Abstract

We report novel dynamical regimes of dissipative vortices supported by a radial-azimuthal potential (RAP) in the 2D complex Ginzburg-Landau (CGL) equation with the cubic-quintic nonlinearity. First, the stable solutions of vortices with intrinsic vorticity S = 1 and 2 are obtained in the CGL equation without potential. The RAP is a model of an active optical medium with respective expanding anti-waveguiding structures with m (integer) annularly periodic modulation. If the potential is strong enough, m jets fundamental of solitons are continuously emitted from the vortices. The influence of m, diffusivity term (viscosity) β, and cubic-gain coefficient ε on the dynamic region is studied. For a weak potential, the shape of vortices are stretched into the polygon, such as square for m = 4. But for a stronger potential, the vortices will be broke into m fundamental solitons.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. López-Mariscal and J. C. Gutiérrez-Vega, “In your phase: all about optical vortices,” Opt. Photonics News20(5), 10–13 (2009).
  2. I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys.74(1), 99–143 (2002).
    [CrossRef]
  3. N. Rosanov, “Solitons in laser systems with absorption,” in Dissipative Solitons, N. Akhmediev and A. Ankievicz, eds. (Springer-Verlag, Berlin, 2005).
  4. B. A. Malomed, “Complex Ginzburg–Landau equation,” in Encyclopedia of Nonlinear Science, A. Scott, ed. (Routledge, New York, 2005), p. 157.
  5. N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Stable soliton pairs in optical transmission lines and fiber lasers,” J. Opt. Soc. Am. B15(2), 515–522 (1998).
    [CrossRef]
  6. L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.63(1 Pt 2), 016605 (2001).
    [PubMed]
  7. J. M. Soto-Crespo, N. Akhmediev, C. Mejia-Cortés, and N. Devine, “Dissipative ring solitons with vorticity,” Opt. Express17(6), 4236–4250 (2009).
    [CrossRef] [PubMed]
  8. D. V. Skryabin and A. G. Vladimirov, “Vortex induced rotation of clusters of localized states in the complex Ginzburg-Landau equation,” Phys. Rev. Lett.89(4), 044101 (2002).
    [CrossRef] [PubMed]
  9. J. M. Soto-Crespo, P. Grelu, and N. Akhmediev, “Optical bullets and “rockets” in nonlinear dissipative systems and their transformations and interactions,” Opt. Express14(9), 4013–4025 (2006).
    [CrossRef] [PubMed]
  10. 10D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A75, 033811 (2007).
  11. 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. A77(3), 033817 (2008).
    [CrossRef]
  12. B. Liu, Y. J. He, Z. R. Qiu, and H. Z. Wang, “Annularly and radially phase-modulated spatiotemporal necklace-ring patterns in the Ginzburg-Landau and Swift-Hohenberg equations,” Opt. Express17(15), 12203–12209 (2009).
    [CrossRef] [PubMed]
  13. B. Liu, X. D. He, and S. J. Li, “Phase controlling of collisions between solitons in the two-dimensional complex Ginzburg-Landau equation without viscosity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.84(5), 056607 (2011).
    [CrossRef] [PubMed]
  14. D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stablevotex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett.97, 073904 (2006).
  15. D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability limits for three-dimensional vortex solitons in the Ginzburg-Landau equation with the cubic-quintic nonlinearity,” Phys. Rev. A76, 045803 (2007).
  16. H. Leblond, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the Ginzburg-Landau model of two-dimensional lasing medium with a transverse grating,” Phys. Rev. A80(3), 033835 (2009).
    [CrossRef]
  17. H. Sakaguchi and B. A. Malomed, “Two-dimensional dissipative gap solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.80(2), 026606 (2009).
    [CrossRef] [PubMed]
  18. Y. J. He, B. A. Malomed, D. Mihalache, B. Liu, H. C. Huang, H. Yang, and H. Z. Wang, “Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg-Landau equations with a linear potential,” Opt. Lett.34(19), 2976–2978 (2009).
    [CrossRef] [PubMed]
  19. B. Liu, Y. J. He, B. A. Malomed, X. S. Wang, P. G. Kevrekidis, T. B. Wang, F. C. Leng, Z. R. Qiu, and H. Z. Wang, “Continuous generation of soliton patterns in two-dimensional dissipative media by razor, dagger, and needle potentials,” Opt. Lett.35(12), 1974–1976 (2010).
    [CrossRef] [PubMed]
  20. D. Mihalache, “Three-dimensional Ginzburg-Landau dissipative solitons supported by a two-dimensional transverse grating,” Proc. Romanian Acad. Ser. A11(2), 142–147 (2010).
  21. B. Liu and X. D. He, “Continuous generation of “light bullets” in dissipative media by an annularly periodic potential,” Opt. Express19(21), 20009–20014 (2011).
    [CrossRef] [PubMed]
  22. Y. J. He, B. A. Malomed, F. Ye, J. Dong, Z. Qiu, H. Z. Wang, and B. Hu, “Splitting broad beams into arrays of dissipative satial solitns by material and virtual gratings,” Phys. Scr.82(6), 065404 (2010).
    [CrossRef]
  23. C. P. Yin, D. Mihalache, and Y. J. He, “Dynamics of two-dimensional dissipative spatial solitons interacting with an umbrella-shaped potential,” J. Opt. Soc. Am. B28(2), 342–346 (2011).
  24. Y. J. He, D. Mihalache, B. A. Malomed, Y. Qiu, Z. Chen, and Y. Li, “Generation of polygonal soliton clusters and fundamental solitons in dissipative systems by necklace-ring beams with radial-azimuthal phase modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.85(6), 066206 (2012).
    [CrossRef] [PubMed]
  25. D. Mihalache, D. Mazilu, V. Skarka, B. Malomed, H. Leblond, N. Aleksić, and F. Lederer, “Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials,” Phys. Rev. A82(2), 023813 (2010).
    [CrossRef]
  26. V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of Stable Vortical Solitons in Ginzburg-Landau Media with Radially Inhomogeneous Losses,” Phys. Rev. Lett.105(21), 213901 (2010).
    [CrossRef] [PubMed]
  27. D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Solitons in a medium with linear dissipation and localized gain,” Opt. Lett.36(7), 1200–1202 (2011).
    [CrossRef] [PubMed]
  28. C. Cleff, B. Gütlich, and C. Denz, “Gradient Induced Motion Control of Drifting Solitary Structures in a Nonlinear Optical Single Feedback Experiment,” Phys. Rev. Lett.100(23), 233902 (2008).
    [CrossRef] [PubMed]
  29. A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica,” Opt. Express14(13), 6055–6062 (2006).
    [CrossRef] [PubMed]
  30. J. Lega, J. V. Moloney, and A. C. Newell, “Swift-Hohenberg equation for Lasers,” Phys. Rev. Lett.73(22), 2978–2981 (1994).
    [CrossRef] [PubMed]

