Abstract

We study dissipative ring solitons with vorticity in the frame of the (2+1)-dimensional cubic-quintic complex Ginzburg-Landau equation. In dissipative media, radially symmetric ring structures with any vorticity m can be stable in a finite range of parameters. Beyond the region of stability, the solitons lose the radial symmetry but may remain stable, keeping the same value of the topological charge. We have found bifurcations into solitons with n-fold bending symmetry, with n independent on m. Solitons without circular symmetry can also display (m + 1)-fold modulation behaviour. A sequence of bifurcations can transform the ring soliton into a pulsating or chaotic state which keeps the same value of the topological charge as the original ring.

© 2009 Optical Society of America

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  1. G. K. Batchelor, An Introduction to Fluid Dynamics, (Cambridge University Press, 1967).
  2. H. Kleinert, Multivalued Fields in Condensed Matter, Electrodynamics, and Gravitation, (World Scientific, Singapore, 2008).
  3. J. G. Cramer, R. L. Forward, M. S. Morris, M. Visser, G. Benford, and G. A. Landis, "Natural Wormholes as Gravitational Lenses," Phys. Rev. D51, 3117-3120 (1995).
  4. V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985-990 (1992).
    [CrossRef]
  5. J. P. Torres, J. M. Soto-Crespo, L. Torner, and D. V. Petrov "Solitary-wave Vortices in Quadratic Nonlinear Media," J. Opt. Soc. Am. B 15, 625-627 (1998).
    [CrossRef]
  6. A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
    [CrossRef]
  7. N. K. Efremidis, K. Hizanidis, B. A. Malomed, and P. Di Trapani, "Three-Dimensional Vortex Solitons in Self-Defocusing Media," Phys. Rev. Lett. 98, 113901 (2007).
    [CrossRef] [PubMed]
  8. B. A. Malomed, L.-C. Crasovan and D. Mihalache, "Stability of vortex solitons in the cubic-quintic model," Physica D 161, 187-201 (2002).
    [CrossRef]
  9. Y. J. He, B. A. Malomed, D. Mihalache and H. Z. Wang, "Crescent vortex solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 023824 (2008).
    [CrossRef]
  10. D. N. Neshev, A. Dreischuh, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, "Observation of polychromatic vortex solitons," Opt. Lett. 33, 1851 (2008).
    [CrossRef] [PubMed]
  11. V. Tikhonenko, Y. Kivshar, V.V. Steblina, and A.A. Zozulya, "Vortex solitons in a saturable optical medium," J. Opt. Soc. Am. B 15, 79-86 (1998).
    [CrossRef]
  12. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 94, 043902 (2005).
    [CrossRef] [PubMed]
  13. J. Wang and J. Yang, "Families of vortex solitons in periodic media," Phys. Rev. A 77, 033834 (2008).
    [CrossRef]
  14. J. Yang, "Stability of vortex solitons in a photorefractive optical lattice," New J. Phys. 6, 47 (2004).
    [CrossRef]
  15. T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, "Asymmetric Vortex Solitons in Nonlinear Periodic Lattices," Phys. Rev. Lett. 93, 063901 (2004).
    [CrossRef] [PubMed]
  16. G. A. Swartzlander, Jr., and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992).
    [CrossRef] [PubMed]
  17. V. Tikhonenko and N. Akhmediev, "Excitation of vortex solitons in a Gaussian beam configuration," Opt. Commun. 126, 108 (1996).
    [CrossRef]
  18. I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schr¨odinger equation," Phys. Lett. A 288, 292 (2001).
    [CrossRef]
  19. Q1. H. Michinel, J. Campo-T’aboas, M. L. Quiroga-Teixeiro, J. R. Salgueiro and R. Garc’ıa-Fern’andez, "Excitation of stable vortex solitons in nonlinear cubic-quintic materials," J. Opt. B: Quantum Semiclass. Opt. 3, 314-317 (2001).
    [CrossRef]
  20. H. Michinel, J. R. Salgueiro, and M. J. Paz-Alonso, "Square vortex solitons with a large angular momentum," Phys. Rev. E 70, 066605 (2004).
    [CrossRef]
  21. S. V. Fedorov, N. Rosanov, A. N. Shatsev, N. A. Veretenov, and A. G. Vladimirov, "Topologically multicharged and multihumped rotating solitons in wide-aperture lasers with a saturable absorber," IEEE J. Quantum Electron. 39, 197 (2003).
    [CrossRef]
  22. N. N. Rosanov, "Solitons in laser systems with saturable absorption," in: Dissipative solitons, (Eds.) N. Akhmediev and A. Ankiewicz, Lecture Notes in Physics, V. 661, Springer, Heidelberg, 2005.
  23. L.-C. Crasovan, B. A. Malomed and D. Mihalache, "Stable vortex solitons in the two-dimensional Ginzburg-Landau equation," Phys. Rev. E 63, 016605 (2001).
    [CrossRef]
  24. D. Mihalache, D. Mazilu, F. Lederer, H. Leblond and B. A. Malomed. "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).
    [CrossRef]
  25. J. M. Soto-Crespo, D. R. Heatley, E. M. Wright and N. Akhmediev, "Stability of the higher-bound states in a saturable self-focusing medium," Phys. Rev. A 44, 636-644 (1991).
    [CrossRef] [PubMed]
  26. A. Ankiewicz, N. Devine, N. Akhmediev and J. M. Soto-Crespo "Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media," Phys. Rev. A 77, 033840 (2008).
    [CrossRef]
  27. N. Akhmediev. J. M. Soto-Crespo, and G. Town, "Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg - Landau equation approach," Phys. Rev. E 63, 056602 (2001).
    [CrossRef]

