Abstract

We present a systematic analysis for three generic collisional outcomes between stable dissipative vortices with intrinsic vorticity S = 0, 1, or 2 upon variation of relative phase in the three-dimensional (3D) cubic-quintic complex Ginzburg-Landau equation. The first type outcome is merger of the vortices into a single one, of which velocity can be effectively controlled by relative phase. With the increase of the collision momentum, the following is creation of an extra vortex, and its velocity also increases with growth of relative phase. However, at largest collision momentum, the variety of relative phase cannot change the third type collisional outcomes, quasielastic interaction. In addition, the dynamic range of the outcome of creating an extra vortex decreases with the reduction of cubic-gain. The above features have potential applications in optical switching and logic gates based on interaction of optical solitons.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  2. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
    [Crossref]
  3. S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
    [Crossref] [PubMed]
  4. F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
    [Crossref]
  5. Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15(22), 1282–1284 (1990).
    [Crossref] [PubMed]
  6. A. B. Aceves and C. De Angelis, “Spatiotemporal pulse dynamics in a periodic nonlinear waveguide,” Opt. Lett. 18(2), 110–112 (1993).
    [Crossref] [PubMed]
  7. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
    [Crossref] [PubMed]
  8. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
    [Crossref]
  9. C. López-Mariscal and J. C. Gutiérrez-Vega, “In your phase: all about optical vortices,” Opt. Photonics News 20(5), 10–13 (2009).
  10. D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Collisions between discrete surface spatiotemporal solitons in nonlinear waveguide arrays,” Phys. Rev. A 79(1), 013811 (2009).
    [Crossref]
  11. D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Discrete light bullets in two-dimensional photonic lattices: Collision scenarios,” Opt. Commun. 282(14), 3000–3006 (2009).
    [Crossref]
  12. I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74(1), 99–143 (2002).
    [Crossref]
  13. N. Rosanov, “Solitons in laser systems with absorption,” chapter in “Dissipative solitons,” edited by N. Akhmediev and A. Ankievicz (Springer-Verlag, Berlin, Heidelberg, 2005).
  14. B. A. Malomed, “Complex Ginzburg–Landau equation,” in Encyclopedia of Nonlinear Science, edited by A. Scott (Routledge, New York, 2005), p. 157.
  15. W. van Saarloos and P. C. Hohenberg, “Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations,” Physica D 56(4), 303–367 (1992).
    [Crossref]
  16. N. N. Akhmediev and A. Ankiewicz, “Dissipative solitons in the Complex Ginzburg-Landau and Swift-Hohenberg Equeations,” in Dissipative solitons (Springer-Verlag, Berlin, Heidelberg, 2005), pp. 1–18.
  17. J. N. Kutz, “Mode-locked soliton lasers,” SIAM Rev. 48(4), 629–678 (2006).
    [Crossref]
  18. N. N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, “Stable soliton pairs in optical transmission lines and fiber lasers,” J. Opt. Soc. Am. B 15(2), 515–522 (1998).
    [Crossref]
  19. P. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Light bullets and dynamic pattern formation in nonlinear dissipative systems,” Opt. Express 13(23), 9352–9630 (2005).
    [Crossref] [PubMed]
  20. J. M. Soto-Crespo, P. Grelu, and N. Akhmediev, “Optical bullets and “rockets” in nonlinear dissipative systems and their transformations and interactions,” Opt. Express 14(9), 4013–4025 (2006).
    [Crossref] [PubMed]
  21. V. Skarka and N. B. Aleksić, “Stability Criterion for Dissipative Soliton Solutions of the One-, Two-, and Three-Dimensional Complex Cubic-Quintic Ginzburg-Landau Equations,” Phys. Rev. Lett. 96(1), 013903 (2006).
    [Crossref] [PubMed]
  22. N. Akhmediev, J. M. Soto-Crespo, and P. Grelu, “Spatiotemporal optical solitons in nonlinear dissipative media: from stationary light bullets to pulsating complexes,” Chaos 17(3), 037112 (2007).
    [Crossref] [PubMed]
  23. D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable Vortex Tori in the Three-Dimensional Cubic-Quintic Ginzburg-Landau Equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
    [Crossref] [PubMed]
  24. D. 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. A 75(3), 033811 (2007).
    [Crossref]
  25. 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. A 76(4), 045803 (2007).
    [Crossref]
  26. 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(3), 033817 (2008).
    [Crossref]
  27. D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between counter-rotating solitary vortices in the three-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(5), 056601 (2008).
    [Crossref] [PubMed]
  28. D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons,” Eur. Phys. J. Spec. Top. 173(1), 245–254 (2009).
    [Crossref]
  29. Y. D. Wu, “New all-optical wavelength auto-router based on spatial solitons,” Opt. Express 12(18), 4172–4177 (2004).
    [Crossref] [PubMed]
  30. Y. D. Wu, “New all-optical switch based on the spatial soliton repulsion,” Opt. Express 14(9), 4005–4012 (2006).
    [Crossref] [PubMed]
  31. D. Chakraborty, A. Peleg, and J.-H. Jung, “Stable long-distance propagation and on-off switching of colliding soliton sequences with dissipative interaction,” Phys. Rev. A 88(2), 023845 (2013).
    [Crossref]
  32. Q. M. Nguyen, A. Peleg, and T. P. Tran, “Robust transmission stabilization and dynamic switching in broadband hybrid waveguide systems with nonlinear gain and loss,” arXiv:1405.7071 (2014).
  33. H. Sakaguchi, “Motion of pulses and vortices in the cubic-quintic complex Ginzburg-Landau equation without viscosity,” Physica D 210(1-2), 138–148 (2005).
    [Crossref]
  34. E. A. Ultanir, G. I. Stegeman, C. H. Lange, and F. Lederer, “Coherent interactions of dissipative spatial solitons,” Opt. Lett. 29(3), 283–285 (2004).
    [Crossref] [PubMed]