2012

Y. J. He, D. Mihalache, B. A. Malomed, Y. Qiu, Z. Chen, and Y. Li, “Generation of polygonal soliton clusters and fundamental solitons in dissipative systems by necklace-ring beams with radial-azimuthal phase modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.85(6), 066206 (2012).
[CrossRef] [PubMed]

2011

2010

B. Liu, Y. J. He, B. A. Malomed, X. S. Wang, P. G. Kevrekidis, T. B. Wang, F. C. Leng, Z. R. Qiu, and H. Z. Wang, “Continuous generation of soliton patterns in two-dimensional dissipative media by razor, dagger, and needle potentials,” Opt. Lett.35(12), 1974–1976 (2010).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, V. Skarka, B. Malomed, H. Leblond, N. Aleksić, and F. Lederer, “Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials,” Phys. Rev. A82(2), 023813 (2010).
[CrossRef]

V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of Stable Vortical Solitons in Ginzburg-Landau Media with Radially Inhomogeneous Losses,” Phys. Rev. Lett.105(21), 213901 (2010).
[CrossRef] [PubMed]

D. Mihalache, “Three-dimensional Ginzburg-Landau dissipative solitons supported by a two-dimensional transverse grating,” Proc. Romanian Acad. Ser. A11(2), 142–147 (2010).

