Abstract

We address the properties of multivortex soliton complexes supported by multiring gain landscapes in focusing Kerr nonlinear media with strong two-photon absorption. Stable complexes incorporating two, three, or four vortices featuring opposite or identical topological charges are shown to exist. In the simplest geometries with two amplifying rings vortex twins with equal topological charges exhibit asymmetric intensity distributions, while vortex anti-twins may be symmetric or asymmetric, depending on the gain level and separation between rings.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  4. 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]
  5. 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]
  6. Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, Phys. Rev. Lett. 95, 123902 (2005).
    [CrossRef] [PubMed]
  7. A. I. Yakimenko, Y. A. Zaliznyak, and Y. S. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
  9. B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  18. J. Keeling and N. G. Berloff, Phys. Rev. Lett. 100, 250401(2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2011 (1)

2010 (5)

2009 (2)

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

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

2008 (3)

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef] [PubMed]

J. Keeling and N. G. Berloff, Phys. Rev. Lett. 100, 250401(2008).
[CrossRef] [PubMed]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Opt. Lett. 33, 198 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

A. Alexandrescu and V. M. Perez-Garcia, Phys. Rev. A 73, 053610 (2006).
[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]

A. I. Yakimenko, Y. A. Zaliznyak, and Y. S. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

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

2004 (2)

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]

2001 (1)

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L.-C. Crasovan, and D. Mihalache, Phys. Lett. A 288, 292 (2001).
[CrossRef]

2000 (1)

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

1997 (1)

Akhmediev, N.

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

N. Akhmediev and A. Ankiewicz, eds., Dissipative Solitons: From Optics to Biology and Medicine, Vol.  751 of Lecture Notes in Physics (Springer, Berlin, 2008).

Aleksic, N. B.

V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

Alexander, T. J.

T. J. Alexander, A. S. Desyatnikov, and Y. S. Kivshar, Opt. Lett. 32, 1293 (2007).
[CrossRef] [PubMed]

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]

Alexandrescu, A.

A. Alexandrescu and V. M. Perez-Garcia, Phys. Rev. A 73, 053610 (2006).
[CrossRef]

Ankiewicz, A.

N. Akhmediev and A. Ankiewicz, eds., Dissipative Solitons: From Optics to Biology and Medicine, Vol.  751 of Lecture Notes in Physics (Springer, Berlin, 2008).

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]

Berloff, N. G.

J. Keeling and N. G. Berloff, Phys. Rev. Lett. 100, 250401(2008).
[CrossRef] [PubMed]

Bludov, Y. V.

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 81, 013625(2010).
[CrossRef]

Borovkova, O. V.

Buccoliero, D.

Buryak, A. V.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L.-C. Crasovan, and D. Mihalache, Phys. Lett. A 288, 292 (2001).
[CrossRef]

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. J. Phys. Special Topics 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. Rev. E 63, 016605 (2000).
[CrossRef]

Crasovan, L.-C.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L.-C. Crasovan, and D. Mihalache, Phys. Lett. A 288, 292 (2001).
[CrossRef]

Denz, C.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef] [PubMed]

Desyatnikov, A. S.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef] [PubMed]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Opt. Lett. 33, 198 (2008).
[CrossRef] [PubMed]

T. J. Alexander, A. S. Desyatnikov, and Y. S. Kivshar, Opt. Lett. 32, 1293 (2007).
[CrossRef] [PubMed]

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]

Hu, B.

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]

Kaiser, F.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef] [PubMed]

Kartashov, Y. V.

Keeling, J.

J. Keeling and N. G. Berloff, Phys. Rev. Lett. 100, 250401(2008).
[CrossRef] [PubMed]

Kivshar, Y.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef] [PubMed]

Kivshar, Y. S.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Opt. Lett. 33, 198 (2008).
[CrossRef] [PubMed]

T. J. Alexander, A. S. Desyatnikov, and Y. S. Kivshar, Opt. Lett. 32, 1293 (2007).
[CrossRef] [PubMed]

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

A. I. Yakimenko, Y. A. Zaliznyak, and Y. S. Kivshar, Phys. Rev. E 71, 065603(R) (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]

Konotop, V. V.

Krolikowski, W.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef] [PubMed]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, Opt. Lett. 33, 198 (2008).
[CrossRef] [PubMed]

Lam, C.-K.

