Abstract
We show the existence of a rich variety of fully stationary vortex structures made of an increasing number of vortices nested in paraxial wave fields confined by symmetric and asymmetric harmonic trapping potentials in both static and rotating reference frames. In the static reference frame the clusters are built by means of Hermite-Gauss functions, being termed H-clusters, whereas in the rotating frame they are generated by using the Laguerre-Gauss functions, being thus termed L-clusters. These complex vortex-structures consist of globally linked vortices, rather than independent vortices and, in symmetric traps, they feature monopolar global wave front. Nonstationary or flipping circular vortex-clusters can be built in symmetric traps and they feature multipolar phase front. In asymmetric traps, the existing stationary vortex clusters can feature multipolar wave fronts, depending on the ratio of the trap frequencies. In the nonlinear case, corresponding to nonrotating Bose-Einstein condensates, the stationary vortex clusters also exist and some of these highly excited collective states display dynamical stability.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
H. J. Lugt, Vortex Flow in Nature and Technology (Krieger, Malabar, FL, 1995).
L. M. Pismen, Vortices in Nonlinear Fields (Clarendon, Oxford, UK, 1999).
A. Ashkin, Opt. Photon. News 10(5), 41 (1999); M. E. J. Friese et al., Nature 394, 348 (1998); M. J. Padgett and L. Allen, Contemp. Phys. 41(5), 275 (2000); L. Paterson et al., Science 292, 912 (2001).
P. Galajda and P. Ormos, Appl. Phys. Lett. 78, 249 (2001).
A. Mair et al., Nature 412, 313 (2001).
G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).
R. J. Donnelly, Quantized Vortices in Hellium II (Cambridge University Press, Cambridge, 1991).
M. R. Matthews et al., Phys. Rev. Lett. 83, 2498 (1999); K. W. Madison et al., Phys. Rev. Lett. 84, 806 (2000).
D. A. Butts and D. S. Rokhsar, Nature (London) 397, 327 (1999).
M. Tsubota, K. Kasamatsu and M. Ueda, Phys. Rev. A 65, 023603 (2002).
O. Horak et al., Phys. Rev. Lett. 88, 043601 (2002).
I. Bialynicki-Birula, Z. Bialynicka-Birula, and C. Śliwa, Phys. Rev. A 61, 032110 (2000); I. Bialynicki-Birula and Z. Bialynicka-Birula, Phys. Rev. A 65, 014101 (2001).
For reviews focused on optical vortices, but relevant to BEC too, see D. Rozas, C. T. Law, and G. A. Swartzlander, J. Opt. Soc. Am. B 14, 3054 (1997); Yu. S. Kivshar et al., Opt. Commun. 152, 198 (1998); M. S. Soskin and M. V. Vasnetsov, Singular Optics, in Progress in Optics, vol. 42, p. 219, E. Wolf ed., (Elsevier, Amsterdam, 2001).
I. Freund, Opt. Commun. 159, 99 (1999).
J. R. Abo-Shaeer et al., Science, 292, 476 (2001).
M. V. Berry, in Singular Optics, M. S. Soskin ed., Proc. SPIE 3487, pp. 1–5, 1998.
I. Freund, Opt. Commun. 181, 19 (2000); I. Freund and D. A. Kessler, Opt. Commun. 187, 71 (2001).
I. Freund, Opt. Lett. 26, 545 (2001).
G. Molina-Terriza, L. Torner, E. M. Wright, J. J. García-Ripoll, V. M. Pérez-García, Opt. Lett. 26, 1601 (2001).
L.-C. Crasovan, G. Molina-Terriza, J. P. Torres, L. Torner, V. M. Perez-Garcia, and D. Mihalache, Phys. Rev. E 66, 036612 (2002).
T. Kobayashi, Physica A 303, 469 (2002).
I. Freund, Opt. Commun. 199, 47 (2001).
D. L. Feder, C. W. Clark, and B. I. Scheneider, Phys. Rev. Lett. 82, 4956 (1999); A. A. Svidzinsky and A. L. Fetter, Phys. Rev. Lett. 84, 5919 (2000).
See e.g. J. J. García-Ripoll, V. M. Pérez-García, Phys. Rev. A 64, 013602 (2001).
J. J. García-Ripoll, V. M. Pérez-García, SIAM J. Sci. Comp. 23, 1315 (2001).
M. Soljacic, S. Sears, and M. Segev, Phys. Rev. Lett. 81, 4851 (1998); A. S. Desyatnikov and Yu. S. Kivshar, Phys. Rev. Lett. 88, 053901 (2002).
Ya. V. Kartashov et al., Phys. Rev. Lett. 89, 273902 (2002); L.-C. Crasovan et al., Phys. Rev. E 67, 046612 (2003).
V. M._ Pérez-García and V. Vekslerchik, Phys. Rev. E 67, 061804 (2003); Phys. Rev. E 68, 016617 (2003).
V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1991); N. R. Heckenberg et al., Opt. Lett. 17, 221 (1992).
J. E. Williams and M. J. Holland, Nature 401, 568 (1999); L. Dobrek et al., Phys. Rev. A 60, R3381 (1999); J. Denschlag et al., Science 287, 97 (2000); G. Andrelczyk et al., Phys. Rev. A 64, 043601 (2001).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Kluwer Academic Publishers
About this paper
Cite this paper
Crasovan, LC., Vekslerchik, V., Mihalache, D., Torres, J.P., Pérez-García, V.M., Torner, L. (2004). Globally-Linked Vortex Clusters. In: Abdullaev, F.K., Konotop, V.V. (eds) Nonlinear Waves: Classical and Quantum Aspects. NATO Science Series II: Mathematics, Physics and Chemistry, vol 153. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2190-9_6
Download citation
DOI: https://doi.org/10.1007/1-4020-2190-9_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-2188-6
Online ISBN: 978-1-4020-2190-9
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)