Abstract

We numerically study the dynamics of two-dimensional spatial solitons on the top of an external umbrella-shaped potential in the cubic-quintic complex Ginzburg-Landau model. Unique scenarios of the dynamics of dissipative spatial solitons interacting with this potential are put forward, such as generation of straight-lined arrays (or “jets”), emission of either one necklace-shaped soliton array or several such soliton arrays, soliton evolution into an oscillatory mode, and soliton spreading. In addition, by changing the number of lateral planes of the external potential, keeping fixed the other parameters of the potential, the various scenarios of soliton dynamics can transform into each other. These results suggest possible applications to signal routing in all-optical information processing devices.

© 2011 Optical Society of America

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2010 (5)

2009 (6)

2008 (2)

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814(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, 233902(2008).
[CrossRef] [PubMed]

2007 (5)

Y. J. He, B. A. Malomed, and H. Z. Wang, “Fusion of necklace-ring patterns into vortex and fundamental solitons in dissipative media,” Opt. Express 15, 17502–17508 (2007).
[CrossRef] [PubMed]

B. A. Malomed, “Solitary pulses in linearly coupled Ginzburg-Landau equations,” Chaos 17, 037117 (2007).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75, 033811 (2007).
[CrossRef]

R. Driben, B. A. Malomed, A. Gubeskys, and J. Zyss, “Cubic-quintic solitons in the checkerboard potential,” Phys. Rev. E 76, 066604 (2007).
[CrossRef]

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

2006 (2)

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, 073904 (2006).
[CrossRef] [PubMed]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature (London) 440, 1166–1169 (2006).
[CrossRef]

2005 (1)

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, “Two-dimensional laser soliton complexes with weak, strong, and mixed coupling,” Appl. Phys. B 81, 937–943 (2005).
[CrossRef]

2004 (2)

2003 (2)

O. V. Sinkin, R. Holzlöhner, J. Zweck, and C. R. Menyuk, “Optimization of the split-step Fourier method in modeling optical-fiber communications systems,” J. Lightwave Technol. 21, 61–68(2003).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically-induced nonlinear photonic lattices,” Nature (London) 422, 147–150 (2003).
[CrossRef]

2002 (3)

Z. Chen and K. McCarthy, “Spatial soliton pixels from partially incoherent light,” Opt. Lett. 27, 2019–2021 (2002).
[CrossRef]

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (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, 044101 (2002).
[CrossRef] [PubMed]

2001 (1)

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

2000 (1)

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E 63, 016605 (2000).
[CrossRef]

1998 (1)

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[CrossRef]

1996 (2)

W. J. Firth and A. J. Scroggie, “Optical bullet holes: Robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).
[CrossRef] [PubMed]

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
[CrossRef]

1995 (1)

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, “Two-dimensional crystals and quasicrystals in nonlinear optics,” Phys. Rev. Lett. 74, 258–261 (1995).
[CrossRef] [PubMed]

1992 (1)

N. N. Rozanov and S. V. Fedorov, “Diffraction switching waves and autosolitons in a laser with saturable absorption,” Opt. Spektrosk. 72, 1394 (1992); English translation: Opt. Spectrosc. (USSR) 72, 782 (1992).

1984 (1)

V. I. Petviashvili and A. M. Sergeev, Dokl. AN SSSR 276, 1380 (1984); English translation: Sov. Phys. Dokl. 29, 493(1984).

Afanasjev, V. V.

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
[CrossRef]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003), pp. 31–60

Akhmediev, N.

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

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

N. Akhmediev and A. Ankiewicz, Dissipative Solitons in the Complex Ginzburg–Landau and Swift–Hohenberg Equations, Lecture Notes in Physics (Springer, 2005), Vol. 661, pp. 1–17.
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
[CrossRef]

Almuneau, G.

R. Kuszelewicz, S. Barbay, G. Tissoni, and G. Almuneau, “Editorial on Dissipative Optical Solitons,” Eur. Phys. J. D 59, 1–2(2010).
[CrossRef]

Ankiewicz, A.

