Abstract

We address the impact of the asymmetric nonlocal diffusion nonlinearity of gap solitons supported by photorefractive crystals with an imprinted optical lattice. We reveal how the asymmetric nonlocal response alters the domains of existence and the stability of solitons originating from different gaps. We find that in such media gap solitons cease to exist above a threshold of the nonlocality degree. We discuss how the interplay between nonlocality and lattice strength modifies the gap soliton mobility.

© 2006 Optical Society of America

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  1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  2. A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. 39, 31 (2003).
    [CrossRef]
  3. N. Akozbek and S. John, Phys. Rev. E 57, 2287 (1998).
    [CrossRef]
  4. S. F. Mingaleev and Y. S. Kivshar, Phys. Rev. Lett. 86, 5474 (2001).
    [CrossRef] [PubMed]
  5. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
    [CrossRef] [PubMed]
  6. B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, Phys. Rev. Lett. 92, 230401 (2004).
    [CrossRef] [PubMed]
  7. P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
    [CrossRef]
  8. N. K. Efremidis and D. N. Christodoulides, Phys. Rev. A 67, 063608 (2003).
    [CrossRef]
  9. D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
    [CrossRef] [PubMed]
  10. D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
    [CrossRef]
  11. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef] [PubMed]
  12. D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
    [CrossRef] [PubMed]
  13. 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]
  14. D. N. Christodoulides and T. H. Coskun, Opt. Lett. 21, 1220 (1996).
    [CrossRef] [PubMed]
  15. W. Krolikowski, N. Akhmediev, B. Luther-Davies, and M. Cronin-Golomb, Phys. Rev. E 54, 5761 (1996).
    [CrossRef]
  16. S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
    [CrossRef]
  17. V. Aleshkevich, Y. V. Kartashov, and V. Vysloukh, Phys. Rev. E 63, 016603 (2001).
    [CrossRef]
  18. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 153903 (2004).
    [CrossRef] [PubMed]
  19. Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
    [CrossRef] [PubMed]

2005 (1)

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef] [PubMed]

2004 (6)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 153903 (2004).
[CrossRef] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (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]

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
[CrossRef]

2003 (5)

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. A 67, 063608 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. 39, 31 (2003).
[CrossRef]

2001 (2)

S. F. Mingaleev and Y. S. Kivshar, Phys. Rev. Lett. 86, 5474 (2001).
[CrossRef] [PubMed]

V. Aleshkevich, Y. V. Kartashov, and V. Vysloukh, Phys. Rev. E 63, 016603 (2001).
[CrossRef]

1998 (1)

N. Akozbek and S. John, Phys. Rev. E 57, 2287 (1998).
[CrossRef]

1996 (4)

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

D. N. Christodoulides and T. H. Coskun, Opt. Lett. 21, 1220 (1996).
[CrossRef] [PubMed]

W. Krolikowski, N. Akhmediev, B. Luther-Davies, and M. Cronin-Golomb, Phys. Rev. E 54, 5761 (1996).
[CrossRef]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
[CrossRef]

Aitchison, J. S.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

Akhmediev, N.

W. Krolikowski, N. Akhmediev, B. Luther-Davies, and M. Cronin-Golomb, Phys. Rev. E 54, 5761 (1996).
[CrossRef]

Akozbek, N.

N. Akozbek and S. John, Phys. Rev. E 57, 2287 (1998).
[CrossRef]

Albiez, M.

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Aleshkevich, V.

V. Aleshkevich, Y. V. Kartashov, and V. Vysloukh, Phys. Rev. E 63, 016603 (2001).
[CrossRef]

Anker, Th.

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Bang, O.

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]

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Carvalho, M. I.

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
[CrossRef]

Christodoulides, D. N.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. A 67, 063608 (2003).
[CrossRef]

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
[CrossRef]

D. N. Christodoulides and T. H. Coskun, Opt. Lett. 21, 1220 (1996).
[CrossRef] [PubMed]

Coskun, T. H.

Cronin-Golomb, M.

W. Krolikowski, N. Akhmediev, B. Luther-Davies, and M. Cronin-Golomb, Phys. Rev. E 54, 5761 (1996).
[CrossRef]

de Sterke, C. M.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[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]

Efremidis, N. K.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. A 67, 063608 (2003).
[CrossRef]

Eggleton, B. J.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Eiermann, B.

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Eisenberg, H. S.

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. 39, 31 (2003).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Hanna, B.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

John, S.

N. Akozbek and S. John, Phys. Rev. E 57, 2287 (1998).
[CrossRef]

Kartashov, Y. V.

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 153903 (2004).
[CrossRef] [PubMed]

V. Aleshkevich, Y. V. Kartashov, and V. Vysloukh, Phys. Rev. E 63, 016603 (2001).
[CrossRef]

Kivshar, Y. S.

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
[CrossRef]

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. 39, 31 (2003).
[CrossRef]

S. F. Mingaleev and Y. S. Kivshar, Phys. Rev. Lett. 86, 5474 (2001).
[CrossRef] [PubMed]

Krolikowski, W.

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]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

W. Krolikowski, N. Akhmediev, B. Luther-Davies, and M. Cronin-Golomb, Phys. Rev. E 54, 5761 (1996).
[CrossRef]

Krug, P. A.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Louis, P. J. Y.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Luther-Davies, B.

