Abstract

We show that localized gain supports the existence of dissipative vortex solitons in periodic Kerr media with strong two-photon absorption. Vortex solitons exist in both focusing and defocusing media, with their propagation constants emerging from semi-infinite or finite gaps in the lattice spectrum. Coincidence of the discrete rotational symmetries of the gain landscape and refractive index distribution is a necessary condition for exciting vortex solitons, which otherwise transform into stable dissipative multipoles.

© 2010 Optical Society of America

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  1. A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, Prog. Opt. 47, 291 (2005).
    [CrossRef]
  2. B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
    [CrossRef]
  3. D. N. 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]
  4. 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]
  5. Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
    [CrossRef] [PubMed]
  6. D. E. Pelinovsky, P. G. Kevrekidis, and D. J. Frantzeskakis, Physica D (Amsterdam) 212, 20 (2005).
  7. C. Hang, V. V. Konotop, and B. Malomed, Phys. Rev. A 80, 023824 (2009).
    [CrossRef]
  8. N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Phys. Rev. Lett. 95, 053903 (2005).
    [CrossRef] [PubMed]
  9. L. C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Rev. E 63, 016605 (2000).
    [CrossRef]
  10. L. C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Lett. A 289, 59 (2001).
    [CrossRef]
  11. J. M. Soto-Crespo, N. Akhmediev, C. Mejia-Cortes, and N. Devine, Opt. Express 17, 4236 (2009).
    [CrossRef] [PubMed]
  12. H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. A 80, 033835 (2009).
    [CrossRef]
  13. C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. Spec. Top. 173, 233 (2009).
    [CrossRef]
  14. Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, Opt. Lett. 35, 1638 (2010).
    [CrossRef] [PubMed]
  15. G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920(1993).
    [CrossRef] [PubMed]
  16. T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
    [CrossRef] [PubMed]

2010 (1)

2009 (4)

J. M. Soto-Crespo, N. Akhmediev, C. Mejia-Cortes, and N. Devine, Opt. Express 17, 4236 (2009).
[CrossRef] [PubMed]

H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. A 80, 033835 (2009).
[CrossRef]

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. Spec. Top. 173, 233 (2009).
[CrossRef]

C. Hang, V. V. Konotop, and B. Malomed, Phys. Rev. A 80, 023824 (2009).
[CrossRef]

2005 (4)

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Phys. Rev. Lett. 95, 053903 (2005).
[CrossRef] [PubMed]

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

D. E. Pelinovsky, P. G. Kevrekidis, and D. J. Frantzeskakis, Physica D (Amsterdam) 212, 20 (2005).

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

2004 (3)

D. N. 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]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

2001 (2)

L. C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Lett. A 289, 59 (2001).
[CrossRef]

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

2000 (1)

L. C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Rev. E 63, 016605 (2000).
[CrossRef]

1993 (1)

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920(1993).
[CrossRef] [PubMed]

Akhmediev, N.

Alexander, T. J.

D. N. 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]

Bartelt, H.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

Chen, Z.

D. N. 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]

Chow, K. W.

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. Spec. Top. 173, 233 (2009).
[CrossRef]

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]

Crasovan, L. C.

L. C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Lett. A 289, 59 (2001).
[CrossRef]

L. C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Rev. E 63, 016605 (2000).
[CrossRef]

Desyatnikov, A. S.

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

Devine, N.

Egorov, A. A.

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

Fedorov, S. V.

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Phys. Rev. Lett. 95, 053903 (2005).
[CrossRef] [PubMed]

Ferrando, A.

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

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.

D. E. Pelinovsky, P. G. Kevrekidis, and D. J. Frantzeskakis, Physica D (Amsterdam) 212, 20 (2005).

Gibbs, H. M.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920(1993).
[CrossRef] [PubMed]

Hang, C.

C. Hang, V. V. Konotop, and B. Malomed, Phys. Rev. A 80, 023824 (2009).
[CrossRef]

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]

Ikegami, T.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920(1993).
[CrossRef] [PubMed]

Iwamura, H.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920(1993).
[CrossRef] [PubMed]

Kartashov, Y. V.

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, Opt. Lett. 35, 1638 (2010).
[CrossRef] [PubMed]

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

Kawamura, Y.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920(1993).
[CrossRef] [PubMed]

Kevrekidis, P. G.

D. E. Pelinovsky, P. G. Kevrekidis, and D. J. Frantzeskakis, Physica D (Amsterdam) 212, 20 (2005).

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

Khitrova, G.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920(1993).
[CrossRef] [PubMed]

Kivshar, Y. S.

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

D. N. 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]

Kobelke, J.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

Konotop, V. V.

Lam, C.-K.