2008

J. Wang and J. Yang, "Families of vortex solitons in periodic media," Phys. Rev. A 77, 033834 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond and B. A. Malomed. "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).
[CrossRef]

A. Ankiewicz, N. Devine, N. Akhmediev and J. M. Soto-Crespo "Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media," Phys. Rev. A 77, 033840 (2008).
[CrossRef]

Y. J. He, B. A. Malomed, D. Mihalache and H. Z. Wang, "Crescent vortex solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 023824 (2008).
[CrossRef]

D. N. Neshev, A. Dreischuh, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, "Observation of polychromatic vortex solitons," Opt. Lett. 33, 1851 (2008).
[CrossRef] [PubMed]

2007

N. K. Efremidis, K. Hizanidis, B. A. Malomed, and P. Di Trapani, "Three-Dimensional Vortex Solitons in Self-Defocusing Media," Phys. Rev. Lett. 98, 113901 (2007).
[CrossRef] [PubMed]

2005

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

2004

J. Yang, "Stability of vortex solitons in a photorefractive optical lattice," New J. Phys. 6, 47 (2004).
[CrossRef]

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, "Asymmetric Vortex Solitons in Nonlinear Periodic Lattices," Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

H. Michinel, J. R. Salgueiro, and M. J. Paz-Alonso, "Square vortex solitons with a large angular momentum," Phys. Rev. E 70, 066605 (2004).
[CrossRef]

2003

S. V. Fedorov, N. Rosanov, A. N. Shatsev, N. A. Veretenov, and A. G. Vladimirov, "Topologically multicharged and multihumped rotating solitons in wide-aperture lasers with a saturable absorber," IEEE J. Quantum Electron. 39, 197 (2003).
[CrossRef]

2002

B. A. Malomed, L.-C. Crasovan and D. Mihalache, "Stability of vortex solitons in the cubic-quintic model," Physica D 161, 187-201 (2002).
[CrossRef]

2001

N. Akhmediev. J. M. Soto-Crespo, and G. Town, "Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg - Landau equation approach," Phys. Rev. E 63, 056602 (2001).
[CrossRef]

L.-C. Crasovan, B. A. Malomed and D. Mihalache, "Stable vortex solitons in the two-dimensional Ginzburg-Landau equation," Phys. Rev. E 63, 016605 (2001).
[CrossRef]

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schr¨odinger equation," Phys. Lett. A 288, 292 (2001).
[CrossRef]