N. Akhmediev and A. Ankiewicz, Dissipative Solitons in the Complex Ginzburg–Landau and Swift–Hohenberg Equations, Lecture Notes in Physics (Springer, 2005), Vol. 661, pp. 1–17.
[CrossRef]

Arecchi, F. T.

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, “Two-dimensional crystals and quasicrystals in nonlinear optics,” Phys. Rev. Lett. 74, 258–261 (1995).
[CrossRef] [PubMed]

Arnold, A. S.

Balle, S.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Barbay, S.

R. Kuszelewicz, S. Barbay, G. Tissoni, and G. Almuneau, “Editorial on Dissipative Optical Solitons,” Eur. Phys. J. D 59, 1–2(2010).
[CrossRef]

Barland, S.

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, “Bistable and addressable localized vortices in semiconductor lasers,” Phys. Rev. Lett. 104, 223902 (2010).
[CrossRef] [PubMed]

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Bartal, G.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature (London) 440, 1166–1169 (2006).
[CrossRef]

Brambilla, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[CrossRef]

Chen, Z.

Chong, A.

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814(2008).
[CrossRef]

Christodoulides, D. N.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature (London) 440, 1166–1169 (2006).
[CrossRef]

Y. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, “Stable soliton complexes in two-dimensional photonic lattices,” Opt. Lett. 29, 1918–1920 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically-induced nonlinear photonic lattices,” Nature (London) 422, 147–150 (2003).
[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, 233902(2008).
[CrossRef] [PubMed]

Cotter, J. P.

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, 073904 (2006).
[CrossRef] [PubMed]

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Errupting, flat-top, and composite spiral solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Lett. A 289, 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 63, 016605 (2000).
[CrossRef]

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, 233902(2008).
[CrossRef] [PubMed]

Devine, N.

Driben, R.

R. Driben, B. A. Malomed, A. Gubeskys, and J. Zyss, “Cubic-quintic solitons in the checkerboard potential,” Phys. Rev. E 76, 066604 (2007).
[CrossRef]

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically-induced nonlinear photonic lattices,” Nature (London) 422, 147–150 (2003).
[CrossRef]

Egorov, A. A.

Fedorov, S. V.

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, “Two-dimensional laser soliton complexes with weak, strong, and mixed coupling,” Appl. Phys. B 81, 937–943 (2005).
[CrossRef]

N. N. Rozanov and S. V. Fedorov, “Diffraction switching waves and autosolitons in a laser with saturable absorption,” Opt. Spektrosk. 72, 1394 (1992); English translation: Opt. Spectrosc. (USSR) 72, 782 (1992).

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Dissipative Solitons: From Optics to Biology and Medicine, N.Akhmediev and A.Ankiewicz, eds., Lecture Notes in Physics (2008), Vol. 751, 93–111 (Springer, 2008).

Firth, W. J.

W. J. Firth and A. J. Scroggie, “Optical bullet holes: Robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).
[CrossRef] [PubMed]

W. J. Firth, Self-Organization in Optical Systems and Applications in Information Technology, M.A.Vorontsov and W.B.Miller, eds. (Springer-Verlag, 1995), p. 69.
[CrossRef]

Fleischer, J. W.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature (London) 440, 1166–1169 (2006).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically-induced nonlinear photonic lattices,” Nature (London) 422, 147–150 (2003).
[CrossRef]

Freedman, B.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature (London) 440, 1166–1169 (2006).
[CrossRef]

Genevet, P.

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, “Bistable and addressable localized vortices in semiconductor lasers,” Phys. Rev. Lett. 104, 223902 (2010).
[CrossRef] [PubMed]

Giudici, M.

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, “Bistable and addressable localized vortices in semiconductor lasers,” Phys. Rev. Lett. 104, 223902 (2010).
[CrossRef] [PubMed]

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Grelu, Ph.

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

Griffin, P. F.

Gubeskys, A.