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. Spec. Top. 173, 233 (2009).
[CrossRef]

Leblond, H.

H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. A 80, 033835 (2009).
[CrossRef]

Lederer, F.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

Makasyuk, I.

D. N. 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.

C. Hang, V. V. Konotop, and B. Malomed, Phys. Rev. A 80, 023824 (2009).
[CrossRef]

Malomed, B. A.

H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. A 80, 033835 (2009).
[CrossRef]

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. Spec. Top. 173, 233 (2009).
[CrossRef]

L. C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Lett. A 289, 59 (2001).
[CrossRef]

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

L. C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Rev. E 63, 016605 (2000).
[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. N. 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]

Mejia-Cortes, C.

Mihalache, D.

H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. A 80, 033835 (2009).
[CrossRef]

L. C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Lett. A 289, 59 (2001).
[CrossRef]

L. C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Rev. E 63, 016605 (2000).
[CrossRef]

Ming, L.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920(1993).
[CrossRef] [PubMed]

Neshev, D. N.

D. N. 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.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

Ostrovskaya, E. A.

D. N. 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]

Pelinovsky, D. E.

D. E. Pelinovsky, P. G. Kevrekidis, and D. J. Frantzeskakis, Physica D (Amsterdam) 212, 20 (2005).

Pertsch, T.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

Peschel, U.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

Rosanov, N. N.

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Phys. Rev. Lett. 95, 053903 (2005).
[CrossRef] [PubMed]

Schuster, K.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

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]

Shatsev, A. N.

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Phys. Rev. Lett. 95, 053903 (2005).
[CrossRef] [PubMed]

Sipe, J. E.

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920(1993).
[CrossRef] [PubMed]

Soto-Crespo, J. M.

Torner, L.

Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, Opt. Lett. 35, 1638 (2010).
[CrossRef] [PubMed]

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

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

Tunnermann, A.

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

Vysloukh, V. A.

Wai, P. K. A.

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. Spec. Top. 173, 233 (2009).
[CrossRef]

Eur. Phys. J. Spec. Top. (1)

C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. Phys. J. Spec. Top. 173, 233 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Lett. A (1)

L. C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Lett. A 289, 59 (2001).
[CrossRef]

Phys. Rev. A (2)

H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. A 80, 033835 (2009).
[CrossRef]

C. Hang, V. V. Konotop, and B. Malomed, Phys. Rev. A 80, 023824 (2009).
[CrossRef]

Phys. Rev. E (2)

L. C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Rev. E 63, 016605 (2000).
[CrossRef]

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

Phys. Rev. Lett. (6)

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

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Phys. Rev. Lett. 95, 053903 (2005).
[CrossRef] [PubMed]

G. Khitrova, H. M. Gibbs, Y. Kawamura, H. Iwamura, T. Ikegami, J. E. Sipe, and L. Ming, Phys. Rev. Lett. 70, 920(1993).
[CrossRef] [PubMed]

T. Pertsch, U. Peschel, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tunnermann, and F. Lederer, Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

Physica D (Amsterdam) (1)

D. E. Pelinovsky, P. G. Kevrekidis, and D. J. Frantzeskakis, Physica D (Amsterdam) 212, 20 (2005).

Prog. Opt. (1)

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

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Figures (3)

Fig. 1
Fig. 1

Energy flow of off-site dissipative vortex solitons versus p i in (a) focusing and (b) defocusing media. The circles correspond to the solitons shown in Figs. 2a, 2b, 2c, 2d. (c) Propagation constant versus p i for solitons in focusing (curve 1) and defocusing (curve 2) media at α = 1 . Dashed lines indicate gap edges.

Fig. 2
Fig. 2

Profiles of off-site vortex solitons in (a), (b) focusing medium at α = 0.1 and (c), (d) defocusing medium at α = 0.5 and the gain γ 1 ( r ) (see the text). Profiles of on-site vortex solitons in (e), (f) focusing medium at α = 0.1 and the gain γ 2 ( r ) . The top and bottom panels show field modulus and phase distributions, respectively.

Fig. 3
Fig. 3

Domains of existence of off-site dissipative vortex solitons in (a) focusing and (b) defocusing media. Vortex solitons in focusing medium exist above the curve p = p i low , while vortex solitons in defocusing medium exist between the curves p = p i low and p = p i upp .

Equations (3)

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

i q ξ = 1 2 2 q + R ( r ) q + i γ ( r ) q σ | q | 2 q i α | q | 2 q .
2 U b = [ σ | w | 4 4 r · v D | w | 2 · r R ( r ) ] d r ,
2 U b = ( 2 σ | w | 4 2 R | w | 2 | w | 2 ) d r .

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