Q1. H. Michinel, J. Campo-T’aboas, M. L. Quiroga-Teixeiro, J. R. Salgueiro and R. Garc’ıa-Fern’andez, "Excitation of stable vortex solitons in nonlinear cubic-quintic materials," J. Opt. B: Quantum Semiclass. Opt. 3, 314-317 (2001).
[CrossRef]

1999

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
[CrossRef]

1998

1996

V. Tikhonenko and N. Akhmediev, "Excitation of vortex solitons in a Gaussian beam configuration," Opt. Commun. 126, 108 (1996).
[CrossRef]

1995

J. G. Cramer, R. L. Forward, M. S. Morris, M. Visser, G. Benford, and G. A. Landis, "Natural Wormholes as Gravitational Lenses," Phys. Rev. D51, 3117-3120 (1995).

1992

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985-990 (1992).
[CrossRef]

G. A. Swartzlander, Jr., and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992).
[CrossRef] [PubMed]

1991

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright and N. Akhmediev, "Stability of the higher-bound states in a saturable self-focusing medium," Phys. Rev. A 44, 636-644 (1991).
[CrossRef] [PubMed]

Akhmediev, N.

A. Ankiewicz, N. Devine, N. Akhmediev and J. M. Soto-Crespo "Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media," Phys. Rev. A 77, 033840 (2008).
[CrossRef]

N. Akhmediev. J. M. Soto-Crespo, and G. Town, "Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg - Landau equation approach," Phys. Rev. E 63, 056602 (2001).
[CrossRef]

V. Tikhonenko and N. Akhmediev, "Excitation of vortex solitons in a Gaussian beam configuration," Opt. Commun. 126, 108 (1996).
[CrossRef]

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright and N. Akhmediev, "Stability of the higher-bound states in a saturable self-focusing medium," Phys. Rev. A 44, 636-644 (1991).
[CrossRef] [PubMed]

Alexander, T. J.

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, "Asymmetric Vortex Solitons in Nonlinear Periodic Lattices," Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

Ankiewicz, A.

A. Ankiewicz, N. Devine, N. Akhmediev and J. M. Soto-Crespo "Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media," Phys. Rev. A 77, 033840 (2008).
[CrossRef]

Bazhenov, V. Yu.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985-990 (1992).
[CrossRef]

Benford, G.

J. G. Cramer, R. L. Forward, M. S. Morris, M. Visser, G. Benford, and G. A. Landis, "Natural Wormholes as Gravitational Lenses," Phys. Rev. D51, 3117-3120 (1995).

Buryak, A. V.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schr¨odinger equation," Phys. Lett. A 288, 292 (2001).
[CrossRef]

Cramer, J. G.

J. G. Cramer, R. L. Forward, M. S. Morris, M. Visser, G. Benford, and G. A. Landis, "Natural Wormholes as Gravitational Lenses," Phys. Rev. D51, 3117-3120 (1995).

Crasovan, L. C.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schr¨odinger equation," Phys. Lett. A 288, 292 (2001).
[CrossRef]

Crasovan, L.-C.

B. A. Malomed, L.-C. Crasovan and D. Mihalache, "Stability of vortex solitons in the cubic-quintic model," Physica D 161, 187-201 (2002).
[CrossRef]

L.-C. Crasovan, B. A. Malomed and D. Mihalache, "Stable vortex solitons in the two-dimensional Ginzburg-Landau equation," Phys. Rev. E 63, 016605 (2001).
[CrossRef]

Desyatnikov, A. S.

Devine, N.

A. Ankiewicz, N. Devine, N. Akhmediev and J. M. Soto-Crespo "Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media," Phys. Rev. A 77, 033840 (2008).
[CrossRef]

Di Trapani, P.

N. K. Efremidis, K. Hizanidis, B. A. Malomed, and P. Di Trapani, "Three-Dimensional Vortex Solitons in Self-Defocusing Media," Phys. Rev. Lett. 98, 113901 (2007).
[CrossRef] [PubMed]

Dreischuh, A.