Y. J. He, B. A. Malomed, F. Ye, J. Dong, Z. Qiu, H. Z. Wang, and B. Hu, “Splitting broad beams into arrays of dissipative satial solitns by material and virtual gratings,” Phys. Scr.82(6), 065404 (2010).
[CrossRef]

2009

H. Leblond, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the Ginzburg-Landau model of two-dimensional lasing medium with a transverse grating,” Phys. Rev. A80(3), 033835 (2009).
[CrossRef]

H. Sakaguchi and B. A. Malomed, “Two-dimensional dissipative gap solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.80(2), 026606 (2009).
[CrossRef] [PubMed]

C. López-Mariscal and J. C. Gutiérrez-Vega, “In your phase: all about optical vortices,” Opt. Photonics News20(5), 10–13 (2009).

J. M. Soto-Crespo, N. Akhmediev, C. Mejia-Cortés, and N. Devine, “Dissipative ring solitons with vorticity,” Opt. Express17(6), 4236–4250 (2009).
[CrossRef] [PubMed]

B. Liu, Y. J. He, Z. R. Qiu, and H. Z. Wang, “Annularly and radially phase-modulated spatiotemporal necklace-ring patterns in the Ginzburg-Landau and Swift-Hohenberg equations,” Opt. Express17(15), 12203–12209 (2009).
[CrossRef] [PubMed]

Y. J. He, B. A. Malomed, D. Mihalache, B. Liu, H. C. Huang, H. Yang, and H. Z. Wang, “Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg-Landau equations with a linear potential,” Opt. Lett.34(19), 2976–2978 (2009).
[CrossRef] [PubMed]

2008

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. A77(3), 033817 (2008).
[CrossRef]

C. Cleff, B. Gütlich, and C. Denz, “Gradient Induced Motion Control of Drifting Solitary Structures in a Nonlinear Optical Single Feedback Experiment,” Phys. Rev. Lett.100(23), 233902 (2008).
[CrossRef] [PubMed]

2007

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability limits for three-dimensional vortex solitons in the Ginzburg-Landau equation with the cubic-quintic nonlinearity,” Phys. Rev. A76, 045803 (2007).

10D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A75, 033811 (2007).

2006

2002

D. V. Skryabin and A. G. Vladimirov, “Vortex induced rotation of clusters of localized states in the complex Ginzburg-Landau equation,” Phys. Rev. Lett.89(4), 044101 (2002).
[CrossRef] [PubMed]

I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys.74(1), 99–143 (2002).
[CrossRef]

2001

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.63(1 Pt 2), 016605 (2001).
[PubMed]

1998

1994

J. Lega, J. V. Moloney, and A. C. Newell, “Swift-Hohenberg equation for Lasers,” Phys. Rev. Lett.73(22), 2978–2981 (1994).
[CrossRef] [PubMed]

Akhmediev, N.

Akhmediev, N. N.

Aleksic, N.

D. Mihalache, D. Mazilu, V. Skarka, B. Malomed, H. Leblond, N. Aleksić, and F. Lederer, “Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials,” Phys. Rev. A82(2), 023813 (2010).
[CrossRef]

Aleksic, N. B.

V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of Stable Vortical Solitons in Ginzburg-Landau Media with Radially Inhomogeneous Losses,” Phys. Rev. Lett.105(21), 213901 (2010).
[CrossRef] [PubMed]

Ankiewicz, A.

Aranson, I. S.

I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys.74(1), 99–143 (2002).
[CrossRef]

Burghoff, J.

Chen, Z.

Y. J. He, D. Mihalache, B. A. Malomed, Y. Qiu, Z. Chen, and Y. Li, “Generation of polygonal soliton clusters and fundamental solitons in dissipative systems by necklace-ring beams with radial-azimuthal phase modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.85(6), 066206 (2012).
[CrossRef] [PubMed]

Cleff, C.

C. Cleff, B. Gütlich, and C. Denz, “Gradient Induced Motion Control of Drifting Solitary Structures in a Nonlinear Optical Single Feedback Experiment,” Phys. Rev. Lett.100(23), 233902 (2008).
[CrossRef] [PubMed]

Crasovan, L.-C.

