Continuous generation of “light bullets” in dissipative media by an annularly periodic potential

Bin Liu; Xing-Dao He

doi:10.1364/OE.19.020009

Continuous generation of “light bullets” in dissipative media by an annularly periodic potential

Bin Liu and Xing-Dao He

Optics Express
Vol. 19,
Issue 21,
pp. 20009-20014
(2011)
•https://doi.org/10.1364/OE.19.020009

Get Citation
Copy Citation Text
Bin Liu and Xing-Dao He, "Continuous generation of “light bullets” in dissipative media by an annularly periodic potential," Opt. Express 19, 20009-20014 (2011)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Get PDF (1112 KB)
Set citation alerts
Save article

Accessible

Open Access

Abstract

We report novel dynamical regimes of “light bullets” supported by an annularly periodic potential in the three-dimensional (3D) complex Ginzburg-Landau equation with the cubic-quintic nonlinearity. This is a model of an active optical medium with respective expanding anti-waveguiding structures with $m \geq 2$ (integer) annularly periodic modulation. If the potentials are strong enough, they give rise to continuous generation of m jets light bullet by an initial light bullet initially placed at the center. The influence of m and diffusivity term (viscosity) β on the corresponding strength of potential is studied. In the case of m = 0 (conical geometry), these are concentric waves expanding in the radial direction.

Full Article | PDF Article

References

View by:
Article Order
|
Year
|
Author
|
Publication

I. S. Aranson and L. Kramer, “The world of the complex Ginzburg–Landau equation,” Rev. Mod. Phys. 74(1), 99–143 (2002).
[Crossref]
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.
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]
A. Ankiewicz, N. Devine, N. Akhmediev, and J. M. Soto-Crespo, “Continuously self-focusing and continuously self-defocusing two-dimensional beams in dissipative media,” Phys. Rev. A 77(3), 033840 (2008).
[Crossref]
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]
A. Desyatnikov, A. Maimistov, and B. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(3), 3107–3113 (2000).
[Crossref]
L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Erupting, flat-top, and composite spiral solitons in two-dimensional Ginzburg-Landau equation,” Phys. Lett. A 289(1-2), 59–65 (2001).
[Crossref]
J. M. Soto-Crespo, N. Akhmediev, C. Mejia-Cortés, and N. Devine, “Dissipative ring solitons with vorticity,” Opt. Express 17(6), 4236–4250 (2009).
[Crossref] [PubMed]
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]
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]
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]
A. Kamagate, P. Grelu, P. Tchofo-Dinda, J. M. Soto-Crespo, and N. Akhmediev, “Stationary and pulsating dissipative light bullets from a collective variable approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026609 (2009).
[Crossref] [PubMed]
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]
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. Express 17(15), 12203–12209 (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. A 80(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]
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, 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]
C. Yin, D. Mihalache, and Y. He, “Dynamics of two-dimensional dissipative spatial solitons interacting with an umbrella-shaped potential,” J. Opt. Soc. Am. B 28(2), 342–346 (2011).
[Crossref]
D. Mihalache, “Three-dimensional Ginzburg-Landau dissipative solitons supported by a two-dimensional transverse grating,” Proc. Rom. Acad. A 11, 142–147 (2010).
Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
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]
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]
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]
Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15(22), 1282–1284 (1990).
[Crossref] [PubMed]
A. B. Aceves and C. De Angelis, “Spatiotemporal pulse dynamics in a periodic nonlinear waveguide,” Opt. Lett. 18(2), 110–112 (1993).
[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]
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]
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]
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. Express 14(13), 6055–6062 (2006).
[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]

2011 (2)

C. Yin, D. Mihalache, and Y. He, “Dynamics of two-dimensional dissipative spatial solitons interacting with an umbrella-shaped potential,” J. Opt. Soc. Am. B 28(2), 342–346 (2011).
[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]

2010 (5)

D. Mihalache, “Three-dimensional Ginzburg-Landau dissipative solitons supported by a two-dimensional transverse grating,” Proc. Rom. Acad. A 11, 142–147 (2010).

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]

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]

2009 (6)

A. Kamagate, P. Grelu, P. Tchofo-Dinda, J. M. Soto-Crespo, and N. Akhmediev, “Stationary and pulsating dissipative light bullets from a collective variable approach,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 79(2), 026609 (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. Express 17(15), 12203–12209 (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. A 80(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]

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]

J. M. Soto-Crespo, N. Akhmediev, C. Mejia-Cortés, and N. Devine, “Dissipative ring solitons with vorticity,” Opt. Express 17(6), 4236–4250 (2009).
[Crossref] [PubMed]

2008 (4)