D. N. Neshev, A. Dreischuh, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, "Observation of polychromatic vortex solitons," Opt. Lett. 33, 1851 (2008).
[CrossRef] [PubMed]

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
[CrossRef]

Efremidis, N. K.

N. K. Efremidis, K. Hizanidis, B. A. Malomed, and P. Di Trapani, "Three-Dimensional Vortex Solitons in Self-Defocusing Media," Phys. Rev. Lett. 98, 113901 (2007).
[CrossRef] [PubMed]

Fedorov, S. V.

S. V. Fedorov, N. Rosanov, A. N. Shatsev, N. A. Veretenov, and A. G. Vladimirov, "Topologically multicharged and multihumped rotating solitons in wide-aperture lasers with a saturable absorber," IEEE J. Quantum Electron. 39, 197 (2003).
[CrossRef]

Forward, R. L.

J. G. Cramer, R. L. Forward, M. S. Morris, M. Visser, G. Benford, and G. A. Landis, "Natural Wormholes as Gravitational Lenses," Phys. Rev. D51, 3117-3120 (1995).

Grasbon, F.

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
[CrossRef]

He, Y. J.

Y. J. He, B. A. Malomed, D. Mihalache and H. Z. Wang, "Crescent vortex solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 023824 (2008).
[CrossRef]

Heatley, D. R.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright and N. Akhmediev, "Stability of the higher-bound states in a saturable self-focusing medium," Phys. Rev. A 44, 636-644 (1991).
[CrossRef] [PubMed]

Hizanidis, K.

N. K. Efremidis, K. Hizanidis, B. A. Malomed, and P. Di Trapani, "Three-Dimensional Vortex Solitons in Self-Defocusing Media," Phys. Rev. Lett. 98, 113901 (2007).
[CrossRef] [PubMed]

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Kivshar, Y.

Kivshar, Y. S.

D. N. Neshev, A. Dreischuh, V. Shvedov, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, "Observation of polychromatic vortex solitons," Opt. Lett. 33, 1851 (2008).
[CrossRef] [PubMed]

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, "Asymmetric Vortex Solitons in Nonlinear Periodic Lattices," Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

Krolikowski, W.

Landis, G. A.

J. G. Cramer, R. L. Forward, M. S. Morris, M. Visser, G. Benford, and G. A. Landis, "Natural Wormholes as Gravitational Lenses," Phys. Rev. D51, 3117-3120 (1995).

Law, C. T.

G. A. Swartzlander, Jr., and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992).
[CrossRef] [PubMed]

Leblond, H.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond and B. A. Malomed. "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).
[CrossRef]

Lederer, F.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond and B. A. Malomed. "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).
[CrossRef]

Malomed, B. A.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond and B. A. Malomed. "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).
[CrossRef]

Y. J. He, B. A. Malomed, D. Mihalache and H. Z. Wang, "Crescent vortex solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 023824 (2008).
[CrossRef]

N. K. Efremidis, K. Hizanidis, B. A. Malomed, and P. Di Trapani, "Three-Dimensional Vortex Solitons in Self-Defocusing Media," Phys. Rev. Lett. 98, 113901 (2007).
[CrossRef] [PubMed]

B. A. Malomed, L.-C. Crasovan and D. Mihalache, "Stability of vortex solitons in the cubic-quintic model," Physica D 161, 187-201 (2002).
[CrossRef]

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schr¨odinger equation," Phys. Lett. A 288, 292 (2001).
[CrossRef]

L.-C. Crasovan, B. A. Malomed and D. Mihalache, "Stable vortex solitons in the two-dimensional Ginzburg-Landau equation," Phys. Rev. E 63, 016605 (2001).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond and B. A. Malomed. "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).
[CrossRef]

Michinel, H.

