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Journal
2008 | 6 | 3 | 582-587
Article title

Three-dimensional dissipative optical solitons

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EN
Abstracts
EN
A brief overview of recent theoretical results in the area of three-dimensional dissipative optical solitons is given. A systematic analysis demonstrates the existence and stability of both fundamental (spinless) and spinning three-dimensional dissipative solitons in both normal and anomalous group-velocity regimes. Direct numerical simulations of the evolution of stationary solitons of the three-dimensional cubic-quintic Ginzburg-Landau equation show full agreement with the predictions based on computation of the instability eigenvalues from the linearized equations for small perturbations. It is shown that the diffusivity in the transverse plane is necessary for the stability of vortex solitons against azimuthal perturbations, while fundamental (zero-vorticity) solitons may be stable in the absence of diffusivity. It has also been found that, at values of the nonlinear gain above the upper border of the soliton existence domain, the three-dimensional dissipative solitons either develop intrinsic pulsations or start to expand in the temporal (longitudinal) direction keeping their structure in the transverse spatial plane.
Publisher
Journal
Year
Volume
6
Issue
3
Pages
582-587
Physical description
Dates
published
1 - 9 - 2008
online
17 - 7 - 2008
References
  • [1] N. Akhmediev, A. Ankiewicz (Eds.), Dissipative Solitons, Lect. Notes Phys. 661 (Springer, Berlin, 2005)
  • [2] N.N. Akhmediev, A. Ankiewicz, Solitons: Nonlinear Pulses and Beams (Chapman & Hall, London, 1997)
  • [3] G. Nicolis, I. Prigogine, Self-organization in nonequilibrium systems (John Wiley and Sons, New York, 1977)
  • [4] G.I. Stegeman, D.N. Christodoulides, M. Segev, IEEE J. Select. Top. Quant. Electron. 6, 1419 (2000) http://dx.doi.org/10.1109/2944.902197[Crossref]
  • [5] Y.S. Kivshar, G.P. Agrawal, Optical Solitons: From Fibers to Photonics Crystals (Academic Press, Amsterdam, 2003)
  • [6] B.A. Malomed, D. Mihalache, F. Wise, L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005) http://dx.doi.org/10.1088/1464-4266/7/5/R02[Crossref]
  • [7] I.S. Aranson, L. Kramer, Rev. Mod. Phys. 74, 99 (2002) http://dx.doi.org/10.1103/RevModPhys.74.99[Crossref]
  • [8] W.J. Firth, D.V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997) http://dx.doi.org/10.1103/PhysRevLett.79.2450[Crossref]
  • [9] L.-C. Crasovan, B.A. Malomed, D. Mihalache, Phys. Rev. E 63, 016605 (2001) http://dx.doi.org/10.1103/PhysRevE.63.016605[Crossref]
  • [10] L.-C. Crasovan, B.A. Malomed, D. Mihalache, Phys. Lett. A 289, 59 (2001) http://dx.doi.org/10.1016/S0375-9601(01)00571-0[Crossref]
  • [11] D. Mihalache et al., Phys. Rev. Lett. 97, 073904 (2006) http://dx.doi.org/10.1103/PhysRevLett.97.073904[Crossref]
  • [12] D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, B.A. Malomed, Phys. Rev. A 75, 033811 (2007) http://dx.doi.org/10.1103/PhysRevA.75.033811[Crossref]
  • [13] D. Mihalache, D. Mazilu, L.-C. Crasovan, B.A. Malomed, F. Lederer, Phys. Rev. E 62, R1505 (2000) http://dx.doi.org/10.1103/PhysRevE.62.R1505[Crossref]