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stablevotex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett.97, 073904 (2006).

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.63(1 Pt 2), 016605 (2001).
[PubMed]

Denz, C.

C. Cleff, B. Gütlich, and C. Denz, “Gradient Induced Motion Control of Drifting Solitary Structures in a Nonlinear Optical Single Feedback Experiment,” Phys. Rev. Lett.100(23), 233902 (2008).
[CrossRef] [PubMed]

Devine, N.

Dong, J.

Y. J. He, B. A. Malomed, F. Ye, J. Dong, Z. Qiu, H. Z. Wang, and B. Hu, “Splitting broad beams into arrays of dissipative satial solitns by material and virtual gratings,” Phys. Scr.82(6), 065404 (2010).
[CrossRef]

Grelu, P.

Gutiérrez-Vega, J. C.

C. López-Mariscal and J. C. Gutiérrez-Vega, “In your phase: all about optical vortices,” Opt. Photonics News20(5), 10–13 (2009).

Gütlich, B.

C. Cleff, B. Gütlich, and C. Denz, “Gradient Induced Motion Control of Drifting Solitary Structures in a Nonlinear Optical Single Feedback Experiment,” Phys. Rev. Lett.100(23), 233902 (2008).
[CrossRef] [PubMed]

He, X. D.

B. Liu, X. D. He, and S. J. Li, “Phase controlling of collisions between solitons in the two-dimensional complex Ginzburg-Landau equation without viscosity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.84(5), 056607 (2011).
[CrossRef] [PubMed]

B. Liu and X. D. He, “Continuous generation of “light bullets” in dissipative media by an annularly periodic potential,” Opt. Express19(21), 20009–20014 (2011).
[CrossRef] [PubMed]

He, Y. J.

Y. J. He, D. Mihalache, B. A. Malomed, Y. Qiu, Z. Chen, and Y. Li, “Generation of polygonal soliton clusters and fundamental solitons in dissipative systems by necklace-ring beams with radial-azimuthal phase modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.85(6), 066206 (2012).
[CrossRef] [PubMed]

C. P. Yin, D. Mihalache, and Y. J. He, “Dynamics of two-dimensional dissipative spatial solitons interacting with an umbrella-shaped potential,” J. Opt. Soc. Am. B28(2), 342–346 (2011).

B. Liu, Y. J. He, B. A. Malomed, X. S. Wang, P. G. Kevrekidis, T. B. Wang, F. C. Leng, Z. R. Qiu, and H. Z. Wang, “Continuous generation of soliton patterns in two-dimensional dissipative media by razor, dagger, and needle potentials,” Opt. Lett.35(12), 1974–1976 (2010).
[CrossRef] [PubMed]

Y. J. He, B. A. Malomed, F. Ye, J. Dong, Z. Qiu, H. Z. Wang, and B. Hu, “Splitting broad beams into arrays of dissipative satial solitns by material and virtual gratings,” Phys. Scr.82(6), 065404 (2010).
[CrossRef]

Y. J. He, B. A. Malomed, D. Mihalache, B. Liu, H. C. Huang, H. Yang, and H. Z. Wang, “Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg-Landau equations with a linear potential,” Opt. Lett.34(19), 2976–2978 (2009).
[CrossRef] [PubMed]

B. Liu, Y. J. He, Z. R. Qiu, and H. Z. Wang, “Annularly and radially phase-modulated spatiotemporal necklace-ring patterns in the Ginzburg-Landau and Swift-Hohenberg equations,” Opt. Express17(15), 12203–12209 (2009).
[CrossRef] [PubMed]

Hu, B.

Y. J. He, B. A. Malomed, F. Ye, J. Dong, Z. Qiu, H. Z. Wang, and B. Hu, “Splitting broad beams into arrays of dissipative satial solitns by material and virtual gratings,” Phys. Scr.82(6), 065404 (2010).
[CrossRef]

Huang, H. C.

Kartashov, Y. V.