H. Michinel, J. R. Salgueiro, and M. J. Paz-Alonso, "Square vortex solitons with a large angular momentum," Phys. Rev. E 70, 066605 (2004).
[CrossRef]

Q1. H. Michinel, J. Campo-T’aboas, M. L. Quiroga-Teixeiro, J. R. Salgueiro and R. Garc’ıa-Fern’andez, "Excitation of stable vortex solitons in nonlinear cubic-quintic materials," J. Opt. B: Quantum Semiclass. Opt. 3, 314-317 (2001).
[CrossRef]

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond and B. A. Malomed. "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).
[CrossRef]

Y. J. He, B. A. Malomed, D. Mihalache and H. Z. Wang, "Crescent vortex solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 023824 (2008).
[CrossRef]

B. A. Malomed, L.-C. Crasovan and D. Mihalache, "Stability of vortex solitons in the cubic-quintic model," Physica D 161, 187-201 (2002).
[CrossRef]

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schr¨odinger equation," Phys. Lett. A 288, 292 (2001).
[CrossRef]

L.-C. Crasovan, B. A. Malomed and D. Mihalache, "Stable vortex solitons in the two-dimensional Ginzburg-Landau equation," Phys. Rev. E 63, 016605 (2001).
[CrossRef]

Morris, M. S.

J. G. Cramer, R. L. Forward, M. S. Morris, M. Visser, G. Benford, and G. A. Landis, "Natural Wormholes as Gravitational Lenses," Phys. Rev. D51, 3117-3120 (1995).

Neshev, D. N.

Paulus, G. G.

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
[CrossRef]

Paz-Alonso, M. J.

H. Michinel, J. R. Salgueiro, and M. J. Paz-Alonso, "Square vortex solitons with a large angular momentum," Phys. Rev. E 70, 066605 (2004).
[CrossRef]

Petrov, D. V.

Rosanov, N.

S. V. Fedorov, N. Rosanov, A. N. Shatsev, N. A. Veretenov, and A. G. Vladimirov, "Topologically multicharged and multihumped rotating solitons in wide-aperture lasers with a saturable absorber," IEEE J. Quantum Electron. 39, 197 (2003).
[CrossRef]

Salgueiro, J. R.

H. Michinel, J. R. Salgueiro, and M. J. Paz-Alonso, "Square vortex solitons with a large angular momentum," Phys. Rev. E 70, 066605 (2004).
[CrossRef]

Sammut, R. A.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schr¨odinger equation," Phys. Lett. A 288, 292 (2001).
[CrossRef]

Shatsev, A. N.

S. V. Fedorov, N. Rosanov, A. N. Shatsev, N. A. Veretenov, and A. G. Vladimirov, "Topologically multicharged and multihumped rotating solitons in wide-aperture lasers with a saturable absorber," IEEE J. Quantum Electron. 39, 197 (2003).
[CrossRef]

Shvedov, V.

Soskin, M. S.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985-990 (1992).
[CrossRef]

Soto-Crespo, J. M.

A. Ankiewicz, N. Devine, N. Akhmediev and J. M. Soto-Crespo "Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media," Phys. Rev. A 77, 033840 (2008).
[CrossRef]

J. P. Torres, J. M. Soto-Crespo, L. Torner, and D. V. Petrov "Solitary-wave Vortices in Quadratic Nonlinear Media," J. Opt. Soc. Am. B 15, 625-627 (1998).
[CrossRef]

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright and N. Akhmediev, "Stability of the higher-bound states in a saturable self-focusing medium," Phys. Rev. A 44, 636-644 (1991).
[CrossRef] [PubMed]

Steblina, V.V.

Sukhorukov, A. A.

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, "Asymmetric Vortex Solitons in Nonlinear Periodic Lattices," Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

Swartzlander, G. A.

G. A. Swartzlander, Jr., and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992).
[CrossRef] [PubMed]

Tikhonenko, V.

V. Tikhonenko, Y. Kivshar, V.V. Steblina, and A.A. Zozulya, "Vortex solitons in a saturable optical medium," J. Opt. Soc. Am. B 15, 79-86 (1998).
[CrossRef]

V. Tikhonenko and N. Akhmediev, "Excitation of vortex solitons in a Gaussian beam configuration," Opt. Commun. 126, 108 (1996).
[CrossRef]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

J. P. Torres, J. M. Soto-Crespo, L. Torner, and D. V. Petrov "Solitary-wave Vortices in Quadratic Nonlinear Media," J. Opt. Soc. Am. B 15, 625-627 (1998).
[CrossRef]

Torres, J. P.

