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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 19, Iss. 3 — Mar. 1, 2002
  • pp: 376–384

Interaction of coupled-vector optical vortices

David R. Andersen and Lubomir M. Kovachev  »View Author Affiliations

JOSA B, Vol. 19, Issue 3, pp. 376-384 (2002)

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Beginning with the Maxwell’s equations for an isotropic nonlinear medium, we have obtained vector slowly varying amplitude equations. The equations are a nonparaxial vector generalization of the well-known scalar 3D+1 nonlinear Schrodinger equation. We have determined the dispersion region and medium parameters necessary for experimental observation of wave propagation described by these equations. We show that these equations admit exact vortex solutions with spin l=1. For the case of two vortices, we also obtain exact analytical expressions describing their interaction. Stability and interaction properties of these vortices are also investigated numerically by a split-step Fourier method. Finally, we discuss applications of these vortices in the area of nuclear fusion and the stabilization of laser pulses.

© 2002 Optical Society of America

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in

David R. Andersen and Lubomir M. Kovachev, "Interaction of coupled-vector optical vortices," J. Opt. Soc. Am. B 19, 376-384 (2002)

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  1. G. A. Swartzlander, Jr. and C. T. Law, “Opical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992). [CrossRef] [PubMed]
  2. J. A. Christou, “Optical vortices in beam propagation dynamics,” Ph.D. dissertation (Australian National University, Canberra, Australia, 1999).
  3. N. N. Rozanov, V. A. Smirnov, and N. V. Vyssotina, “Numerical simulation of interaction of bright spatial solitons in medium with saturable nonlinearity,” Chaos 4, 1767–1782 (1994).
  4. A. L. Dyshko, V. N. Lugovoi, and A. M. Prokhorov, “Self-focusing of intense light beams,” JETP Lett. 6, 146–148 (1967).
  5. M. D. Feit and J. A. Fleck, Jr., “Beam nonparaxiality, filament formation, and beam breakup in the self-focusing of optical beams,” J. Opt. Soc. Am. B 5, 633–640 (1988). [CrossRef]
  6. Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15, 1282–1285 (1990). [CrossRef] [PubMed]
  7. V. Tikhonenko, J. Christou, and B. Luther-Davies, “Spiraling bright spatial solitons formed by breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B 12, 2046–2052 (1995). [CrossRef]
  8. D. E. Edmundson and R. H. Enns, “Fully three-dimensional collisions of bistable light bullets,” Opt. Lett. 18, 1609–1611 (1993). [CrossRef] [PubMed]
  9. D. E. Edmundson and R. H. Enns, “Partical-like nature of colliding three dimensional optical solitons,” Phys. Rev. A 51, 2491–2498 (1995). [CrossRef] [PubMed]
  10. R. McLeod, K. Wagner, and S. Blair, “(3+1)-dimensional optical soliton dragging logic,” Phys. Rev. A 52, 3254–3278 (1995). [CrossRef] [PubMed]
  11. C. T. Law and G. A. Swartzlander, Jr., “Polarized optical vortex solitons; instabilities and dynamics in Kerr nonlinear media,” Chaos 4, 1759–1766 (1994).
  12. A. C. Newell and J. V. Moloney, Nonlinear Optics (Addison-Wesley, Reading, Mass., 1992).
  13. P. D. Maker and R. W. Terhune, “Study of optical effects due to an induced polarization in third order in the electric field strength,” Phys. Rev. A 137, 801–817 (1965). [CrossRef]
  14. R. W. Boyd, Nonlinear Optics (Academic, New York, 1992).
  15. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Nauka, Moscow, 1978).
  16. L. de Broglie, “Sur la fréquence propre de l’électron,” C. R. Acad. Sci. 180, 498–500 (1925).
  17. A. O. Barut, “The Schrodinger and Dirac equations: linear, nonlinear and integrodifferential,” Proceedings of the International Meeting on Geometric and Algebraic Aspects of Nonlinear Field Theory S. de Filippo, (Elsevier, Amsterdam, 1989), pp. 37–51.
  18. L. M. Kovachev, “Influence of cross-phase modulation and four photon parametric mixing on the relative motion of op-tical pulses,” Opt. Quantum Electron. 23, 1091–1102 (1991). [CrossRef]
  19. I. Velchev, A. Dreischuh, D. Nechev, and S. Dinev, “Interactions of optical vortex solitons superimposed on different background beams,” Opt. Commun. 130, 385–392 (1996). [CrossRef]
  20. A. V. Gaponov and M. A. Miller, “Potential for charges particles in high frequency electromagnetic field,” JETP 34, 242–243 (1958).

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