2013 (1)

D. Chakraborty, A. Peleg, and J.-H. Jung, “Stable long-distance propagation and on-off switching of colliding soliton sequences with dissipative interaction,” Phys. Rev. A 88(2), 023845 (2013).
[Crossref]

2011 (1)

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[Crossref]

2010 (3)

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

2009 (4)

C. López-Mariscal and J. C. Gutiérrez-Vega, “In your phase: all about optical vortices,” Opt. Photonics News 20(5), 10–13 (2009).

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Collisions between discrete surface spatiotemporal solitons in nonlinear waveguide arrays,” Phys. Rev. A 79(1), 013811 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Discrete light bullets in two-dimensional photonic lattices: Collision scenarios,” Opt. Commun. 282(14), 3000–3006 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons,” Eur. Phys. J. Spec. Top. 173(1), 245–254 (2009).
[Crossref]

2008 (2)

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(3), 033817 (2008).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between counter-rotating solitary vortices in the three-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(5), 056601 (2008).
[Crossref] [PubMed]

2007 (3)

D. 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. A 75(3), 033811 (2007).
[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. A 76(4), 045803 (2007).
[Crossref]

N. Akhmediev, J. M. Soto-Crespo, and P. Grelu, “Spatiotemporal optical solitons in nonlinear dissipative media: from stationary light bullets to pulsating complexes,” Chaos 17(3), 037112 (2007).
[Crossref] [PubMed]

2006 (5)

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable Vortex Tori in the Three-Dimensional Cubic-Quintic Ginzburg-Landau Equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[Crossref] [PubMed]

J. M. Soto-Crespo, P. Grelu, and N. Akhmediev, “Optical bullets and “rockets” in nonlinear dissipative systems and their transformations and interactions,” Opt. Express 14(9), 4013–4025 (2006).
[Crossref] [PubMed]

V. Skarka and N. B. Aleksić, “Stability Criterion for Dissipative Soliton Solutions of the One-, Two-, and Three-Dimensional Complex Cubic-Quintic Ginzburg-Landau Equations,” Phys. Rev. Lett. 96(1), 013903 (2006).
[Crossref] [PubMed]

J. N. Kutz, “Mode-locked soliton lasers,” SIAM Rev. 48(4), 629–678 (2006).
[Crossref]

Y. D. Wu, “New all-optical switch based on the spatial soliton repulsion,” Opt. Express 14(9), 4005–4012 (2006).
[Crossref] [PubMed]

