Skip to main content
SpringerLink
Log in

Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

We report results of the first analysis of collisions between stable fundamental (alias spinless) and vortical (spinning) three-dimensional dissipative solitons in a model of a laser cavity. The systematic analysis is carried out for values S=1 and S=2 of the vorticity of the latter soliton. With the increase of the collision momentum, Χ, the same generic scenarios are observed in either case: merger into a single fundamental soliton at both small and relatively large values of Χ, and the formation of two fundamental solitons in an intermediate interval of variation of the collision momentum Χ. At very large values of Χ, the collision seems quasi-elastic, but the vortex soliton eventually splits into two nonspinning fragments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • I.S. Aranson, L. Kramer, Rev. Mod. Phys. 74, 99 (2002) ; P. Mandel, M. Tlidi, J. Opt. B: Quantum Semiclass. Opt. 6, R60 (2004) ; B.A. Malomed, Encyclopedia of Nonlinear Science, edited by A. Scott (Routledge, New York, 2005), p. 157

  • N. Akhmediev, A. Ankiewicz (eds.), Dissipative Solitons, Lect. Notes Phys. 661 (Springer, Berlin, 2005)

  • S. Barland, J.R. Tredicce, M. Brambilla, L.A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knodl, M. Miller, R. Jager, Nature (London) 419, 699 (2002) ; Z. Bakonyi, D. Michaelis, U. Peschel, G. Onishchukov, F. Lederer, J. Opt. Soc. Am. B 19, 487 (2002) ; E.A. Ultanir, G.I. Stegeman, D. Michaelis, C.H. Lange, F. Lederer, Phys. Rev. Lett. 90, 253903 (2003) ; N.N. Rosanov, S.V. Fedorov, A.N. Shatsev, Phys. Rev. Lett. 95, 053903 (2005)

  • N.N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, Berlin, 2002)

  • B.A. Malomed, D. Mihalache, F. Wise, L. Torner, J. Opt. B: Quantum Semiclass. Opt. 7, R53 (2005)

  • A.S. Desyatnikov, Y.S. Kivshar, L. Torner, Progr. Opt. 47, 291 (2005)

    Google Scholar 

  • V.I. Petviashvili, A.M. Sergeev, Dokl. Akad. Nauk SSSR 276, 1380 (1984) ; Sov. Phys. Dokl. 29, 493 (1984)

    Google Scholar 

  • B.A. Malomed, Physica D 29, 155 (1987) ; O. Thual, S. Fauve, J. Phys. (Paris) 49, 1829 (1988) ; S. Fauve, O. Thual, Phys. Rev. Lett. 64, 282 (1990) ; W. van Saarloos, P.C. Hohenberg, Phys. Rev. Lett. 64, 749 (1990) ; V. Hakim, P. Jakobsen, Y. Pomeau, Europhys. Lett. 11, 19 (1990) ; B.A. Malomed, A.A. Nepomnyashchy, Phys. Rev. A 42, 6009 (1990) ; P. Marcq, H. Chaté, R. Conte, Physica D 73, 305 (1994) ; N. Akhmediev, V.V. Afanasjev, Phys. Rev. Lett. 75, 2320 (1995) ; H.R. Brand, R.J. Deissler, Phys. Rev. Lett. 63, 2801 (1989) ; R.J. Deissler, H.R. Brand, Phys. Rev. Lett. 72, 478 (1994) ; 74, 4847 (1995); 81, 3856 (1998) ; V.V. Afanasjev, N. Akhmediev, J.M. Soto-Crespo, Phys. Rev. E 53, 1931 (1996) ; J.M. Soto-Crespo, N. Akhmediev, A. Ankiewicz, Phys. Rev. Lett. 85, 2937 (2000)

  • F. Smektala, C. Quemard, V. Couderc, A. Barthélémy, J. Non-Cryst. Solids 274, 232 (2000) ; G. Boudebs, S. Cherukulappurath, H. Leblond, J. Troles, F. Smektala, F. Sanchez, Opt. Commun. 219, 427 (2003)

    Google Scholar 

  • C. Zhan, D. Zhang, D. Zhu, D. Wang, Y. Li, D. Li, Z. Lu, L. Zhao, Y. Nie, J. Opt. Soc. Am. B 19, 369 (2002)

    Google Scholar 

  • G.S. Agarwal, S. Dutta Gupta, Phys. Rev. A 38, 5678 (1988) ; E.L. Falcão-Filho, C.B. de Araújo, J.J. Rodrigues, Jr., J. Opt. Soc. Am. B 24, 2948 (2007)

    Google Scholar 

  • R.A. Ganeev, M. Baba, M. Morita, A.I. Ryasnyansky, M. Suzuki, M. Turu, H. Kuroda, J. Opt. A: Pure Appl. Opt. 6, 282 (2004)

    Google Scholar 

  • L.-C. Crasovan, B.A. Malomed, D. Mihalache, Phys. Rev. E 63, 016605 (2001) ; Phys. Lett. A 289, 59 (2001)

    Google Scholar 

  • P. Grelu, J.M. Soto-Crespo, N. Akhmediev, Opt. Exp. 13, 9352 (2005)

    Google Scholar 

  • J.M. Soto-Crespo, P. Grelu, N. Akhmediev, Opt. Exp. 14, 4013 (2006)

    Google Scholar 

  • V. Skarka, N.B. Aleksić, Phys. Rev. Lett. 96, 013903 (2006)