R. Driben, B. A. Malomed, A. Gubeskys, and J. Zyss, “Cubic-quintic solitons in the checkerboard potential,” Phys. Rev. E 76, 066604 (2007).
[CrossRef]

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, 233902(2008).
[CrossRef] [PubMed]

He, Y. J.

He, Y.-J.

Hinds, E. A.

Holzlöhner, R.

Hu, B.

Hu, B. B.

Huang, H. C.

Jäger, R.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Kartashov, Y. V.

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, 073904 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, “Stable soliton complexes in two-dimensional photonic lattices,” Opt. Lett. 29, 1918–1920 (2004).
[CrossRef] [PubMed]

Kevrekidis, P. G.

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003), pp. 31–60

Knödl, T.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Kuszelewicz, R.

R. Kuszelewicz, S. Barbay, G. Tissoni, and G. Almuneau, “Editorial on Dissipative Optical Solitons,” Eur. Phys. J. D 59, 1–2(2010).
[CrossRef]

Laliotis, A.

Leblond, H.

H. Leblond, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the Ginzburg-Landau model of a two-dimensional lasing medium with a transverse grating,” Phys. Rev. A 80, 033835 (2009).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75, 033811 (2007).
[CrossRef]

Lederer, F.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75, 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, 073904 (2006).
[CrossRef] [PubMed]

Leng, F.

Lifshitz, R.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature (London) 440, 1166–1169 (2006).
[CrossRef]

Liu, B.

Lugiato, L. A.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[CrossRef]

Maggipinto, T.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Malomed, B. A.

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

Y.-J. He, B. A. Malomed, F. Ye, and B. Hu, “Dynamics of dissipative spatial solitons over a sharp potential,” J. Opt. Soc. Am. B 27, 1139–1142 (2010).
[CrossRef]

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

H. Leblond, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the Ginzburg-Landau model of a two-dimensional lasing medium with a transverse grating,” Phys. Rev. A 80, 033835 (2009).
[CrossRef]

Y. J. He, B. A. Malomed, and H. Z. Wang, “Fusion of necklace-ring patterns into vortex and fundamental solitons in dissipative media,” Opt. Express 15, 17502–17508 (2007).
[CrossRef] [PubMed]

B. A. Malomed, “Solitary pulses in linearly coupled Ginzburg-Landau equations,” Chaos 17, 037117 (2007).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75, 033811 (2007).
[CrossRef]

R. Driben, B. A. Malomed, A. Gubeskys, and J. Zyss, “Cubic-quintic solitons in the checkerboard potential,” Phys. Rev. E 76, 066604 (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, 073904 (2006).
[CrossRef] [PubMed]

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Errupting, flat-top, and composite spiral solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Lett. A 289, 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 63, 016605 (2000).
[CrossRef]

B. A. Malomed, “Complex Ginzburg-Landau Equation,” in Encyclopedia of Nonlinear Science, A.Scott, ed. (Routledge, 2005) pp. 157–160.

Mandel, P.

P. Mandel and M. Tlidi, “Transverse dynamics in cavity nonlinear optics,” J. Opt. Soc. Am. B 6, R60–R75 (2004).

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75, 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, 073904 (2006).
[CrossRef] [PubMed]

McCarthy, K.

Mejía-Cortés, C.

Menyuk, C. R.

Mihalache, D.

Y. J. He, D. Mihalache, and B. B. Hu, “Annular light beams induced by coupling a dissipative spatial soliton on the top of a sharp external potential,” J. Opt. Soc. Am. B 27, 2174–2179(2010).
[CrossRef]

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

H. Leblond, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the Ginzburg-Landau model of a two-dimensional lasing medium with a transverse grating,” Phys. Rev. A 80, 033835 (2009).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75, 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, 073904 (2006).
[CrossRef] [PubMed]

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Errupting, flat-top, and composite spiral solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Lett. A 289, 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 63, 016605 (2000).
[CrossRef]

Miller, M.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Pampaloni, E.

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, “Two-dimensional crystals and quasicrystals in nonlinear optics,” Phys. Rev. Lett. 74, 258–261 (1995).
[CrossRef] [PubMed]

Petviashvili, V. I.