D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Solitons in a medium with linear dissipation and localized gain,” Opt. Lett.36(7), 1200–1202 (2011).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stablevotex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett.97, 073904 (2006).

Kevrekidis, P. G.

Konotop, V. V.

Kramer, L.

I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys.74(1), 99–143 (2002).
[CrossRef]

Leblond, H.

V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of Stable Vortical Solitons in Ginzburg-Landau Media with Radially Inhomogeneous Losses,” Phys. Rev. Lett.105(21), 213901 (2010).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, V. Skarka, B. Malomed, H. Leblond, N. Aleksić, and F. Lederer, “Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials,” Phys. Rev. A82(2), 023813 (2010).
[CrossRef]

H. Leblond, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the Ginzburg-Landau model of two-dimensional lasing medium with a transverse grating,” Phys. Rev. A80(3), 033835 (2009).
[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. A77(3), 033817 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability limits for three-dimensional vortex solitons in the Ginzburg-Landau equation with the cubic-quintic nonlinearity,” Phys. Rev. A76, 045803 (2007).

10D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A75, 033811 (2007).

Lederer, F.

D. Mihalache, D. Mazilu, V. Skarka, B. Malomed, H. Leblond, N. Aleksić, and F. Lederer, “Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials,” Phys. Rev. A82(2), 023813 (2010).
[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. A77(3), 033817 (2008).
[CrossRef]

10D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A75, 033811 (2007).

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability limits for three-dimensional vortex solitons in the Ginzburg-Landau equation with the cubic-quintic nonlinearity,” Phys. Rev. A76, 045803 (2007).

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stablevotex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett.97, 073904 (2006).

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, “Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica,” Opt. Express14(13), 6055–6062 (2006).
[CrossRef] [PubMed]

Lega, J.

J. Lega, J. V. Moloney, and A. C. Newell, “Swift-Hohenberg equation for Lasers,” Phys. Rev. Lett.73(22), 2978–2981 (1994).
[CrossRef] [PubMed]

Leng, F. C.

Li, S. J.

B. Liu, X. D. He, and S. J. Li, “Phase controlling of collisions between solitons in the two-dimensional complex Ginzburg-Landau equation without viscosity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.84(5), 056607 (2011).
[CrossRef] [PubMed]

Li, Y.

Y. J. He, D. Mihalache, B. A. Malomed, Y. Qiu, Z. Chen, and Y. Li, “Generation of polygonal soliton clusters and fundamental solitons in dissipative systems by necklace-ring beams with radial-azimuthal phase modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.85(6), 066206 (2012).
[CrossRef] [PubMed]

Liu, B.

López-Mariscal, C.

C. López-Mariscal and J. C. Gutiérrez-Vega, “In your phase: all about optical vortices,” Opt. Photonics News20(5), 10–13 (2009).

Malomed, B.

D. Mihalache, D. Mazilu, V. Skarka, B. Malomed, H. Leblond, N. Aleksić, and F. Lederer, “Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials,” Phys. Rev. A82(2), 023813 (2010).
[CrossRef]

Malomed, B. A.

Y. J. He, D. Mihalache, B. A. Malomed, Y. Qiu, Z. Chen, and Y. Li, “Generation of polygonal soliton clusters and fundamental solitons in dissipative systems by necklace-ring beams with radial-azimuthal phase modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.85(6), 066206 (2012).
[CrossRef] [PubMed]

V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of Stable Vortical Solitons in Ginzburg-Landau Media with Radially Inhomogeneous Losses,” Phys. Rev. Lett.105(21), 213901 (2010).
[CrossRef] [PubMed]

Y. J. He, B. A. Malomed, F. Ye, J. Dong, Z. Qiu, H. Z. Wang, and B. Hu, “Splitting broad beams into arrays of dissipative satial solitns by material and virtual gratings,” Phys. Scr.82(6), 065404 (2010).
[CrossRef]

B. Liu, Y. J. He, B. A. Malomed, X. S. Wang, P. G. Kevrekidis, T. B. Wang, F. C. Leng, Z. R. Qiu, and H. Z. Wang, “Continuous generation of soliton patterns in two-dimensional dissipative media by razor, dagger, and needle potentials,” Opt. Lett.35(12), 1974–1976 (2010).
[CrossRef] [PubMed]