2005 (3)

H. Sakaguchi, “Motion of pulses and vortices in the cubic-quintic complex Ginzburg-Landau equation without viscosity,” Physica D 210(1-2), 138–148 (2005).
[Crossref]

P. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Light bullets and dynamic pattern formation in nonlinear dissipative systems,” Opt. Express 13(23), 9352–9630 (2005).
[Crossref] [PubMed]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

2004 (2)

2002 (1)

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

1998 (1)

1993 (1)

1992 (1)

W. van Saarloos and P. C. Hohenberg, “Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations,” Physica D 56(4), 303–367 (1992).
[Crossref]

1990 (1)

Abdollahpour, D.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Aceves, A. B.

Akhmediev, N.

Akhmediev, N. N.

Aleksic, N. B.

V. Skarka and N. B. Aleksić, “Stability Criterion for Dissipative Soliton Solutions of the One-, Two-, and Three-Dimensional Complex Cubic-Quintic Ginzburg-Landau Equations,” Phys. Rev. Lett. 96(1), 013903 (2006).
[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]

Bartelt, H.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[Crossref]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Chakraborty, D.

D. Chakraborty, A. Peleg, and J.-H. Jung, “Stable long-distance propagation and on-off switching of colliding soliton sequences with dissipative interaction,” Phys. Rev. A 88(2), 023845 (2013).
[Crossref]

Chong, A.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Christodoulides, D. N.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Crasovan, L.-C.

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable Vortex Tori in the Three-Dimensional Cubic-Quintic Ginzburg-Landau Equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[Crossref] [PubMed]

De Angelis, C.

Eilenberger, F.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[Crossref]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Grelu, P.

Gutiérrez-Vega, J. C.

C. López-Mariscal and J. C. Gutiérrez-Vega, “In your phase: all about optical vortices,” Opt. Photonics News 20(5), 10–13 (2009).

Hohenberg, P. C.

W. van Saarloos and P. C. Hohenberg, “Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations,” Physica D 56(4), 303–367 (1992).
[Crossref]

Jung, J.-H.

D. Chakraborty, A. Peleg, and J.-H. Jung, “Stable long-distance propagation and on-off switching of colliding soliton sequences with dissipative interaction,” Phys. Rev. A 88(2), 023845 (2013).
[Crossref]

Kartashov, Y. V.

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable Vortex Tori in the Three-Dimensional Cubic-Quintic Ginzburg-Landau Equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[Crossref] [PubMed]

Kivshar, Y. S.

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Discrete light bullets in two-dimensional photonic lattices: Collision scenarios,” Opt. Commun. 282(14), 3000–3006 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Collisions between discrete surface spatiotemporal solitons in nonlinear waveguide arrays,” Phys. Rev. A 79(1), 013811 (2009).
[Crossref]

Kobelke, J.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[Crossref]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

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]

Kutz, J. N.

J. N. Kutz, “Mode-locked soliton lasers,” SIAM Rev. 48(4), 629–678 (2006).
[Crossref]

Lange, C. H.

Leblond, H.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons,” Eur. Phys. J. Spec. Top. 173(1), 245–254 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons,” Eur. Phys. J. Spec. Top. 173(1), 245–254 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between counter-rotating solitary vortices in the three-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(5), 056601 (2008).
[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. A 77(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. A 76(4), 045803 (2007).
[Crossref]

D. 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. A 75(3), 033811 (2007).
[Crossref]

Lederer, F.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[Crossref]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Discrete light bullets in two-dimensional photonic lattices: Collision scenarios,” Opt. Commun. 282(14), 3000–3006 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Collisions between discrete surface spatiotemporal solitons in nonlinear waveguide arrays,” Phys. Rev. A 79(1), 013811 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons,” Eur. Phys. J. Spec. Top. 173(1), 245–254 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons,” Eur. Phys. J. Spec. Top. 173(1), 245–254 (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. A 77(3), 033817 (2008).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between counter-rotating solitary vortices in the three-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(5), 056601 (2008).
[Crossref] [PubMed]

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. A 76(4), 045803 (2007).
[Crossref]

D. 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. A 75(3), 033811 (2007).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable Vortex Tori in the Three-Dimensional Cubic-Quintic Ginzburg-Landau Equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[Crossref] [PubMed]

E. A. Ultanir, G. I. Stegeman, C. H. Lange, and F. Lederer, “Coherent interactions of dissipative spatial solitons,” Opt. Lett. 29(3), 283–285 (2004).
[Crossref] [PubMed]

López-Mariscal, C.

