N. Akhmediev, G. I. Stegeman, J. U. Kang, and J. S. Aitchison, J. Opt. Soc. Am. B 14, 880 (1997).
[Crossref]

L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, Opt. Commun. 138, 105 (1997).
[Crossref]

J. M. Soto-Crespo and N. N. Akhmediev, Phys. Rev. E 51, 3547 (1995).
[Crossref]

Bang, O.

L. Berge, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 84, 3302 (2000).
[Crossref] [PubMed]

Berge, L.

L. Berge, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 84, 3302 (2000).
[Crossref] [PubMed]

Bezryadina, A.

Bishop, A. R.

J. Gomez-Gardenes, L. M. Floria, M. Peyrard, and A. R. Bishop, Chaos 14, 1130 (2004).
[Crossref] [PubMed]

Campbell, D. K.

Y. S. Kivshar and D. K. Campbell, Phys. Rev. E 48, 3077 (1993).
[Crossref]

Chen, Z.

Christodoulides, D.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[Crossref] [PubMed]

Christodoulides, D. N.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[Crossref]

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[Crossref]

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 53 (1988).
[Crossref] [PubMed]

Crasovan, L.-C.

D. Mihalache, D. Mazilu, and L.-C. Crasovan, Phys. Rev. E 60, 7504 (1999).
[Crossref]

Darmanyan, S.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[Crossref]

De Angelis, C.

Eisenberg, H. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[Crossref]

Firth, W. J.

E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
[Crossref]

Floria, L. M.

J. Gomez-Gardenes, L. M. Floria, M. Peyrard, and A. R. Bishop, Chaos 14, 1130 (2004).
[Crossref] [PubMed]

Gomez-Gardenes, J.

J. Gomez-Gardenes, L. M. Floria, M. Peyrard, and A. R. Bishop, Chaos 14, 1130 (2004).
[Crossref] [PubMed]

Hudock, J.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[Crossref]

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[Crossref] [PubMed]

Joseph, R. I.

Kang, J. U.

Kartashov, Y. V.

Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, Phys. Rev. E 70, 066623 (2004).
[Crossref]

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 766 (2004).
[Crossref] [PubMed]

Kevrekidis, P. G.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[Crossref]

Kivshar, Y. S.

R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, Opt. Lett. 29, 2905 (2004).
[Crossref]

E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
[Crossref]

Y. S. Kivshar and D. K. Campbell, Phys. Rev. E 48, 3077 (1993).
[Crossref]

Kobyakov, A.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[Crossref]

Krolikowski, W.

L. Berge, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 84, 3302 (2000).
[Crossref] [PubMed]

Lederer, F.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[Crossref]

Makasyuk, I.

Malomed, B. A.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[Crossref]

Manakov, V.

V. Manakov, Sov. Phys. JETP 38, 248 (1974).

Mazilu, D.

D. Mihalache, D. Mazilu, and L.-C. Crasovan, Phys. Rev. E 60, 7504 (1999).
[Crossref]

D. Mihalache, D. Mazilu, and L. Torner, Phys. Rev. Lett. 81, 4353 (1998).
[Crossref]

L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, Opt. Commun. 138, 105 (1997).
[Crossref]

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[Crossref] [PubMed]

Meier, J.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[Crossref] [PubMed]

Menyuk, C. R.

Mihalache, D.

D. Mihalache, D. Mazilu, and L.-C. Crasovan, Phys. Rev. E 60, 7504 (1999).
[Crossref]

D. Mihalache, D. Mazilu, and L. Torner, Phys. Rev. Lett. 81, 4353 (1998).
[Crossref]

L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, Opt. Commun. 138, 105 (1997).
[Crossref]

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[Crossref] [PubMed]

Mitchell, M.

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[Crossref]

Molina, M. I.

Morandotti, R.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[Crossref]

Ostrovskaya, E. A.

E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
[Crossref]

E. A. Ostrovskaya, N. N. Akhmediev, G. I. Stegeman, J. U. Kang, and J. S. Aitchison, J. Opt. Soc. Am. B 14, 880 (1997).
[Crossref]

Peschel, U.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[Crossref]

Peyrard, M.

J. Gomez-Gardenes, L. M. Floria, M. Peyrard, and A. R. Bishop, Chaos 14, 1130 (2004).
[Crossref] [PubMed]

Schmidt, E.

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[Crossref]

Segev, M.

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[Crossref]

Silberberg, Y.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[Crossref] [PubMed]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[Crossref]

Skryabin, D. V.

E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
[Crossref]

Soto-Crespo, J. M.

J. M. Soto-Crespo and N. N. Akhmediev, Phys. Rev. E 51, 3547 (1995).
[Crossref]

Stegeman, G.

