Abstract

We address vortex solitons supported by optical lattices featuring modulation of both the linear and nonlinear refractive indices. We find that when the modulation is out of phase the competition between both effects results in remarkable shape transformations of the solitons that profoundly affect their properties and stability. Nonlinear refractive index modulation is found to impose restrictions on the maximal power of off-site solitons, which are shown to be stable only below a maximum nonlinearity modulation depth.

© 2008 Optical Society of America

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  1. A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, Prog. Opt. 47, 291 (2005).
    [CrossRef]
  2. B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
    [CrossRef]
  3. P. G. Kevrekidis, B. A. Malomed, Z. Chen, and D. J. Frantzeskakis, Phys. Rev. E 70, 056612 (2004).
    [CrossRef]
  4. J. Yang and Z. H. Musslimani, Opt. Lett. 28, 2094 (2003).
    [CrossRef] [PubMed]
  5. D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
    [CrossRef] [PubMed]
  6. J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
    [CrossRef] [PubMed]
  7. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
    [CrossRef] [PubMed]
  8. Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
    [CrossRef] [PubMed]
  9. D. Blömer, A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Express 14, 2151 (2006).
    [CrossRef] [PubMed]
  10. M. Öster, M. Johansson, and A. Eriksson, Phys. Rev. E 67, 056606 (2003).
    [CrossRef]
  11. F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
    [CrossRef]
  12. H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
    [CrossRef]
  13. G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
    [CrossRef]
  14. Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616 (2006).
    [CrossRef]
  15. J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
    [CrossRef] [PubMed]
  16. F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, Phys. Lett. A 367, 149 (2007).
    [CrossRef]
  17. Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
    [CrossRef]
  18. Y. Kominis and K. Hizanidis, Opt. Lett. 31, 2888 (2006).
    [CrossRef] [PubMed]
  19. H. Sakaguchi and B. A. Malomed, Phys. Rev. E 73, 026601 (2006).
    [CrossRef]
  20. M. Öster and M. Johansson, arXiv.org e-Print archive, 26 May 2008, arXiv:0805.3814v1 (nlin.PS).

2008 (1)

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[CrossRef]

2007 (3)

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, Phys. Lett. A 367, 149 (2007).
[CrossRef]

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

2006 (5)

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

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616 (2006).
[CrossRef]

D. Blömer, A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, and A. Tünnermann, Opt. Express 14, 2151 (2006).
[CrossRef] [PubMed]

Y. Kominis and K. Hizanidis, Opt. Lett. 31, 2888 (2006).
[CrossRef] [PubMed]

2005 (4)

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, Prog. Opt. 47, 291 (2005).
[CrossRef]

2004 (3)

P. G. Kevrekidis, B. A. Malomed, Z. Chen, and D. J. Frantzeskakis, Phys. Rev. E 70, 056612 (2004).
[CrossRef]

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

2003 (2)

M. Öster, M. Johansson, and A. Eriksson, Phys. Rev. E 67, 056606 (2003).
[CrossRef]

J. Yang and Z. H. Musslimani, Opt. Lett. 28, 2094 (2003).
[CrossRef] [PubMed]

2001 (1)

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Abdullaev, F.

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, Phys. Lett. A 367, 149 (2007).
[CrossRef]

Abdullaev, F. K.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[CrossRef]

Abdumalikov, A.

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, Phys. Lett. A 367, 149 (2007).
[CrossRef]

Alexander, T. J.

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Bartal, G.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Belmonte-Beitia, J.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Blömer, D.

Bludov, Y. V.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[CrossRef]

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616 (2006).
[CrossRef]

Chen, Z.

P. G. Kevrekidis, B. A. Malomed, Z. Chen, and D. J. Frantzeskakis, Phys. Rev. E 70, 056612 (2004).
[CrossRef]

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Christodoulides, D. N.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Cohen, O.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Desyatnikov, A. S.

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, Prog. Opt. 47, 291 (2005).
[CrossRef]

Dmitriev, S. V.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[CrossRef]

Dreisow, F.

Egorov, A. A.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

Eriksson, A.

M. Öster, M. Johansson, and A. Eriksson, Phys. Rev. E 67, 056606 (2003).
[CrossRef]

Ferrando, A.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

Fibich, G.

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Frantzeskakis, D. J.

P. G. Kevrekidis, B. A. Malomed, Z. Chen, and D. J. Frantzeskakis, Phys. Rev. E 70, 056612 (2004).
[CrossRef]

Galimzyanov, R.

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, Phys. Lett. A 367, 149 (2007).
[CrossRef]

Hizanidis, K.

Hudock, J.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Johansson, M.