    Google Scholar 

  • N. Akhmediev, J.M. Soto-Crespo, P. Grelu, Chaos 17, 037112 (2007)

    Google Scholar 

  • J.M. Soto-Crespo, N. Akhmediev, P. Grelu, Phys. Rev. E 74, 046612 (2006)

    Google Scholar 

  • D. Mihalache, D. Mazilu, F. Lederer, Y.V. Kartashov, L.-C. Crasovan, L. Torner, B.A. Malomed, Phys. Rev. Lett. 97, 073904 (2006)

    Google Scholar 

  • D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, B.A. Malomed, Phys. Rev. A 75, 033811 (2007) ; Phys. Rev. A 76, 045803 (2007) ; D. Mihalache, D. Mazilu, Rom. Rep. Phys. 60, 749 (2008)

    Google Scholar 

  • D. Mihalache, Cent. Eur. J. Phys. 6, 582 (2008)

    Google Scholar 

  • M. Soljacic, S. Sears, M. Segev, Phys. Rev. Lett. 81, 4851 (1998)

    Google Scholar 

  • A.S. Desyatnikov, Y.S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002)

    Google Scholar 

  • Y.V. Kartashov, L.-C. Crasovan, D. Mihalache, L. Torner, Phys. Rev. Lett. 89, 273902 (2002) ; L.-C. Crasovan, G. Molina-Terriza, J.P. Torres, L. Torner, V.M. Perez-Garcia, D. Mihalache, Phys. Rev. E 66, 036612 (2002) ; D. Mihalache, D. Mazilu, L.-C. Crasovan, B.A. Malomed, F. Lederer, L. Torner, Phys. Rev. E 68, 046612 (2003) ; L.-C. Crasovan, Y.V. Kartashov, D. Mihalache, L. Torner, Y.S. Kivshar, V.M. Perez-Garcia, Phys. Rev. E 67, 046610 (2003); D. Mihalache, D. Mazilu, L.-C. Crasovan, B.A. Malomed, F. Lederer, L. Torner, J. Opt. B: Quantum Semiclass. Opt. 6, S333 (2004)

  • D.V. Skryabin, A.G. Vladimirov, Phys. Rev. Lett. 89, 044101 (2002)

    Google Scholar 

  • W.P. Zhong, L. Yi, R.H. Xie, M. Belić, G. Chen, J. Phys. B 41, 025402 (2008) ; Y.Q. Wang, Q. Guo, Chin. Phys. B 17, 2527 (2008) ; M.M. Petroski, M.S. Petrović, M.R. Belić, Opt. Commun. 279, 196 (2007) ; A. Fratalocchi, A. Piccardi, M. Peccianti, G. Assanto, Phys. Rev. A 75, 063835 (2007) ; D. Buccoliero, A.S. Desyatnikov, W. Królikowski, Y.S. Kivshar, Phys. Rev. Lett. 98, 053901 (2007) ; Y.J. He, B.A. Malomed, D. Mihalache, H.Z. Wang, Phys. Rev. A 77, 043826 (2008)

    Google Scholar 

  • Y.J. He, B.A. Malomed, H.Z. Wang, Opt. Exp. 15, 17502 (2007)

    Google Scholar 

  • D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, B.A. Malomed, Phys. Rev. A 77, 033817 (2008)

    Google Scholar 

  • D. Mihalache, D. Mazilu, F. Lederer, H. Leblond, B.A. Malomed, Phys. Rev. E 78, 056601 (2008)

    Google Scholar 

  • H. Sakaguchi, Physica D 210, 138 (2005)

  • E.A. Ultanir, G.I. Stegeman, C.H. Lange, F. Lederer, Opt. Lett. 29, 283 (2004)

    Google Scholar 

  • J. Lega, J.V. Moloney, A.C. Newell, Phys. Rev. Lett. 73, 2978 (1994) ; Physica D 83, 478 (1995)

    Google Scholar 

  • A. Desyatnikov, A. Maimistov, B. Malomed, Phys. Rev. E 61, 3107 (2000) ; D. Mihalache, D. Mazilu, L.-C. Crasovan, B.A. Malomed, F. Lederer, Phys. Rev. E 61, 7142 (2000) ; D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A.V. Buryak, B.A. Malomed, L. Torner, J.P. Torres, F. Lederer, Phys. Rev. Lett. 88, 073902 (2002)

Download references

Author information

Authors and Affiliations

  1. Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, 077125, Magurele-Bucharest, Romania

    D. Mihalache & D. Mazilu

  2. Institute of Solid State Theory and Theoretical Optics, Friedrich-Schiller Universität Jena, Max-Wien-Platz 1, 07743, Jena, Germany

    F. Lederer

  3. Laboratoire POMA, CNRS FRE 2988, Université d’Angers, 2 Bd. Lavoisier, 49045, Angers Cedex 01, France

    H. Leblond

  4. Department of Physical Electronics, Faculty of Engineering, Tel Aviv University, Tel Aviv, 69978, Israel

    B. A. Malomed

Authors
  1. D. Mihalache
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Mazilu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. Lederer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. Leblond
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. B. A. Malomed
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Mihalache.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mihalache, D., Mazilu, D., Lederer, F. et al. Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons. Eur. Phys. J. Spec. Top. 173, 245–254 (2009). https://doi.org/10.1140/epjst/e2009-01077-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2009-01077-7

Keywords

Search

Navigation