Towers, I.

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schr¨odinger equation," Phys. Lett. A 288, 292 (2001).
[CrossRef]

Vasnetsov, M. V.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985-990 (1992).
[CrossRef]

Veretenov, N. A.

S. V. Fedorov, N. Rosanov, A. N. Shatsev, N. A. Veretenov, and A. G. Vladimirov, "Topologically multicharged and multihumped rotating solitons in wide-aperture lasers with a saturable absorber," IEEE J. Quantum Electron. 39, 197 (2003).
[CrossRef]

Visser, M.

J. G. Cramer, R. L. Forward, M. S. Morris, M. Visser, G. Benford, and G. A. Landis, "Natural Wormholes as Gravitational Lenses," Phys. Rev. D51, 3117-3120 (1995).

Vladimirov, A. G.

S. V. Fedorov, N. Rosanov, A. N. Shatsev, N. A. Veretenov, and A. G. Vladimirov, "Topologically multicharged and multihumped rotating solitons in wide-aperture lasers with a saturable absorber," IEEE J. Quantum Electron. 39, 197 (2003).
[CrossRef]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Walther, H.

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
[CrossRef]

Wang, H. Z.

Y. J. He, B. A. Malomed, D. Mihalache and H. Z. Wang, "Crescent vortex solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 023824 (2008).
[CrossRef]

Wang, J.

J. Wang and J. Yang, "Families of vortex solitons in periodic media," Phys. Rev. A 77, 033834 (2008).
[CrossRef]

Wright, E. M.

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright and N. Akhmediev, "Stability of the higher-bound states in a saturable self-focusing medium," Phys. Rev. A 44, 636-644 (1991).
[CrossRef] [PubMed]

Yang, J.

J. Wang and J. Yang, "Families of vortex solitons in periodic media," Phys. Rev. A 77, 033834 (2008).
[CrossRef]

J. Yang, "Stability of vortex solitons in a photorefractive optical lattice," New J. Phys. 6, 47 (2004).
[CrossRef]

Zacher, F.

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
[CrossRef]

Zozulya, A.A.

IEEE J. Quantum Electron.

S. V. Fedorov, N. Rosanov, A. N. Shatsev, N. A. Veretenov, and A. G. Vladimirov, "Topologically multicharged and multihumped rotating solitons in wide-aperture lasers with a saturable absorber," IEEE J. Quantum Electron. 39, 197 (2003).
[CrossRef]

J. Mod. Opt.

V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, "Screw dislocations in light wavefronts," J. Mod. Opt. 39, 985-990 (1992).
[CrossRef]

J. Opt. B: Quantum Semiclass. Opt.

Q1. H. Michinel, J. Campo-T’aboas, M. L. Quiroga-Teixeiro, J. R. Salgueiro and R. Garc’ıa-Fern’andez, "Excitation of stable vortex solitons in nonlinear cubic-quintic materials," J. Opt. B: Quantum Semiclass. Opt. 3, 314-317 (2001).
[CrossRef]

J. Opt. Soc. Am. B

New J. Phys.

J. Yang, "Stability of vortex solitons in a photorefractive optical lattice," New J. Phys. 6, 47 (2004).
[CrossRef]

Opt. Commun.

V. Tikhonenko and N. Akhmediev, "Excitation of vortex solitons in a Gaussian beam configuration," Opt. Commun. 126, 108 (1996).
[CrossRef]

Opt. Lett.

Phys. Lett. A

I. Towers, A. V. Buryak, R. A. Sammut, B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schr¨odinger equation," Phys. Lett. A 288, 292 (2001).
[CrossRef]

Phys. Rev.

J. G. Cramer, R. L. Forward, M. S. Morris, M. Visser, G. Benford, and G. A. Landis, "Natural Wormholes as Gravitational Lenses," Phys. Rev. D51, 3117-3120 (1995).

