Abstract

We address the existence and properties of solitons in layered thermal media made of alternating focusing and defocusing layers. Such structures support robust bright solitons even if the averaged nonlinearity is defocusing. We show that nonoscillating solitons may form in any of the focusing domains, even in those located close to the sample edge, in contrast to uniform thermal media, where light beams always oscillate when not launched exactly on the sample center. Stable multipole solitons may include more than four spots in layered media.

© 2008 Optical Society of America

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  1. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
    [CrossRef] [PubMed]
  2. M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, Opt. Lett. 27, 1460 (2002).
    [CrossRef]
  3. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (2005).
    [CrossRef] [PubMed]
  4. B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. Christodoulides, Opt. Lett. 32, 154 (2007).
    [CrossRef]
  5. I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, JETP Lett. 31, 304 (1980).
  6. X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
    [CrossRef]
  7. Z. Xu, Y. V. Kartashov, and L. Torner, Opt. Lett. 30, 3171 (2005).
    [CrossRef] [PubMed]
  8. D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
    [CrossRef]
  9. S. Lopez-Aguayo, A. S. Desyatnikov, Y. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, Opt. Lett. 31, 1100 (2006).
    [CrossRef] [PubMed]
  10. Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, Opt. Lett. 31, 1483 (2006).
    [CrossRef] [PubMed]
  11. C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
    [CrossRef] [PubMed]
  12. S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
    [CrossRef]
  13. A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
    [CrossRef]
  14. H. Sakaguchi and B. A. Malomed, Phys. Rev. E 72, 046610 (2005).
    [CrossRef]
  15. F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).
    [CrossRef]
  16. G. Fibich, Y. Sivan, and M. I. Weinstein, Physica D 217, 31 (2006).
    [CrossRef]
  17. Y. V. Bludov and V. V. Konotop, Phys. Rev. A 74, 043616 (2006).
    [CrossRef]
  18. J. Belmonte-Beitia, V. M. Perez-Garcia, V. Vekslerchik, and P. J. Torres, Phys. Rev. Lett. 98, 064102 (2007).
    [CrossRef] [PubMed]

2007 (2)

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. Christodoulides, Opt. Lett. 32, 154 (2007).
[CrossRef]

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

2006 (8)

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. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

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]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
[CrossRef] [PubMed]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
[CrossRef]

2005 (4)

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

F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).
[CrossRef]

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

Z. Xu, Y. V. Kartashov, and L. Torner, Opt. Lett. 30, 3171 (2005).
[CrossRef] [PubMed]

2004 (2)

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

2002 (1)

1980 (1)

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, JETP Lett. 31, 304 (1980).

Abdullaev, F. K.

F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).
[CrossRef]

Adamski, A.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Alfassi, B.

Assanto, G.

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, Opt. Lett. 27, 1460 (2002).
[CrossRef]

Bang, O.

Belmonte-Beitia, J.

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

Bludov, Y. V.

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

Brzdakiewicz, K. A.

Cambournac, C.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Carmon, T.

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

Christodoulides, D.

Cohen, O.

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, Opt. Lett. 31, 3312 (2006).
[CrossRef] [PubMed]

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

Conti, C.

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

Crasovan, L.-C.

D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Desyatnikov, A. S.

Edmundson, D.

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

Fibich, G.

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

Garnier, J.

F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).
[CrossRef]

Haelterman, M.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Hutsebaut, X.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Kartashov, Y. V.

Kivshar, Y. S.

Kolchugina, I. A.

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, JETP Lett. 31, 304 (1980).

Konotop, V. V.

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

Krolikowski, W.

Lashkin, V. M.

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
[CrossRef]

Lederer, F.

D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Lopez-Aguayo, S.

Malomed, B. A.

D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

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

Manela, O.

B. Alfassi, C. Rotschild, O. Manela, M. Segev, and D. Christodoulides, Opt. Lett. 32, 154 (2007).
[CrossRef]

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

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

Y. V. Kartashov, L. Torner, V. A. Vysloukh, and D. Mihalache, Opt. Lett. 31, 1483 (2006).
[CrossRef] [PubMed]

Mironov, V. A.

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, JETP Lett. 31, 304 (1980).

Neyts, K.

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Peccianti, M.

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

M. Peccianti, K. A. Brzdakiewicz, and G. Assanto, Opt. Lett. 27, 1460 (2002).
[CrossRef]

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]

Prikhodko, O. O.

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
[CrossRef]

Rotschild, C.

Sakaguchi, H.

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

Segev, M.

Sergeev, A. M.

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, JETP Lett. 31, 304 (1980).

Sivan, Y.

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

Skupin, S.

Torner, L.

Torres, P. J.

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

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.

Weinstein, M. I.

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

Xu, Z.

Yakimenko, A. I.

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
[CrossRef]

JETP Lett. (1)

I. A. Kolchugina, V. A. Mironov, and A. M. Sergeev, JETP Lett. 31, 304 (1980).

Opt. Commun. (1)

X. Hutsebaut, C. Cambournac, M. Haelterman, A. Adamski, and K. Neyts, Opt. Commun. 233, 211 (2004).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. A (2)

F. K. Abdullaev and J. Garnier, Phys. Rev. A 72, 061605(R) (2005).
[CrossRef]

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

Phys. Rev. E (4)

D. Mihalache, D. Mazilu, F. Lederer, L.-C. Crasovan, Y. V. Kartashov, L. Torner, and B. A. Malomed, Phys. Rev. E 74, 066614 (2006).
[CrossRef]

S. Skupin, O. Bang, D. Edmundson, and W. Krolikowski, Phys. Rev. E 73, 066603 (2006).
[CrossRef]

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, Phys. Rev. E 73, 066605 (2006).
[CrossRef]

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

Phys. Rev. Lett. (3)

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, Phys. Rev. Lett. 95, 213904 (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]

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Figures (3)

Fig. 1
Fig. 1

Profiles of (a) fundamental, (b) even, (c) dipole, and (d) triple-mode solitons for η c = 0 . (e) Profiles of fundamental solitons for η c = 10 . (f) Profile of refractive index σ T for fundamental solitons with b = 0.9 , η c = 0 (red, or gray online, curve), and b = 6.5 , η c = 10 (black curve). In shaded regions σ > 0 , while in white regions σ < 0 . In all cases σ b = 0 .

Fig. 2
Fig. 2

U versus b for (a) fundamental and (b) dipole solitons. Circles in (a) and (b) correspond to solitons shown in Figs. 1a, 1c, respectively. (c) Cutoffs for fundamental and dipole solitons versus η c . δ r versus b for (d) even solitons at η c = 0 , (e) a dipole soliton at η c = 1 , (f) a triple-mode soliton at η c = 18 . In all cases σ b = 0 .

Fig. 3
Fig. 3

(a) Profiles and (b) refractive index distributions for fundamental solitons with b = 0.5 , η c = 0 for σ b = 0.2 (red, or gray online, curves), and σ b = 0.6 (black curves). (c) Instability domain (shaded) for dipole solitons with η c = 1 on the ( σ b , b ) plane.

Equations (4)

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i q ξ = 1 2 2 q η 2 σ ( η ) q T ,
2 T η 2 = q 2 .
δ u = 1 2 d 2 v d η 2 σ T v + b v ,
δ v = 1 2 d 2 u d η 2 + σ T u + σ Δ T w b u ,

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