M. Öster, M. Johansson, and A. Eriksson, Phys. Rev. E 67, 056606 (2003).
[CrossRef]

M. Öster and M. Johansson, arXiv.org e-Print archive, 26 May 2008, arXiv:0805.3814v1 (nlin.PS).

Jones, C. K. R. T.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Kevrekidis, P. G.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[CrossRef]

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

P. G. Kevrekidis, B. A. Malomed, Z. Chen, and D. J. Frantzeskakis, Phys. Rev. E 70, 056612 (2004).
[CrossRef]

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Kivshar, Y. S.

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, Prog. Opt. 47, 291 (2005).
[CrossRef]

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Kominis, Y.

Konotop, V. V.

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[CrossRef]

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616 (2006).
[CrossRef]

Makasyuk, I.

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Malomed, B. A.

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

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
[CrossRef]

P. G. Kevrekidis, B. A. Malomed, Z. Chen, and D. J. Frantzeskakis, Phys. Rev. E 70, 056612 (2004).
[CrossRef]

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Manela, O.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Martin, H.

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Musslimani, Z. H.

Neshev, D.

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Nolte, S.

Öster, M.

M. Öster, M. Johansson, and A. Eriksson, Phys. Rev. E 67, 056606 (2003).
[CrossRef]

M. Öster and M. Johansson, arXiv.org e-Print archive, 26 May 2008, arXiv:0805.3814v1 (nlin.PS).

Ostrovskaya, E. A.

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Perez-Garcia, V. M.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Pertsch, T.

Rapti, Z.

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

Sakaguchi, H.

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

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
[CrossRef]

Segev, M.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Sivan, Y.

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

Szameit, A.

Torner, L.

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, Prog. Opt. 47, 291 (2005).
[CrossRef]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Torres, P. J.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Tünnermann, A.

Vekslerchik, V.

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Weinstein, M. I.

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

Yang, J.

J. Phys. A (1)

Z. Rapti, P. G. Kevrekidis, V. V. Konotop, and C. K. R. T. Jones, J. Phys. A 40, 14151 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Lett. A (1)

F. Abdullaev, A. Abdumalikov, and R. Galimzyanov, Phys. Lett. A 367, 149 (2007).
[CrossRef]

Phys. Rev. A (1)

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616 (2006).
[CrossRef]

Phys. Rev. E (6)

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

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

P. G. Kevrekidis, B. A. Malomed, Z. Chen, and D. J. Frantzeskakis, Phys. Rev. E 70, 056612 (2004).
[CrossRef]

M. Öster, M. Johansson, and A. Eriksson, Phys. Rev. E 67, 056606 (2003).
[CrossRef]

F. K. Abdullaev, Y. V. Bludov, S. V. Dmitriev, P. G. Kevrekidis, and V. V. Konotop, Phys. Rev. E 77, 016604 (2008).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
[CrossRef]

Phys. Rev. Lett. (5)

D. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
[CrossRef] [PubMed]

Physica D (1)

G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
[CrossRef]

Prog. Opt. (1)

A. S. Desyatnikov, L. Torner, and Y. S. Kivshar, Prog. Opt. 47, 291 (2005).
[CrossRef]

Other (1)

M. Öster and M. Johansson, arXiv.org e-Print archive, 26 May 2008, arXiv:0805.3814v1 (nlin.PS).

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Figures (3)

Fig. 1
Fig. 1

Field modulus distributions for vortex solitons at (a) b = 5 , σ = 0.7 ; (b) b = 9.6 , σ = 0.7 ; (c) b = 6 , σ = 1 , lower branch; and (d) b = 6 , σ = 1 , upper branch. White lines indicate positions of maxima of linear lattice.

Fig. 2
Fig. 2

Power versus b at (a) σ = 0.5 and 0.7, and (b) σ = 1 . Circles in (a) correspond to solitons in Figs. 1a, 1b, while circles in (b) correspond to solitons from Figs. 1c, 1d. (c) Cutoff and critical propagation constant versus σ. (d) Stability domain (shaded) for vortex solitons on ( σ , b ) plane. δ r versus b for b values close to cutoff (e) and b values close to inflection point of U ( b ) curve (f).

Fig. 3
Fig. 3

Propagation dynamics of perturbed vortex solitons with (a) b = 3.2 , (b) 5, and (c) 7 at σ = 0.7 . White noise with variance σ noise 2 = 0.01 was added into input distributions. Field modulus distributions are shown at different distances.

Equations (3)

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

i q ξ = 1 2 ( 2 q η 2 + 2 q ζ 2 ) [ 1 σ R ( η , ζ ) ] q 2 q p R ( η , ζ ) q .
δ u p = 1 2 ( 2 v p η 2 + 2 v p ζ 2 ) + b v p ( 1 σ R ) v p ( u 2 + 3 v 2 ) 2 ( 1 σ R ) u v u p p R v p ,
δ v p = 1 2 ( 2 u p η 2 + 2 u p ζ 2 ) b u p + ( 1 σ R ) u p ( 3 u 2 + v 2 ) + 2 ( 1 σ R ) u v v p + p R u p ,

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