C. López-Mariscal and J. C. Gutiérrez-Vega, “In your phase: all about optical vortices,” Opt. Photonics News 20(5), 10–13 (2009).

Malomed, B. A.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons,” Eur. Phys. J. Spec. Top. 173(1), 245–254 (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. A 77(3), 033817 (2008).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between counter-rotating solitary vortices in the three-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(5), 056601 (2008).
[Crossref] [PubMed]

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. A 76(4), 045803 (2007).
[Crossref]

D. 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. A 75(3), 033811 (2007).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable Vortex Tori in the Three-Dimensional Cubic-Quintic Ginzburg-Landau Equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[Crossref] [PubMed]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Collisions between discrete surface spatiotemporal solitons in nonlinear waveguide arrays,” Phys. Rev. A 79(1), 013811 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Discrete light bullets in two-dimensional photonic lattices: Collision scenarios,” Opt. Commun. 282(14), 3000–3006 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons,” Eur. Phys. J. Spec. Top. 173(1), 245–254 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons,” Eur. Phys. J. Spec. Top. 173(1), 245–254 (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. A 77(3), 033817 (2008).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between counter-rotating solitary vortices in the three-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(5), 056601 (2008).
[Crossref] [PubMed]

D. 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. A 75(3), 033811 (2007).
[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. A 76(4), 045803 (2007).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable Vortex Tori in the Three-Dimensional Cubic-Quintic Ginzburg-Landau Equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[Crossref] [PubMed]

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Discrete light bullets in two-dimensional photonic lattices: Collision scenarios,” Opt. Commun. 282(14), 3000–3006 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Collisions between discrete surface spatiotemporal solitons in nonlinear waveguide arrays,” Phys. Rev. A 79(1), 013811 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons,” Eur. Phys. J. Spec. Top. 173(1), 245–254 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons,” Eur. Phys. J. Spec. Top. 173(1), 245–254 (2009).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between counter-rotating solitary vortices in the three-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(5), 056601 (2008).
[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. A 77(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. A 76(4), 045803 (2007).
[Crossref]

D. 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. A 75(3), 033811 (2007).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable Vortex Tori in the Three-Dimensional Cubic-Quintic Ginzburg-Landau Equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[Crossref] [PubMed]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

Minardi, S.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[Crossref]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Nolte, S.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[Crossref]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Papazoglou, D. G.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Peleg, A.

D. Chakraborty, A. Peleg, and J.-H. Jung, “Stable long-distance propagation and on-off switching of colliding soliton sequences with dissipative interaction,” Phys. Rev. A 88(2), 023845 (2013).
[Crossref]

Pertsch, T.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[Crossref]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Renninger, W. H.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Röpke, U.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[Crossref]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Sakaguchi, H.

H. Sakaguchi, “Motion of pulses and vortices in the cubic-quintic complex Ginzburg-Landau equation without viscosity,” Physica D 210(1-2), 138–148 (2005).
[Crossref]

Schuster, K.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[Crossref]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Silberberg, Y.

Skarka, V.

V. Skarka and N. B. Aleksić, “Stability Criterion for Dissipative Soliton Solutions of the One-, Two-, and Three-Dimensional Complex Cubic-Quintic Ginzburg-Landau Equations,” Phys. Rev. Lett. 96(1), 013903 (2006).
[Crossref] [PubMed]

Soto-Crespo, J. M.

Stegeman, G. I.

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Szameit, A.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[Crossref]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Torner, L.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[Crossref]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable Vortex Tori in the Three-Dimensional Cubic-Quintic Ginzburg-Landau Equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[Crossref] [PubMed]

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

Tünnermann, A.

