Abstract

We discover that a spatially localized gain supports stable vortex solitons in media with cubic nonlinearity and two-photon absorption. The interplay between nonlinear losses and gain in amplifying rings results in the suppression of otherwise ubiquitous azimuthal modulation instabilities of radially symmetric vortex solitons. We find that the topology of the gain profile imposes restrictions on the maximal possible charge of vortex solitons. Symmetry breaking occurs at high gain levels, resulting in the formation of necklace vortex solitons composed of asymmetric bright spots.

© 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. M. Quiroga-Teixeiro and H. Michinel, J. Opt. Soc. Am. B 14, 2004 (1997).
    [Crossref]
  3. I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L.-C. Crasovan, and D. Mihalache, Phys. Lett. A 288, 292 (2001).
    [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]
  8. Dissipative Solitons: from Optics to Biology and Medicine, N. Akhmediev and A. Ankiewicz, eds., 751 of Lecture Notes in Physics (Springer, 2008).
  9. N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, 2010).
  10. N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Phys. Rev. Lett. 95, 053903 (2005).
    [Crossref] [PubMed]
  11. L. C. Crasovan, B. A. Malomed, and D. Mihalache, Phys. Rev. E 63, 016605 (2000).
    [Crossref]
  12. J. M. Soto-Crespo, N. Akhmediev, C. Mejia-Cortes, and N. Devine, Opt. Express 17, 4236 (2009).
    [Crossref] [PubMed]
  13. H. Leblond, B. A. Malomed, and D. Mihalache, Phys. Rev. A 80, 033835 (2009).
    [Crossref]
  14. C.-K. Lam, B. A. Malomed, K. W. Chow, and P. K. A. Wai, Eur. J. Phys. Special Topics 173, 233 (2009).
    [Crossref]
  15. Y. V. Kartashov, V. V. Konotop, V. A. Vysloukh, and L. Torner, Opt. Lett. 35, 1638 (2010).
    [Crossref] [PubMed]
  16. Y. V. Bludov and V. V. Konotop, Phys. Rev. A 81, 013625 (2010).
    [Crossref]
  17. O. Katz, Y. Lahini, and Y. Silberberg, Opt. Lett. 33, 2830 (2008).
    [Crossref] [PubMed]
  18. M. J. Connelly, Semiconductor Optical Amplifiers (Springer, 2002).

2010 (2)

2009 (3)

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. J. Phys. Special Topics 173, 233 (2009).
[Crossref]

2008 (1)

2005 (4)

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]

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

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.

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]

Bludov, Y. V.

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

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]

Connelly, M. J.

M. J. Connelly, Semiconductor Optical Amplifiers (Springer, 2002).

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]

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]

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]

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]

Katz, O.

Kivshar, Y. S.

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.

Lahini, Y.

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.

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

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.

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. 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.

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

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]

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]

Quiroga-Teixeiro, M.

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, 2010).

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]

Silberberg, Y.

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]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, 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]

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]

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. (2)

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]

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

Phys. Rev. E (2)

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

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

Phys. Rev. Lett. (4)

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Phys. Rev. Lett. 95, 053903 (2005).
[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 (3)

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

N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, 2010).

M. J. Connelly, Semiconductor Optical Amplifiers (Springer, 2002).

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Figures (4)

Fig. 1
Fig. 1

Field modulus (top) and phase distribution (bottom) for vortex solitons with (a) m = 1 , (b) m = 2 , and (c) m = 3 at α = 2 , p i = 3 . White circles stand for the maxima of ring with gain.

Fig. 2
Fig. 2

(a) Energy flow and angular momentum of m = 2 vortex soliton versus gain parameter at α = 2 . (b) Minimal gain required for existence of stable vortex solitons with m = 1 and m = 3 versus α.

Fig. 3
Fig. 3

(a) Field modulus (top) and phase distribution (bottom) for vortex solitons with (a),(b) n = 3 , m = 1 ; (c),(d) n = 5 , m = 2 ; and (e),(f) n = 6 , m = 2 . Panels (a),(c),(e) correspond to p i = 3.2 , while panels (b),(d),(f) correspond to p i = 5.5 . In all cases, α = 2 .

Fig. 4
Fig. 4

Energy flow of m = 2 vortex solitons versus (a) p i and versus (b) b at α = 2 . (c) Angular momentum of m = 2 vortex solitons versus gain parameter at α = 2 . (d) Minimal gain required for existence of stable m = 2 vortex solitons versus α.

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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