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

Leblond, H.

V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

Lobanov, V. E.

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. A.

V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

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

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L.-C. Crasovan, and D. Mihalache, Phys. Lett. A 288, 292 (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.

Michinel, H.

Mihalache, D.

V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L.-C. Crasovan, and D. Mihalache, Phys. Lett. A 288, 292 (2001).
[CrossRef]

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

Neshev, D. N.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef] [PubMed]

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]

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]

Perez-Garcia, V. M.

A. Alexandrescu and V. M. Perez-Garcia, Phys. Rev. A 73, 053610 (2006).
[CrossRef]

Quiroga-Teixeiro, M.

Richter, T.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef] [PubMed]

Rosanov, N. N.

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

N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, Berlin, 2002).

Sammut, R. A.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L.-C. Crasovan, and D. Mihalache, Phys. Lett. A 288, 292 (2001).
[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]

Shatsev, A. N.

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

Skarka, V.

V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

Soto-Crespo, J. M.

Terhalle, B.

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef] [PubMed]

Torner, L.

Towers, I.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L.-C. Crasovan, and D. Mihalache, Phys. Lett. A 288, 292 (2001).
[CrossRef]

Vysloukh, V. A.

Wai, P. K. A.

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

Yakimenko, A. I.

A. I. Yakimenko, Y. A. Zaliznyak, and Y. S. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

Ye, F.

Zaliznyak, Y. A.

A. I. Yakimenko, Y. A. Zaliznyak, and Y. S. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

Eur. J. Phys. Special Topics (1)

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

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Opt. Lett. (6)

Phys. Lett. A (1)

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L.-C. Crasovan, and D. Mihalache, Phys. Lett. A 288, 292 (2001).
[CrossRef]

Phys. Rev. A (2)

Y. V. Bludov and V. V. Konotop, Phys. Rev. A 81, 013625(2010).
[CrossRef]

A. Alexandrescu and V. M. Perez-Garcia, Phys. Rev. A 73, 053610 (2006).
[CrossRef]

Phys. Rev. E (2)

A. I. Yakimenko, Y. A. Zaliznyak, and Y. S. Kivshar, Phys. Rev. E 71, 065603(R) (2005).
[CrossRef]

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

Phys. Rev. Lett. (7)

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

V. Skarka, N. B. Aleksic, H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. Lett. 105, 213901 (2010).
[CrossRef]

J. Keeling and N. G. Berloff, Phys. Rev. Lett. 100, 250401(2008).
[CrossRef] [PubMed]

B. Terhalle, T. Richter, A. S. Desyatnikov, D. N. Neshev, W. Krolikowski, F. Kaiser, C. Denz, and Y. Kivshar, Phys. Rev. Lett. 101, 013903 (2008).
[CrossRef] [PubMed]

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]

Prog. Opt. (1)

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

Other (2)

N. Akhmediev and A. Ankiewicz, eds., Dissipative Solitons: From Optics to Biology and Medicine, Vol.  751 of Lecture Notes in Physics (Springer, Berlin, 2008).

N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, Berlin, 2002).

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Figures (3)

Fig. 1
Fig. 1

(a) Symmetric vortex-antivortex mode at p i = 3.7 . (b) Asymmetric vortex-antivortex soliton at p i = 5 . (c) Asymmetric vortex-vortex mode at p i = 4 . Top row: field modulus distributions, bottom row: phase distributions. In all cases s = 1.5 .

Fig. 2
Fig. 2

(a) Energy flow of vortex-antivortex soliton versus p i at s = 1.5 . (b) Energy flow of vortex-vortex and vortex-antivortex solitons versus s at p i = 4 . The branches corresponding to symmetric solitons are shown black, while branches of asymmetric solitons are shown red. (c) Minimal gain required for existence of stable vortex-antivortex solitons versus s.

Fig. 3
Fig. 3

Multivortex solitons in gain landscapes with three (a), (b), and four (c) rings. In (a)  p i = 3 , while in (b), (c)  p i = 4 . Top row shows field modulus distributions, while bottom row shows phase distributions. In all cases s = 1.5 .

Equations (1)

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i q ξ = 1 2 ( 2 q η 2 + 2 q ζ 2 ) q | q | 2 + i γ ( η , ζ ) q i α q | q | 2 .

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