Phys. Rev. A

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond and B. A. Malomed. "Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation," Phys. Rev. A 77, 033817 (2008).
[CrossRef]

J. M. Soto-Crespo, D. R. Heatley, E. M. Wright and N. Akhmediev, "Stability of the higher-bound states in a saturable self-focusing medium," Phys. Rev. A 44, 636-644 (1991).
[CrossRef] [PubMed]

A. Ankiewicz, N. Devine, N. Akhmediev and J. M. Soto-Crespo "Continuously self-focusing and continuously self-defocusing 2-D beams in dissipative media," Phys. Rev. A 77, 033840 (2008).
[CrossRef]

J. Wang and J. Yang, "Families of vortex solitons in periodic media," Phys. Rev. A 77, 033834 (2008).
[CrossRef]

Y. J. He, B. A. Malomed, D. Mihalache and H. Z. Wang, "Crescent vortex solitons in strongly nonlocal nonlinear media," Phys. Rev. A 78, 023824 (2008).
[CrossRef]

Phys. Rev. E

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
[CrossRef]

H. Michinel, J. R. Salgueiro, and M. J. Paz-Alonso, "Square vortex solitons with a large angular momentum," Phys. Rev. E 70, 066605 (2004).
[CrossRef]

N. Akhmediev. J. M. Soto-Crespo, and G. Town, "Pulsating solitons, chaotic solitons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg - Landau equation approach," Phys. Rev. E 63, 056602 (2001).
[CrossRef]

L.-C. Crasovan, B. A. Malomed and D. Mihalache, "Stable vortex solitons in the two-dimensional Ginzburg-Landau equation," Phys. Rev. E 63, 016605 (2001).
[CrossRef]

Phys. Rev. Lett.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices," Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, "Asymmetric Vortex Solitons in Nonlinear Periodic Lattices," Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

G. A. Swartzlander, Jr., and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992).
[CrossRef] [PubMed]

N. K. Efremidis, K. Hizanidis, B. A. Malomed, and P. Di Trapani, "Three-Dimensional Vortex Solitons in Self-Defocusing Media," Phys. Rev. Lett. 98, 113901 (2007).
[CrossRef] [PubMed]

Physica D

B. A. Malomed, L.-C. Crasovan and D. Mihalache, "Stability of vortex solitons in the cubic-quintic model," Physica D 161, 187-201 (2002).
[CrossRef]

Other

N. N. Rosanov, "Solitons in laser systems with saturable absorption," in: Dissipative solitons, (Eds.) N. Akhmediev and A. Ankiewicz, Lecture Notes in Physics, V. 661, Springer, Heidelberg, 2005.

G. K. Batchelor, An Introduction to Fluid Dynamics, (Cambridge University Press, 1967).

H. Kleinert, Multivalued Fields in Condensed Matter, Electrodynamics, and Gravitation, (World Scientific, Singapore, 2008).

Supplementary Material (7)

» Media 1: MPG (1406 KB)     
» Media 2: MPG (1406 KB)     
» Media 3: MPG (1406 KB)     
» Media 4: MPG (1125 KB)     
» Media 5: MPG (1125 KB)     
» Media 6: MPG (1124 KB)     
» Media 7: MPG (1125 KB)     

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Figures (15)

Fig. 1.
Fig. 1.

The power Q vs ε for the radially symmetric vortex dissipative solitons with m = 1,2,3,4 and 5. Note the logarithmic scale along the vertical axis.

Fig. 2.
Fig. 2.

Power Q versus ε diagram for the ring solitons with vorticity m = 1. The red and blue curves and the solid part of the green curve correspond to stable solutions, while the dashed green one is for unstable ones. Solutions on the red curve have a radially symmetric amplitude profile while other solutions are radially asymmetric. The yellow inset in the lower right corner is a magnification of the curves enclosed into the small yellow rectangle in the upper left part of the main diagram. This magnification shows more clearly the bifurcation of the pulsating vortex solutions (blue stripe) from the stationary radially asymmetric ones (green curve).

Fig. 3.
Fig. 3.

2D vortex soliton profiles for m = 1 for the equation parameters, written in the upper left part of the figure. In the cases (a) and (b) the power, Q is constant, while for (c) the power is a periodic function of z, as it is shown on top of the panel (c).