V. I. Petviashvili and A. M. Sergeev, Dokl. AN SSSR 276, 1380 (1984); English translation: Sov. Phys. Dokl. 29, 493(1984).

Pollock, S.

Prati, F.

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[CrossRef]

Qiu, Z.

Ramazza, P. L.

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, “Two-dimensional crystals and quasicrystals in nonlinear optics,” Phys. Rev. Lett. 74, 258–261 (1995).
[CrossRef] [PubMed]

Renninger, W. H.

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814(2008).
[CrossRef]

Residori, S.

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, “Two-dimensional crystals and quasicrystals in nonlinear optics,” Phys. Rev. Lett. 74, 258–261 (1995).
[CrossRef] [PubMed]

Riis, E.

Rosanov, N. N.

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, “Two-dimensional laser soliton complexes with weak, strong, and mixed coupling,” Appl. Phys. B 81, 937–943 (2005).
[CrossRef]

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Dissipative Solitons: From Optics to Biology and Medicine, N.Akhmediev and A.Ankiewicz, eds., Lecture Notes in Physics (2008), Vol. 751, 93–111 (Springer, 2008).

Rozanov, N. N.

N. N. Rozanov, “Dissipative optical solitons,” J. Opt. Technol. 76, 187–198 (2009).
[CrossRef]

N. N. Rozanov and S. V. Fedorov, “Diffraction switching waves and autosolitons in a laser with saturable absorption,” Opt. Spektrosk. 72, 1394 (1992); English translation: Opt. Spectrosc. (USSR) 72, 782 (1992).

Scroggie, A. J.

W. J. Firth and A. J. Scroggie, “Optical bullet holes: Robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).
[CrossRef] [PubMed]

Segev, M.

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature (London) 440, 1166–1169 (2006).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically-induced nonlinear photonic lattices,” Nature (London) 422, 147–150 (2003).
[CrossRef]

Sergeev, A. M.

V. I. Petviashvili and A. M. Sergeev, Dokl. AN SSSR 276, 1380 (1984); English translation: Sov. Phys. Dokl. 29, 493(1984).

Shatsev, A. N.

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, “Two-dimensional laser soliton complexes with weak, strong, and mixed coupling,” Appl. Phys. B 81, 937–943 (2005).
[CrossRef]

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Dissipative Solitons: From Optics to Biology and Medicine, N.Akhmediev and A.Ankiewicz, eds., Lecture Notes in Physics (2008), Vol. 751, 93–111 (Springer, 2008).

Sinkin, O. V.

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, 044101 (2002).
[CrossRef] [PubMed]

Soto-Crespo, J. M.

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

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

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
[CrossRef]

Spinelli, L.

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[CrossRef]

Tissoni, G.

R. Kuszelewicz, S. Barbay, G. Tissoni, and G. Almuneau, “Editorial on Dissipative Optical Solitons,” Eur. Phys. J. D 59, 1–2(2010).
[CrossRef]

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[CrossRef]

Tlidi, M.

P. Mandel and M. Tlidi, “Transverse dynamics in cavity nonlinear optics,” J. Opt. Soc. Am. B 6, R60–R75 (2004).

Torner, L.

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, 073904 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, A. A. Egorov, L. Torner, and D. N. Christodoulides, “Stable soliton complexes in two-dimensional photonic lattices,” Opt. Lett. 29, 1918–1920 (2004).
[CrossRef] [PubMed]

Tredicce, J. R.

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, “Bistable and addressable localized vortices in semiconductor lasers,” Phys. Rev. Lett. 104, 223902 (2010).
[CrossRef] [PubMed]

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

Vangeleyn, M.

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, 044101 (2002).
[CrossRef] [PubMed]

Wang, H.

Wang, H. Z.

Wang, T.

Wang, X.

Wise, F. W.

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814(2008).
[CrossRef]

Yang, H.

Ye, F.

Zweck, J.

Zyss, J.