Y. J. He, B. A. Malomed, D. Mihalache, B. Liu, H. C. Huang, H. Yang, and H. Z. Wang, “Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg-Landau equations with a linear potential,” Opt. Lett.34(19), 2976–2978 (2009).
[CrossRef] [PubMed]

H. Sakaguchi and B. A. Malomed, “Two-dimensional dissipative gap solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.80(2), 026606 (2009).
[CrossRef] [PubMed]

H. Leblond, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the Ginzburg-Landau model of two-dimensional lasing medium with a transverse grating,” Phys. Rev. A80(3), 033835 (2009).
[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. A77(3), 033817 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability limits for three-dimensional vortex solitons in the Ginzburg-Landau equation with the cubic-quintic nonlinearity,” Phys. Rev. A76, 045803 (2007).

10D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A75, 033811 (2007).

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stablevotex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett.97, 073904 (2006).

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.63(1 Pt 2), 016605 (2001).
[PubMed]

Mazilu, D.

D. Mihalache, D. Mazilu, V. Skarka, B. Malomed, H. Leblond, N. Aleksić, and F. Lederer, “Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials,” Phys. Rev. A82(2), 023813 (2010).
[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. A77(3), 033817 (2008).
[CrossRef]

10D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A75, 033811 (2007).

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability limits for three-dimensional vortex solitons in the Ginzburg-Landau equation with the cubic-quintic nonlinearity,” Phys. Rev. A76, 045803 (2007).

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stablevotex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett.97, 073904 (2006).

Mejia-Cortés, C.

Mihalache, D.

Y. J. He, D. Mihalache, B. A. Malomed, Y. Qiu, Z. Chen, and Y. Li, “Generation of polygonal soliton clusters and fundamental solitons in dissipative systems by necklace-ring beams with radial-azimuthal phase modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.85(6), 066206 (2012).
[CrossRef] [PubMed]

C. P. Yin, D. Mihalache, and Y. J. He, “Dynamics of two-dimensional dissipative spatial solitons interacting with an umbrella-shaped potential,” J. Opt. Soc. Am. B28(2), 342–346 (2011).

D. Mihalache, D. Mazilu, V. Skarka, B. Malomed, H. Leblond, N. Aleksić, and F. Lederer, “Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials,” Phys. Rev. A82(2), 023813 (2010).
[CrossRef]

V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of Stable Vortical Solitons in Ginzburg-Landau Media with Radially Inhomogeneous Losses,” Phys. Rev. Lett.105(21), 213901 (2010).
[CrossRef] [PubMed]

D. Mihalache, “Three-dimensional Ginzburg-Landau dissipative solitons supported by a two-dimensional transverse grating,” Proc. Romanian Acad. Ser. A11(2), 142–147 (2010).

H. Leblond, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the Ginzburg-Landau model of two-dimensional lasing medium with a transverse grating,” Phys. Rev. A80(3), 033835 (2009).
[CrossRef]

Y. J. He, B. A. Malomed, D. Mihalache, B. Liu, H. C. Huang, H. Yang, and H. Z. Wang, “Bound states of one-, two-, and three-dimensional solitons in complex Ginzburg-Landau equations with a linear potential,” Opt. Lett.34(19), 2976–2978 (2009).
[CrossRef] [PubMed]

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. A77(3), 033817 (2008).
[CrossRef]

10D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A75, 033811 (2007).

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability limits for three-dimensional vortex solitons in the Ginzburg-Landau equation with the cubic-quintic nonlinearity,” Phys. Rev. A76, 045803 (2007).

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stablevotex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett.97, 073904 (2006).

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.63(1 Pt 2), 016605 (2001).
[PubMed]

Moloney, J. V.

J. Lega, J. V. Moloney, and A. C. Newell, “Swift-Hohenberg equation for Lasers,” Phys. Rev. Lett.73(22), 2978–2981 (1994).
[CrossRef] [PubMed]

Newell, A. C.

