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 m2 (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.

© 2011 OSA

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2011 (2)

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]

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]

2010 (5)

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]

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]

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

2009 (6)

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]

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]

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]

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]

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 (4)

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]

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]

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)

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)

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

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]

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)

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)

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.

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]

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]

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]

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]

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]

Akhmediev, N. N.

Ankiewicz, A.

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]

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]

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]

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.

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.

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]

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]

De Angelis, C.

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]

Desyatnikov, A.

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]

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]

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]

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.

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, Y.

He, Y. J.

Huang, H. C.

Kamagate, A.

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]

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]

Kevrekidis, P. G.

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]

Leblond, H.

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]

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 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, 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]

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]

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.

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]

Malomed, B.

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]

Malomed, B. A.

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]

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. A 80(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. 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]

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]

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]

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, 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]

Mejia-Cortés, C.

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).

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]

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. 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]

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]

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]

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]

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]

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.

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]

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]

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]

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]

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]

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.

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 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.

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.

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.

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]

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]

Tchofo-Dinda, P.

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]

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]

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]

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]

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]

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.

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)

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)

Opt. Lett. (4)

Phys. Lett. A (1)

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]

Phys. Rev. A (5)

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. 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]

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. 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]

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]

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]

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. 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]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (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]

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]

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]

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]

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]

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).

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Figures (4)

Fig. 1
Fig. 1

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

Fig. 2
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.

Fig. 3
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.

Fig. 4
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).

Equations (4)

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i u z +iδu+(1/2iβ)( u xx + u yy )+(Diγ) u tt +(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
E(z)= | u(x,y,t,z) | 2 dtdxdy.
F(x,y)=ar,r= x 2 + y 2 .

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