R. Driben, B. A. Malomed, A. Gubeskys, and J. Zyss, “Cubic-quintic solitons in the checkerboard potential,” Phys. Rev. E 76, 066604 (2007).
[CrossRef]

Appl. Phys. B (1)

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, “Two-dimensional laser soliton complexes with weak, strong, and mixed coupling,” Appl. Phys. B 81, 937–943 (2005).
[CrossRef]

Chaos (2)

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

B. A. Malomed, “Solitary pulses in linearly coupled Ginzburg-Landau equations,” Chaos 17, 037117 (2007).
[CrossRef] [PubMed]

Dokl. AN SSSR (1)

V. I. Petviashvili and A. M. Sergeev, Dokl. AN SSSR 276, 1380 (1984); English translation: Sov. Phys. Dokl. 29, 493(1984).

Eur. Phys. J. D (1)

R. Kuszelewicz, S. Barbay, G. Tissoni, and G. Almuneau, “Editorial on Dissipative Optical Solitons,” Eur. Phys. J. D 59, 1–2(2010).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (3)

J. Opt. Technol. (1)

Nature (London) (3)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, “Cavity solitons as pixels in semiconductor microcavities,” Nature (London) 419, 699–702 (2002).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically-induced nonlinear photonic lattices,” Nature (London) 422, 147–150 (2003).
[CrossRef]

B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature (London) 440, 1166–1169 (2006).
[CrossRef]

Opt. Express (4)

Opt. Lett. (4)

Opt. Spektrosk. (1)

N. N. Rozanov and S. V. Fedorov, “Diffraction switching waves and autosolitons in a laser with saturable absorption,” Opt. Spektrosk. 72, 1394 (1992); English translation: Opt. Spectrosc. (USSR) 72, 782 (1992).

Phys. Lett. A (1)

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

Phys. Rev. A (4)

H. Leblond, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the Ginzburg-Landau model of a two-dimensional lasing medium with a transverse grating,” Phys. Rev. A 80, 033835 (2009).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, and B. A. Malomed, “Stability of dissipative optical solitons in three-dimensional cubic-quintic Ginzburg-Landau equation,” Phys. Rev. A 75, 033811 (2007).
[CrossRef]

L. Spinelli, G. Tissoni, M. Brambilla, F. Prati, and L. A. Lugiato, “Spatial solitons in semiconductor microcavities,” Phys. Rev. A 58, 2542–2559 (1998).
[CrossRef]

W. H. Renninger, A. Chong, and F. W. Wise, “Dissipative solitons in normal-dispersion fiber lasers,” Phys. Rev. A 77, 023814(2008).
[CrossRef]

Phys. Rev. E (3)

N. N. Akhmediev, V. V. Afanasjev, and J. M. Soto-Crespo, “Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation,” Phys. Rev. E 53, 1190–1201 (1996).
[CrossRef]

L.-C. Crasovan, B. A. Malomed, and D. Mihalache, “Stable vortex solitons in the two-dimensional Ginzburg-Landau equation,” Phys. Rev. E 63, 016605 (2000).
[CrossRef]

R. Driben, B. A. Malomed, A. Gubeskys, and J. Zyss, “Cubic-quintic solitons in the checkerboard potential,” Phys. Rev. E 76, 066604 (2007).
[CrossRef]

Phys. Rev. Lett. (6)

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, 073904 (2006).
[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, 044101 (2002).
[CrossRef] [PubMed]

P. Genevet, S. Barland, M. Giudici, and J. R. Tredicce, “Bistable and addressable localized vortices in semiconductor lasers,” Phys. Rev. Lett. 104, 223902 (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, 233902(2008).
[CrossRef] [PubMed]

E. Pampaloni, P. L. Ramazza, S. Residori, and F. T. Arecchi, “Two-dimensional crystals and quasicrystals in nonlinear optics,” Phys. Rev. Lett. 74, 258–261 (1995).
[CrossRef] [PubMed]

W. J. Firth and A. J. Scroggie, “Optical bullet holes: Robust controllable localized states of a nonlinear cavity,” Phys. Rev. Lett. 76, 1623–1626 (1996).
[CrossRef] [PubMed]

Other (6)

S.Trillo and W.Torruellas eds., Spatial Solitons (Springer, 2001), pp. 87–125.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, 2003), pp. 31–60

W. J. Firth, Self-Organization in Optical Systems and Applications in Information Technology, M.A.Vorontsov and W.B.Miller, eds. (Springer-Verlag, 1995), p. 69.
[CrossRef]

N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Dissipative Solitons: From Optics to Biology and Medicine, N.Akhmediev and A.Ankiewicz, eds., Lecture Notes in Physics (2008), Vol. 751, 93–111 (Springer, 2008).