J. Lega, J. V. Moloney, and A. C. Newell, “Swift-Hohenberg equation for Lasers,” Phys. Rev. Lett.73(22), 2978–2981 (1994).
[CrossRef] [PubMed]

Nolte, S.

Pertsch, T.

Qiu, Y.

Y. J. He, D. Mihalache, B. A. Malomed, Y. Qiu, Z. Chen, and Y. Li, “Generation of polygonal soliton clusters and fundamental solitons in dissipative systems by necklace-ring beams with radial-azimuthal phase modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.85(6), 066206 (2012).
[CrossRef] [PubMed]

Qiu, Z.

Y. J. He, B. A. Malomed, F. Ye, J. Dong, Z. Qiu, H. Z. Wang, and B. Hu, “Splitting broad beams into arrays of dissipative satial solitns by material and virtual gratings,” Phys. Scr.82(6), 065404 (2010).
[CrossRef]

Qiu, Z. R.

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, “Two-dimensional dissipative gap solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.80(2), 026606 (2009).
[CrossRef] [PubMed]

Skarka, V.

V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of Stable Vortical Solitons in Ginzburg-Landau Media with Radially Inhomogeneous Losses,” Phys. Rev. Lett.105(21), 213901 (2010).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, V. Skarka, B. Malomed, H. Leblond, N. Aleksić, and F. Lederer, “Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials,” Phys. Rev. A82(2), 023813 (2010).
[CrossRef]

Skryabin, D. V.

D. V. Skryabin and A. G. Vladimirov, “Vortex induced rotation of clusters of localized states in the complex Ginzburg-Landau equation,” Phys. Rev. Lett.89(4), 044101 (2002).
[CrossRef] [PubMed]

Soto-Crespo, J. M.

Szameit, A.

Torner, L.

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stablevotex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett.97, 073904 (2006).

Tünnermann, A.

Vladimirov, A. G.

D. V. Skryabin and A. G. Vladimirov, “Vortex induced rotation of clusters of localized states in the complex Ginzburg-Landau equation,” Phys. Rev. Lett.89(4), 044101 (2002).
[CrossRef] [PubMed]

Wang, H. Z.

Wang, T. B.

Wang, X. S.

Yang, H.

Ye, F.

Y. J. He, B. A. Malomed, F. Ye, J. Dong, Z. Qiu, H. Z. Wang, and B. Hu, “Splitting broad beams into arrays of dissipative satial solitns by material and virtual gratings,” Phys. Scr.82(6), 065404 (2010).
[CrossRef]

Yin, C. P.

Zezyulin, D. A.

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Opt. Photonics News

C. López-Mariscal and J. C. Gutiérrez-Vega, “In your phase: all about optical vortices,” Opt. Photonics News20(5), 10–13 (2009).

Phys. Rev. A

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability limits for three-dimensional vortex solitons in the Ginzburg-Landau equation with the cubic-quintic nonlinearity,” Phys. Rev. A76, 045803 (2007).

H. Leblond, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the Ginzburg-Landau model of two-dimensional lasing medium with a transverse grating,” Phys. Rev. A80(3), 033835 (2009).
[CrossRef]

10D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in the three-dimensional cubic-quintic Ginzburg–Landau equation,” Phys. Rev. A75, 033811 (2007).

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. A77(3), 033817 (2008).
[CrossRef]

D. Mihalache, D. Mazilu, V. Skarka, B. Malomed, H. Leblond, N. Aleksić, and F. Lederer, “Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials,” Phys. Rev. A82(2), 023813 (2010).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

H. Sakaguchi and B. A. Malomed, “Two-dimensional dissipative gap solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.80(2), 026606 (2009).
[CrossRef] [PubMed]

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.63(1 Pt 2), 016605 (2001).
[PubMed]

B. Liu, X. D. He, and S. J. Li, “Phase controlling of collisions between solitons in the two-dimensional complex Ginzburg-Landau equation without viscosity,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.84(5), 056607 (2011).
[CrossRef] [PubMed]

Y. J. He, D. Mihalache, B. A. Malomed, Y. Qiu, Z. Chen, and Y. Li, “Generation of polygonal soliton clusters and fundamental solitons in dissipative systems by necklace-ring beams with radial-azimuthal phase modulation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.85(6), 066206 (2012).
[CrossRef] [PubMed]

Phys. Rev. Lett.