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[Crossref] [PubMed]

Stegeman, G. I.

Torner, L.

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 766 (2004).
[Crossref] [PubMed]

Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, Phys. Rev. E 70, 066623 (2004).
[Crossref]

D. Mihalache, D. Mazilu, and L. Torner, Phys. Rev. Lett. 81, 4353 (1998).
[Crossref]

L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, Opt. Commun. 138, 105 (1997).
[Crossref]

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[Crossref] [PubMed]

Trillo, S.

Vicencio, R. A.

Vysloukh, V. A.

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 766 (2004).
[Crossref] [PubMed]

Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, Phys. Rev. E 70, 066623 (2004).
[Crossref]

Wabnitz, S.

Yang, J.

Zelenina, A. S.

Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, Phys. Rev. E 70, 066623 (2004).
[Crossref]

Y. V. Kartashov, A. S. Zelenina, L. Torner, and V. A. Vysloukh, Opt. Lett. 29, 766 (2004).
[Crossref] [PubMed]

Chaos (1)

J. Gomez-Gardenes, L. M. Floria, M. Peyrard, and A. R. Bishop, Chaos 14, 1130 (2004).
[Crossref] [PubMed]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

L. Torner, D. Mihalache, D. Mazilu, and N. N. Akhmediev, Opt. Commun. 138, 105 (1997).
[Crossref]

Opt. Lett. (5)

Phys. Rev. E (6)

Y. S. Kivshar and D. K. Campbell, Phys. Rev. E 48, 3077 (1993).
[Crossref]

J. M. Soto-Crespo and N. N. Akhmediev, Phys. Rev. E 51, 3547 (1995).
[Crossref]

D. Mihalache, D. Mazilu, and L.-C. Crasovan, Phys. Rev. E 60, 7504 (1999).
[Crossref]

Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, and L. Torner, Phys. Rev. E 70, 066623 (2004).
[Crossref]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, Phys. Rev. E 57, 3520 (1998).
[Crossref]

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[Crossref]

Phys. Rev. Lett. (8)

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[Crossref] [PubMed]

D. Mihalache, D. Mazilu, and L. Torner, Phys. Rev. Lett. 81, 4353 (1998).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 2726 (1999).
[Crossref]

M. Mitchell, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 80, 4657 (1998).
[Crossref]

E. A. Ostrovskaya, Y. S. Kivshar, D. V. Skryabin, and W. J. Firth, Phys. Rev. Lett. 83, 296 (1999).
[Crossref]

L. Berge, O. Bang, and W. Krolikowski, Phys. Rev. Lett. 84, 3302 (2000).
[Crossref] [PubMed]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[Crossref] [PubMed]

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[Crossref] [PubMed]

Sov. Phys. JETP (1)

V. Manakov, Sov. Phys. JETP 38, 248 (1974).

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Figures (4)

Fig. 1
Fig. 1

Profiles of (a) x and (b) y components of elliptically polarized vector soliton at b = 4.2 , α = 1.4 . In gray regions R ( η ) 0 , while in white regions R ( η ) < 0 . (c) U versus b for x-, y-, and elliptically polarized solitons at α = 1.4 . (d) S x and S y versus b at α = 1.4 . Points in (c) and (d) correspond to solitons in (a) and (b). (e) Cutoff for existence of elliptically polarized soliton versus α. (f) δ r versus b for y- and elliptically polarized solitons at α = 1.4 . In all cases p = 4 .

Fig. 2
Fig. 2

(a) Dynamics of x component at p = 0.50 (1), 0.36 (2), and 0.22 (3) when input beam corresponds to vector soliton obtained at b = 6 , p = 4 . (b) The same as in (a) but for sech-shaped input beams and p = 0.60 (1), 0.32 (2), and 0.23 (3). Distributions corresponding to different p are superimposed. In all cases α = 1.4 .

Fig. 3
Fig. 3

Number of the output channel versus p at α = 1.4 for elliptically polarized input vector soliton with (a) U = 6.38 , (b) 6.78, (c) 6.98, and (d) 7.15 obtained at p = 4 . Vertical dashed lines indicate critical lattice depth.

Fig. 4
Fig. 4

p cr versus U for (a) elliptically polarized input vector soliton and (b) sech-shaped input beams at α = 1.4 .

Equations (2)

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i q x ξ = 1 2 2 q x η 2 i α q x η q x ( q x 2 + 2 3 q y 2 ) 1 3 q x * q y 2 exp ( i β ξ ) p R ( η ) q x ,
i q y ξ = 1 2 2 q y η 2 q y ( q y 2 + 2 3 q x 2 ) 1 3 q y * q x 2 exp ( + i β ξ ) p R ( η ) q y .

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