W. Krolikowski, N. Akhmediev, B. Luther-Davies, and M. Cronin-Golomb, Phys. Rev. E 54, 5761 (1996).
[CrossRef]

Mandelik, D.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

Marzlin, K.-P.

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Mingaleev, S. F.

S. F. Mingaleev and Y. S. Kivshar, Phys. Rev. Lett. 86, 5474 (2001).
[CrossRef] [PubMed]

Morandotti, R.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
[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]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

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]

Oberthaler, M. K.

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Ostrovskaya, E. A.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Pelinovsky, D. E.

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
[CrossRef]

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]

Savage, C. M.

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

Segev, M.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Silberberg, Y.

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. 39, 31 (2003).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Singh, S. R.

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
[CrossRef]

Sipe, J. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Slusher, R. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Sukhorukov, A. A.

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
[CrossRef]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. 39, 31 (2003).
[CrossRef]

Taglieber, M.

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Torner, L.

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 153903 (2004).
[CrossRef] [PubMed]

Treutlein, P.

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

Vysloukh, V.

V. Aleshkevich, Y. V. Kartashov, and V. Vysloukh, Phys. Rev. E 63, 016603 (2001).
[CrossRef]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 153903 (2004).
[CrossRef] [PubMed]

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.

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quantum Electron. 39, 31 (2003).
[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]

Nature (1)

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

S. R. Singh, M. I. Carvalho, and D. N. Christodoulides, Opt. Commun. 130, 288 (1996).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

P. J. Y. Louis, E. A. Ostrovskaya, C. M. Savage, and Y. S. Kivshar, Phys. Rev. A 67, 013602 (2003).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. A 67, 063608 (2003).
[CrossRef]

Phys. Rev. E (4)

D. E. Pelinovsky, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 70, 036618 (2004).
[CrossRef]

N. Akozbek and S. John, Phys. Rev. E 57, 2287 (1998).
[CrossRef]

W. Krolikowski, N. Akhmediev, B. Luther-Davies, and M. Cronin-Golomb, Phys. Rev. E 54, 5761 (1996).
[CrossRef]

V. Aleshkevich, Y. V. Kartashov, and V. Vysloukh, Phys. Rev. E 63, 016603 (2001).
[CrossRef]

Phys. Rev. Lett. (8)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 153903 (2004).
[CrossRef] [PubMed]

Z. Xu, Y. V. Kartashov, and L. Torner, Phys. Rev. Lett. 95, 113901 (2005).
[CrossRef] [PubMed]

S. F. Mingaleev and Y. S. Kivshar, Phys. Rev. Lett. 86, 5474 (2001).
[CrossRef] [PubMed]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

B. Eiermann, Th. Anker, M. Albiez, M. Taglieber, P. Treutlein, K.-P. Marzlin, and M. K. Oberthaler, Phys. Rev. Lett. 92, 230401 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna, W. Krolikowski, and Y. S. Kivshar, Phys. Rev. Lett. 93, 083905 (2004).
[CrossRef] [PubMed]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Bandgap structure of periodic lattice and domains of existence of gap solitons in the presence of nonlocal nonlinearity with μ = 0.4 . Shaded areas, bands; unshaded areas, gaps. (b) Energy flow versus propagation constant for soliton from the first finite gap at p = 3 and μ = 0.5 . Points marked by circles correspond to profiles shown in Figs. 2a, 2b. (c) Domains of existence of solitons from the first finite gap on ( μ , b ) plane. (d) Real part of perturbation growth rate versus propagation constant for soliton from the first finite gap at p = 3 and μ = 0.1 . (e) Domains of existence of solitons from the second finite gap on ( μ , b ) plane. (f) Energy flow versus propagation constant for soliton originating from the second finite gap at p = 10 and μ = 0.05 . The point marked by the circle corresponds to profile shown in Fig. 2c.

Fig. 2
Fig. 2

Profiles of solitons from the first finite gap, with (a) b = 1.2 and (b) b = 2.9 at p = 3 and μ = 0.5 . Profiles of solitons from the second finite gap, when (c) μ = 0.05 and (d) μ = 0.28 at b = 9 and p = 10 . Shaded areas, R ( η ) 0 ; unshaded areas, R ( η ) > 0 .

Fig. 3
Fig. 3

(a) Stable propagation of solitons from the first finite gap corresponding to b = 0.57 , p = 3 , and μ = 0.1 in the presence of white input noise with variance σ noise 2 = 0.01 . (b) Drift of soliton from the first finite gap corresponding to b = 0.6 , p = 3 , and μ = 0 , launched into a nonlocal medium with μ = 0.07 . Excitation of gap solitons by a Gaussian beam with (c) A = 1.6 and (d) 1.8 at p = 2 and μ = 0.2 .

Fig. 4
Fig. 4

Trajectories of propagation for soliton from the first finite gap launched into a nonlocal medium. In (a) we set b = 0.6 , p = 3 , and vary the nonlocality degree. In (b) we set b = 1 , μ = 0.2 , and vary the lattice depth.

Equations (3)

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i q ξ = 1 2 2 q η 2 + q q 2 + μ q η q 2 p R ( η ) q .
δ u = 1 2 d 2 v d η 2 + b v p R v + 2 μ w d w d η v + w 2 v ,
δ v = 1 2 d 2 u d η 2 b u + p R u 4 μ w d w d η u 3 w 2 u 2 μ w 2 d u d η ,

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