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stablevotex tori in the three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. Lett.97, 073904 (2006).

D. V. Skryabin and A. G. Vladimirov, “Vortex induced rotation of clusters of localized states in the complex Ginzburg-Landau equation,” Phys. Rev. Lett.89(4), 044101 (2002).
[CrossRef] [PubMed]

V. Skarka, N. B. Aleksić, H. Leblond, B. A. Malomed, and D. Mihalache, “Varieties of Stable Vortical Solitons in Ginzburg-Landau Media with Radially Inhomogeneous Losses,” Phys. Rev. Lett.105(21), 213901 (2010).
[CrossRef] [PubMed]

C. Cleff, B. Gütlich, and C. Denz, “Gradient Induced Motion Control of Drifting Solitary Structures in a Nonlinear Optical Single Feedback Experiment,” Phys. Rev. Lett.100(23), 233902 (2008).
[CrossRef] [PubMed]

J. Lega, J. V. Moloney, and A. C. Newell, “Swift-Hohenberg equation for Lasers,” Phys. Rev. Lett.73(22), 2978–2981 (1994).
[CrossRef] [PubMed]

Phys. Scr.

Y. J. He, B. A. Malomed, F. Ye, J. Dong, Z. Qiu, H. Z. Wang, and B. Hu, “Splitting broad beams into arrays of dissipative satial solitns by material and virtual gratings,” Phys. Scr.82(6), 065404 (2010).
[CrossRef]

Proc. Romanian Acad. Ser. A

D. Mihalache, “Three-dimensional Ginzburg-Landau dissipative solitons supported by a two-dimensional transverse grating,” Proc. Romanian Acad. Ser. A11(2), 142–147 (2010).

Rev. Mod. Phys.

I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys.74(1), 99–143 (2002).
[CrossRef]

Other

N. Rosanov, “Solitons in laser systems with absorption,” in Dissipative Solitons, N. Akhmediev and A. Ankievicz, eds. (Springer-Verlag, Berlin, 2005).

B. A. Malomed, “Complex Ginzburg–Landau equation,” in Encyclopedia of Nonlinear Science, A. Scott, ed. (Routledge, New York, 2005), p. 157.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

(a) The profile of a stable vortex with S = 1 in (x, y)-plane, (c) is the phase; (b) The profile of a stable vortex with S = 2, (d) is the phase.

Fig. 2
Fig. 2

(a), (b), (c), and (d): Isosurface plots of total intensity | u(x,y) | 2 , evolutions of the central vortex with S = 1 at (a = 0.3, m = 4), (a = 0.3, m = 5) (a = 0.08, m = 4), and (a = 0.6, m = 4). (e) Region of a for continuous emission of fundamental solitons by the variety of m. (f) Evolutions of energy at m = 4 with a = 0.5 (blue line) and 0.3 (red line).

Fig. 3
Fig. 3

(a), (b), and (c) Isosurface plots of total intensity | u(x,y) | 2 , evolutions of the central vortex with S = 2 at (a = 0.12, m = 8), (a = 0.3, m = 8), and (a = 0.4, m = 8). (d) Region of a for continuous emission of fundamental solitons by the variety of m. (e) Evolutions of the energy E at m = 8 for a = 0.25 (blue line) and 0.3 (red line).

Fig. 4
Fig. 4

(a) and (b): Regions of a for continuous emission of fundamental solitons by the variety of ε at m = 4. (c) and (d): Regions of a for continuous emission by the variety of β at m = 4.

Equations (4)

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

i u z +iδu+(1/2iβ)( u xx + u yy )+(1iε) | u | 2 u(νiμ) | u | 4 u=F(x,y)u,
F(x,y)=ar| cos(mθ/2) |, r= x 2 + y 2 , m2
u(z=0,x,y)=A | r | S exp[ ( x 2 + y 2 ) w 2 ]exp(iSθ),
E(z)= | u(x,y) | 2 dxdy,

Metrics