  • [14] D. Mihalache, D. Mazilu, L.-C. Crasovan, B.A. Malomed, F. Lederer, Phys. Rev. E 61, 7142 (2000) http://dx.doi.org/10.1103/PhysRevE.61.7142[Crossref]
  • [15] A.V. Buryak, Yu.S. Kivshar, S. Trillo, Opt. Lett. 20, 1961 (1995) [PubMed]
  • [16] M.A. Karpierz, Opt. Lett. 20, 1677 (1995) http://dx.doi.org/10.1364/OL.20.001677[Crossref]
  • [17] I. Towers, A.V. Buryak, R.A. Sammut, B.A. Malomed, Phys. Rev. E 63, 055601(R) (2001) http://dx.doi.org/10.1103/PhysRevE.63.055601[Crossref]
  • [18] M. Quiroga-Teixeiro, H. Michinel, J. Opt. Soc. Am. B 14, 2004 (1997) http://dx.doi.org/10.1364/JOSAB.14.002004[Crossref]
  • [19] I. Towers et al., Phys. Lett. A 288, 292 (2001) http://dx.doi.org/10.1016/S0375-9601(01)00565-5[Crossref]
  • [20] B.A. Malomed, L.-C. Crasovan, D. Mihalache, Physica D 161, 187 (2002) http://dx.doi.org/10.1016/S0167-2789(01)00362-1[Crossref]
  • [21] R.L. Pego, H.A. Warchall, J. Nonlinear Sci. 12, 347 (2002) http://dx.doi.org/10.1007/s00332-002-0475-3[Crossref]
  • [22] T.A. Davydova, A.I. Yakimenko, Yu.A. Zaliznyak, Phys. Rev. E 67, 026402 (2003) http://dx.doi.org/10.1103/PhysRevE.67.026402[Crossref]
  • [23] D. Mihalache, D. Mazilu, B.A. Malomed, F. Lederer, Phys. Rev. E 69, 066614 (2004) http://dx.doi.org/10.1103/PhysRevE.69.066614[Crossref]
  • [24] D. Mihalache, D. Mazilu, B.A. Malomed, F. Lederer, J. Opt. B: Quantum Semiclassical Opt. 6, S341 (2004) http://dx.doi.org/10.1088/1464-4266/6/5/024[Crossref]
  • [25] D. Mihalache et al., Phys. Rev. Lett. 88, 073902 (2002) http://dx.doi.org/10.1103/PhysRevLett.88.073902[Crossref]
  • [26] D. Mihalache et al., Phys. Rev. E 66, 016613 (2002) http://dx.doi.org/10.1103/PhysRevE.66.016613[Crossref]
  • [27] D. Mihalache, D. Mazilu, I. Towers, B.A. Malomed, F. Lederer, Phys. Rev. E 67, 056608 (2003) http://dx.doi.org/10.1103/PhysRevE.67.056608[Crossref]
  • [28] D.V. Skryabin, A.G. Vladimirov, Phys. Rev. Lett. 89, 044101 (2002) http://dx.doi.org/10.1103/PhysRevLett.89.044101[Crossref]
  • [29] A.S. Desyatnikov, Y.S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002) http://dx.doi.org/10.1103/PhysRevLett.88.053901[Crossref]
  • [30] Y.V. Kartashov, L.-C. Crasovan, D. Mihalache, L. Torner, Phys. Rev. Lett. 89, 273902 (2002) http://dx.doi.org/10.1103/PhysRevLett.89.273902[Crossref]
  • [31] L.-C. Crasovan et al., Phys. Rev. E 67, 046610 (2003) http://dx.doi.org/10.1103/PhysRevE.67.046610[Crossref]
  • [32] D. Mihalache et al., Phys. Rev. E 68, 046612 (2003) http://dx.doi.org/10.1103/PhysRevE.68.046612[Crossref]
  • [33] D. Mihalache et al., J. Opt. B: Quantum Semiclassical Opt. 6, S333 (2004) http://dx.doi.org/10.1088/1464-4266/6/5/023[Crossref]
  • [34] P. Grelu, J.M. Soto-Crespo, N. Akhmediev, Opt. Express 13, 9352 (2005) http://dx.doi.org/10.1364/OPEX.13.009352[Crossref]
  • [35] J.M. Soto-Crespo, P. Grelu, N. Akhmediev, Opt. Express 14, 4013 (2006) http://dx.doi.org/10.1364/OE.14.004013[Crossref]
  • [36] V. Skarka, N.B. Aleksic, Phys. Rev. Lett. 96, 013903 (2006) http://dx.doi.org/10.1103/PhysRevLett.96.013903[Crossref]
  • [37] H. Sakaguchi, B.A. Malomed, Physica D 167, 123 (2002) http://dx.doi.org/10.1016/S0167-2789(02)00532-8[Crossref]
  • [38] S. Skupin et al., Phys. Rev. E 70, 046602 (2004) http://dx.doi.org/10.1103/PhysRevE.70.046602[Crossref]
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-008-0083-4
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