Fig. 4.
Fig. 4.

(Upper row) Contour color plots of the soliton profiles shown in Fig. 3. (Lower row) Contour color plots of the phase profiles for the same solutions. The periodic evolution of the soliton profile shown in (c1) can be seen in the linked movie (Media 1).

Fig. 5.
Fig. 5.

Regions of existence of vortex solitons with m = 2. The red curve corresponds to the radially symmetric ring solitons. Solitons represented by the blue curve are radially asymmetric. The thick filled green circle indicates the location, in the parameter space, of the vortex soliton whose intensity and phase profiles are shown in Fig. 6.

Fig. 6.
Fig. 6.

Radially asymmetric ring vortex soliton with m = 2. (a) 3-D plot of the intensity profile. (b) Color contour plot of the same intensity profile in the (x, y)-plane. (c) Color contour plot of the phase profile. The system parameters are chosen at the thick filled green circle in Fig. 5.

Fig. 7.
Fig. 7.

Regions of existence of vortex solitons with m = 3 in the ε domain. The solid (dashed) red curve represents stable (unstable) radially symmetric solitons. The solid blue and green curves correspond to stable radially asymmetric ring solitons while the blue dashed curve stands for unstable ones.

Fig. 8.
Fig. 8.

3-D intensity profiles of the radially asymmetric ring vortex solutions whose location in the parameter space is indicated in Fig. 7 by the gray filled circles. The two profiles belong to (a) the green and b) the blue branches of solitons in Fig. 7 respectively. The green profile is stable while the blue one is slightly unstable and converges, on propagation, to the green one. The profile (b) has four-fold bending symmetry while the profile in (a) is completely asymmetric. Fig. 9 shows more clearly the difference between them.

Fig. 9.
Fig. 9.

(upper row) Color contour plots of the intensity in the (x,y) plane of the ring solitons with m = 3 shown in Fig. 8. (lower row) Phase profiles for the same solitons. The right column corresponds to the upper grey filled circle in Fig. 7 while the left column to the lower circle. Evolution of each ring soliton can also be seen in animation, i.e. a1) (Media 2) b1) (Media 3).

Fig. 10.
Fig. 10.

Bifurcation diagram for the ring vortex solitons with m = 4. The upper left yellow inset is a magnified part of the diagram in the lower small yellow box. In the inset, instead or representing the allowed values of Q on propagation, only maxima (red) and minima (blue) of Q(z) are shown

Fig. 11.
Fig. 11.

Two examples of radially asymmetric ring solitons with m = 4. Each one can be seen in animation (Media 4 and Media 5).

Fig. 12.
Fig. 12.

Evolution of Q for stationary (light blue curve), quasi-periodic pulsating (magenta) and chaotic (orange) vortex solitons. The colors correspond to the thick vertical lines in Fig. 10.

Fig. 13.
Fig. 13.

(a) Three-dimensional plot of the ring soliton with m = 9 for ε = 0.745. Color contour plots of (b) the intensity and (c) the phase of the same vortex dissipative soliton.

Fig. 14.
Fig. 14.

Double periodic evolution of Q vs z for vortex dissipative soliton with m = 9 (blue curve). The yellow inset on the top of the figure shows a magnified part of the blue curve enclosed into a small yellow box to the right of z = 0.

Fig. 15.
Fig. 15.

(a) Movie (Media 6) showing the fast clockwise rotation of the nine maxima of the vortex dissipative soliton with m = 9. (b) Movie (Media 7) showing the slow rotation of the dissipative soliton with four-fold bending symmetry in the opposite direction.

Equations (4)

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

i ψ z + D 2 2 ψ + ψ 2 ψ + ν ψ 4 ψ = iδψ + ψ 2 ψ + 2 ψ + ψ 4 ψ .
2 = x 2 + 2 y 2
Q ( z ) = ψ ( x , y , z ) 2 dxdy ,
ψ ( x , y , 0 ) = A 0 r m exp ( r 2 w 2 + i m θ )

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