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[Crossref]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

Tzortzakis, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

Ultanir, E. A.

van Saarloos, W.

W. van Saarloos and P. C. Hohenberg, “Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations,” Physica D 56(4), 303–367 (1992).
[Crossref]

Wise, F.

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

Wise, F. W.

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Wu, Y. D.

Chaos (1)

N. Akhmediev, J. M. Soto-Crespo, and P. Grelu, “Spatiotemporal optical solitons in nonlinear dissipative media: from stationary light bullets to pulsating complexes,” Chaos 17(3), 037112 (2007).
[Crossref] [PubMed]

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

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons,” Eur. Phys. J. Spec. Top. 173(1), 245–254 (2009).
[Crossref]

J. Opt. B Quantum Semiclassical Opt. (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B Quantum Semiclassical Opt. 7(5), R53–R72 (2005).
[Crossref]

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

Nat. Photonics (1)

A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, “Airy–Bessel wave packets as versatile linear light bullets,” Nat. Photonics 4(2), 103–106 (2010).
[Crossref]

Opt. Commun. (1)

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Discrete light bullets in two-dimensional photonic lattices: Collision scenarios,” Opt. Commun. 282(14), 3000–3006 (2009).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

Opt. Photonics News (1)

C. López-Mariscal and J. C. Gutiérrez-Vega, “In your phase: all about optical vortices,” Opt. Photonics News 20(5), 10–13 (2009).

Phys. Rev. A (6)

D. Mihalache, D. Mazilu, F. Lederer, and Y. S. Kivshar, “Collisions between discrete surface spatiotemporal solitons in nonlinear waveguide arrays,” Phys. Rev. A 79(1), 013811 (2009).
[Crossref]

F. Eilenberger, S. Minardi, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Evolution dynamics of discrete-continuous light bullets,” Phys. Rev. A 84(1), 013836 (2011).
[Crossref]

D. Chakraborty, A. Peleg, and J.-H. Jung, “Stable long-distance propagation and on-off switching of colliding soliton sequences with dissipative interaction,” Phys. Rev. A 88(2), 023845 (2013).
[Crossref]

D. 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. A 75(3), 033811 (2007).
[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. A 76(4), 045803 (2007).
[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(3), 033817 (2008).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Collisions between counter-rotating solitary vortices in the three-dimensional Ginzburg-Landau equation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 78(5), 056601 (2008).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

D. Mihalache, D. Mazilu, F. Lederer, Y. V. Kartashov, L.-C. Crasovan, L. Torner, and B. A. Malomed, “Stable Vortex Tori in the Three-Dimensional Cubic-Quintic Ginzburg-Landau Equation,” Phys. Rev. Lett. 97(7), 073904 (2006).
[Crossref] [PubMed]

S. Minardi, F. Eilenberger, Y. V. Kartashov, A. Szameit, U. Röpke, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, L. Torner, F. Lederer, A. Tünnermann, and T. Pertsch, “Three-Dimensional Light Bullets in Arrays of Waveguides,” Phys. Rev. Lett. 105(26), 263901 (2010).
[Crossref] [PubMed]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, “Spatiotemporal airy light bullets in the linear and nonlinear regimes,” Phys. Rev. Lett. 105(25), 253901 (2010).
[Crossref] [PubMed]

V. Skarka and N. B. Aleksić, “Stability Criterion for Dissipative Soliton Solutions of the One-, Two-, and Three-Dimensional Complex Cubic-Quintic Ginzburg-Landau Equations,” Phys. Rev. Lett. 96(1), 013903 (2006).
[Crossref] [PubMed]

Physica D (2)

W. van Saarloos and P. C. Hohenberg, “Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations,” Physica D 56(4), 303–367 (1992).
[Crossref]

H. Sakaguchi, “Motion of pulses and vortices in the cubic-quintic complex Ginzburg-Landau equation without viscosity,” Physica D 210(1-2), 138–148 (2005).
[Crossref]

Rev. Mod. Phys. (1)

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

SIAM Rev. (1)

J. N. Kutz, “Mode-locked soliton lasers,” SIAM Rev. 48(4), 629–678 (2006).
[Crossref]

Other (5)

Q. M. Nguyen, A. Peleg, and T. P. Tran, “Robust transmission stabilization and dynamic switching in broadband hybrid waveguide systems with nonlinear gain and loss,” arXiv:1405.7071 (2014).