A. Ankiewicz, N. Devine, N. Akhmediev, and J. M. Soto-Crespo, “Continuously self-focusing and continuously self-defocusing two-dimensional beams in dissipative media,” Phys. Rev. A 77(3), 033840 (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, “Collisions between coaxial vortex solitons in the three-dimensional cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. A 77(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 (1)

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]

2006 (2)

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]

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. Express 14(13), 6055–6062 (2006).
[Crossref] [PubMed]

2005 (2)

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]

2002 (2)

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 (2)

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]

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Erupting, flat-top, and composite spiral solitons in two-dimensional Ginzburg-Landau equation,” Phys. Lett. A 289(1-2), 59–65 (2001).
[Crossref]

2000 (1)

A. Desyatnikov, A. Maimistov, and B. Malomed, “Three-dimensional spinning solitons in dispersive media with the cubic-quintic nonlinearity,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 61(3), 3107–3113 (2000).
[Crossref]

1998 (1)

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]

1994 (1)

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

1993 (1)

A. B. Aceves and C. De Angelis, “Spatiotemporal pulse dynamics in a periodic nonlinear waveguide,” Opt. Lett. 18(2), 110–112 (1993).
[Crossref] [PubMed]

1990 (1)

Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15(22), 1282–1284 (1990).
[Crossref] [PubMed]

Abdollahpour, D.

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.

Burghoff, J.

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]

Cleff, C.

Crasovan, L.-C.

De Angelis, C.

A. B. Aceves and C. De Angelis, “Spatiotemporal pulse dynamics in a periodic nonlinear waveguide,” Opt. Lett. 18(2), 110–112 (1993).
[Crossref] [PubMed]

Denz, C.

Desyatnikov, A.

Devine, N.

J. M. Soto-Crespo, N. Akhmediev, C. Mejia-Cortés, and N. Devine, “Dissipative ring solitons with vorticity,” Opt. Express 17(6), 4236–4250 (2009).
[Crossref] [PubMed]

Eilenberger, F.

Grelu, P.

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]

Gütlich, B.

He, Y.

C. Yin, D. Mihalache, and Y. He, “Dynamics of two-dimensional dissipative spatial solitons interacting with an umbrella-shaped potential,” J. Opt. Soc. Am. B 28(2), 342–346 (2011).
[Crossref]

He, Y. J.

Huang, H. C.

Kamagate, A.

Kartashov, Y. V.

Kevrekidis, P. G.

Kobelke, J.

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.

Lederer, F.

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.

Liu, B.

Maimistov, A.

Malomed, B.

Malomed, B. A.

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]

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.

Mejia-Cortés, C.

J. M. Soto-Crespo, N. Akhmediev, C. Mejia-Cortés, and N. Devine, “Dissipative ring solitons with vorticity,” Opt. Express 17(6), 4236–4250 (2009).
[Crossref] [PubMed]

Mihalache, D.

C. Yin, D. Mihalache, and Y. He, “Dynamics of two-dimensional dissipative spatial solitons interacting with an umbrella-shaped potential,” J. Opt. Soc. Am. B 28(2), 342–346 (2011).
[Crossref]

D. Mihalache, “Three-dimensional Ginzburg-Landau dissipative solitons supported by a two-dimensional transverse grating,” Proc. Rom. Acad. A 11, 142–147 (2010).

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.

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.

Papazoglou, D. G.

Pertsch, T.

Qiu, Z. R.

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.

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]

Schuster, K.

Silberberg, Y.

Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15(22), 1282–1284 (1990).
[Crossref] [PubMed]

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.

J. M. Soto-Crespo, N. Akhmediev, C. Mejia-Cortés, and N. Devine, “Dissipative ring solitons with vorticity,” Opt. Express 17(6), 4236–4250 (2009).
[Crossref] [PubMed]

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]

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]

Suntsov, S.

Szameit, A.

Tchofo-Dinda, P.

Torner, L.

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.

Tzortzakis, S.

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.

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]

Yang, H.

Yin, C.

C. Yin, D. Mihalache, and Y. He, “Dynamics of two-dimensional dissipative spatial solitons interacting with an umbrella-shaped potential,” J. Opt. Soc. Am. B 28(2), 342–346 (2011).
[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 (2)

C. Yin, D. Mihalache, and Y. He, “Dynamics of two-dimensional dissipative spatial solitons interacting with an umbrella-shaped potential,” J. Opt. Soc. Am. B 28(2), 342–346 (2011).
[Crossref]

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]

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. Express (5)

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]

J. M. Soto-Crespo, N. Akhmediev, C. Mejia-Cortés, and N. Devine, “Dissipative ring solitons with vorticity,” Opt. Express 17(6), 4236–4250 (2009).
[Crossref] [PubMed]

Opt. Lett. (4)

Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15(22), 1282–1284 (1990).
[Crossref] [PubMed]

A. B. Aceves and C. De Angelis, “Spatiotemporal pulse dynamics in a periodic nonlinear waveguide,” Opt. Lett. 18(2), 110–112 (1993).
[Crossref] [PubMed]

Phys. Lett. A (1)

Phys. Rev. A (5)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (4)

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]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

Phys. Rev. Lett. (5)

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]

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

Proc. Rom. Acad. A (1)

D. Mihalache, “Three-dimensional Ginzburg-Landau dissipative solitons supported by a two-dimensional transverse grating,” Proc. Rom. Acad. A 11, 142–147 (2010).