N. Akhmediev and A. Ankiewicz, Dissipative Solitons in the Complex Ginzburg–Landau and Swift–Hohenberg Equations, Lecture Notes in Physics (Springer, 2005), Vol. 661, pp. 1–17.
[CrossRef]

B. A. Malomed, “Complex Ginzburg-Landau Equation,” in Encyclopedia of Nonlinear Science, A.Scott, ed. (Routledge, 2005) pp. 157–160.

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Figures (7)

Fig. 1
Fig. 1

(a) Umbrella-shaped potential with p = 1 , n = 3 , and m = 12 . (b) Intensity distribution | u | of inputted soliton.

Fig. 2
Fig. 2

Soliton dynamics for various depths p of the UP with n = 3 and m = 12 . (a) Soliton spreading for p = 0.02 , (b) soliton spreading accompanied by the formation of holes arranged into a ring structure for p = 0.06 , (c) soliton splitting into jets for p = 0.08 , (d) soliton splitting into several necklace-shaped arrays for p = 0.8 , (e) soliton splitting into a single necklace-shaped array for p = 1.2 , (f) soliton evolution into an oscillatory mode for p = 1.4 . The transverse domain is (a) ( 50 , 50 ) × ( 50 , 50 ) , (b) ( 80 , 80 ) × ( 80 , 80 ) , (c) ( 50 , 50 ) × ( 50 , 50 ) , (d) ( 60 , 60 ) × ( 60 , 60 ) , (e) ( 65 , 65 ) × ( 65 , 65 ) , and (f) ( 20 , 20 ) × ( 20 , 20 ) .

Fig. 3
Fig. 3

Regions in the parameter plane ( n , p ) showing various dynamical regimes of the input soliton; here m = 12 . A: soliton spreading; B: formation of jets nested with a necklace-shaped holes array; C: generation of jets; D: emission of a cluster of necklace-shaped arrays; E: emission of single necklace-shaped array; F: formation of an oscillatory mode; G: soliton decay.

Fig. 4
Fig. 4

Soliton evolving into (a) jets accompanied by necklace-shaped holes array when m = 12 and (c) jets without the necklace-shaped holes array when m = 24 . (b) and (d) corresponding two-dimensional plots of | u | in the transverse plane ( x , y ) . The transverse domain is ( 80 , 80 ) × ( 80 , 80 ) . The other parameters of the UP are p = 0.06 and n = 3 .

Fig. 5
Fig. 5

Soliton emitting (a) several necklace-shaped arrays for m = 14 and (b) a single necklace-shaped array for m = 24 . The other parameters of the UP are p = 0.8 and n = 3 . The transverse domain is ( 60 , 60 ) × ( 60 , 60 ) .

Fig. 6
Fig. 6

(a) Soliton emitting a single necklace-shaped array for m = 12 , (b) formation of an oscillatory mode for m = 18 . The other parameters of the UP are p = 1.6 and n = 4 . The transverse domain is (a) ( 65 , 65 ) × ( 65 , 65 ) and (b) ( 25 , 25 ) × ( 25 , 25 ) .

Fig. 7
Fig. 7

Soliton collapse in the case β = 0 , for the octahedral UP and for p = 1 and n = 2 .

Equations (2)

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i u z + ( 1 / 2 ) Δ u + | u | 2 u + ν | u | 4 u = i R [ u ] + V ( x , y ) u ,
V ( x , y ) = p r [ cos ( m θ ) ] 1 / n .

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