N. N. Akhmediev and A. Ankiewicz, “Dissipative solitons in the Complex Ginzburg-Landau and Swift-Hohenberg Equeations,” in Dissipative solitons (Springer-Verlag, Berlin, Heidelberg, 2005), pp. 1–18.

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

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

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

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 (5)

Fig. 1
Fig. 1

Three outcomes of collision between two in-phase 3D DS pairs with coaxial vorticities ( S 1 =1 , S 2 =1 ). (a): merger of the two vortices at χ = 1. (b): add an extra coaxial vortex at χ = 2. (c): quasi-elastic passage through each other at χ = 2.5.

Fig. 2
Fig. 2

Relative phase controls outcomes of collision between two 3D fundamental solitons ( S 1 = 0 , S 2 = 0 ). (a): for ϕ = 0.1 π , merger of the two solitons into one acquires motion in t axis at χ = 1. (b): for ϕ = 0. 2 π ϕ max , solitons bounce off each other at χ = 1. (c): for ϕ = 0.2 π , the extra solitons acquires motion in t axis at χ = 1.7. (d): for ϕ = 0.3 π ϕ max , (e): the relationship between ϕ max and χ for the dynamics of merger. (f): the relationship between ϕ max and χ for dynamics of adding extra soliton.

Fig. 3
Fig. 3

Relative phase controls outcomes of collision between two coaxial vortices with ( S 1 = 1 , S 2 = 1 ). (a): merger of the two vortices into one acquires motion in t axis for ϕ = 0.1 π , at χ = 1. (b): the extra vortex acquires motion in t axis for ϕ = 0.3 π , at χ = 2. (c): quasi-elastic passage through each other for ϕ = 0.3 π , at χ = 2.5. (d): the relationship between ϕ max and χ for the dynamics of merger of the two vortices. (e): the relationship between ϕ max and χ for the dynamics of adding extra vortex.

Fig. 4
Fig. 4

Relative phase controls outcomes of collision between two coaxial vortices with ( S 1 = 2 , S 2 = 2 ). (a): merger of the two vortices into one acquires motion in t axis for ϕ = 0.1 π , at χ = 1. (b): the extra vortex acquires motion in t axis for ϕ = 0.3 π , at χ = 1.8. (c): the relationship between ϕ max and χ for the dynamics of merger of the two vortices. (d): the relationship between ϕ max and χ for the dynamics of adding extra vortex.

Fig. 5
Fig. 5

(a), (b), and (c): The region of the three types of collisions by the variety of ε between two vortices with ( S 1 = 0 , S 2 = 0 ), ( S 1 = 1 , S 2 = 1 ), and ( S 1 = 2 , S 2 = 2 ).

Equations (6)

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

i u z + i δ u + ( 1 / 2 i β ) ( u x x + u y y ) + ( D 2 + i γ ) u t t + ( 1 i ε ) | u | 2 u ( ν i μ ) | u | 4 u = 0 ,
u ( z , x , y , t ) = ψ ( r , t ) exp ( i k z + i S θ ) ,
( 1 2 i β ) ( ψ r r + 1 r ψ r S 2 r 2 ψ ) + D 2 ψ t t + [ i δ + ( 1 i ε ) | ψ | 2 ( ν i μ ) | ψ | 4 ] ψ = k ψ ,
i Ψ z + ( 1 2 i β ) ( Ψ r r + 1 r Ψ r S 2 r 2 Ψ ) + D 2 Ψ t t + [ i δ + ( 1 i ε ) | Ψ | 2 ( ν i μ ) | Ψ | 4 ] Ψ = 0 ,
E = 2 π 0 r d r + d t | u ( r , t ) | 2 ,
u ( 0 , r , t ) = ψ ( r , t + t 0 2 ) exp ( i S θ ) exp ( i χ t ) + ψ ( r , t - t 0 2 ) exp ( i S θ ) exp ( i χ t ) exp ( ± i ϕ ) ,

Metrics