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]

Other (3)

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.

Click here to see a list of articles that cite this paper

Fig. 1

(Color online) The profile of a stable STS in Eq. (1) without the external potential.

Download Full Size | PPT Slide | PDF

Fig. 2

(Color online) (a) (b) Isosurfaces plot of total intensity ${| u (x, y, t) |}^{2}$ , evolutions of the central STS at (a = 0.08, m = 4) and (a = 0.07, m = 8). (c) Evolutions of energy at m = 4 with a = 0.08 (blue line) and 0.09 (black line). (d) Region of a for continuous generation depend on m. (e) Region of a depend on β, at m = 4.

Download Full Size | PPT Slide | PDF

Fig. 3

(Color online) (a) (b) Isosurfaces plot of total intensity ${| u (x, y, t) |}^{2}$ , evolutions of the central STS at (a = 0.12, m = 4) and (a = 0.04, m = 4). (c) Evolutions of the energy E at m = 4 for different a. The black, blue, red, pink and green lines correspond to a = 0.02, 0.03, 0.15, 0.2 and 1, respectively. (d) Region of a for dynamical regime in Fig. 3(b) depend on m.

Download Full Size | PPT Slide | PDF

Fig. 4

(Color online) (Color online) (a) (b) Isosurfaces plot of total intensity ${| u (x, y, t) |}^{2}$ , evolutions of the central STS at a = 0.12 and 0.45. (c) Evolutions of the energy E at a = 0.12 (blue line) and 0.15 (red line). (d) Evolutions of E at a = 0.02 (blue line) and 0.025 (red line). (e) Evolutions of E at a = 0.45 (black line), 0.5 (blue line) and 0.6 (red line).

Download Full Size | PPT Slide | PDF

Equations (4)

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

i u_{z} + i δ \cdot u + (1 / 2 - i β) (u_{x x} + u_{y y}) + (D - i γ) u_{t t} + (1 - i ε) {| u |}^{2} u - (ν - i μ) {| u |}^{4} u = F (x, y) u,

F (x, y) = - a r | \cos (m θ / 2) |, \begin{matrix}  \end{matrix} r = \sqrt{x^{2} + y^{2}}, \begin{matrix}  \end{matrix} m \geq 2

E (z) = {\int_{- \infty}^{\infty} \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} | u (x, y, t, z) |}^{2} d t d x d y .

F (x, y) = - a r, r = \sqrt{x^{2} + y^{2}} .

Abstract

References

2011 (2)

2010 (5)

2009 (6)

2008 (4)

2007 (1)

2006 (2)

2005 (2)

2002 (2)

2001 (2)

2000 (1)

1998 (1)

1994 (1)

1993 (1)

1990 (1)

Abdollahpour, D.

Aceves, A. B.

Akhmediev, N.

Akhmediev, N. N.

Ankiewicz, A.

Aranson, I. S.

Bartelt, H.

Burghoff, J.

Chong, A.

Christodoulides, D. N.

Cleff, C.

Crasovan, L.-C.

De Angelis, C.

Denz, C.

Desyatnikov, A.

Devine, N.

Eilenberger, F.

Grelu, P.

Gütlich, B.

He, Y.

He, Y. J.

Huang, H. C.

Kamagate, A.

Kartashov, Y. V.

Kevrekidis, P. G.

Kobelke, J.

Kramer, L.

Leblond, H.

Lederer, F.

Lega, J.

Leng, F. C.

Liu, B.

Maimistov, A.

Malomed, B.

Malomed, B. A.

Mazilu, D.

Mejia-Cortés, C.

Mihalache, D.

Minardi, S.

Moloney, J. V.

Newell, A. C.

Nolte, S.

Papazoglou, D. G.

Pertsch, T.

Qiu, Z. R.

Renninger, W. H.

Röpke, U.

Sakaguchi, H.

Schuster, K.

Silberberg, Y.

Skryabin, D. V.

Soto-Crespo, J. M.

Suntsov, S.

Szameit, A.

Tchofo-Dinda, P.

Torner, L.

Tünnermann, A.

Tzortzakis, S.

Vladimirov, A. G.

Wang, H. Z.

Wang, T. B.

Wang, X. S.

Wise, F.

Wise, F. W.