Abstract

Composite optical vortices may form when two or more beams interfere. Using analytical and numerical techniques, we describe the motion of these optical phase singularities as the relative phase or amplitude of two interfering collinear nonconcentric beams is varied. The creation and the annihilation of vortices are found, as well as vortices having translational velocities exceeding the speed of light.

© 2003 Optical Society of America

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  1. M. Vasnetsov and K. Staliunas, eds., Optical Vortices, Vol. 228 in Horizons in World Physics (Nova Science, Huntington, N.Y., 1999).
  2. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  3. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
  4. N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetski, and V. V. Shkunov, “Speckle-inhomogeneous field wavefront dislocation,” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981)].
  5. J. F. Nye, “Optical caustics in the near field from liquid drops,” Proc. R. Soc. London Ser. A 361, 21–41 (1978).
  6. A. M. Deykoon, M. S. Soskin, and G. A. Swartzlander, Jr., “Nonlinear optical catastrophe from a smooth initial beam,” Opt. Lett. 24, 1224–1226 (1999).
  7. G. A. Swartlander, Jr. and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).
  8. A. W. Snyder, L. Poladian, and D. J. Michell, “Parallel spatial solitons,” Opt. Lett. 17, 789–791 (1992).
  9. G. A. Swartlander, Jr., “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26, 497–499 (2001).
  10. D. Palacios, D. Rozas, and G. A. Swartzlander, “Observed scattering into a dark optical vortex core,” Phys. Rev. Lett. 88, 103902 (2002).
  11. D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).
  12. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
  13. I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
  14. V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis’ma Zh. Eks. Teor. Fiz. 52, 1037–1039 (1990) [JETP Lett. 52, 429–431 (1990)].
  15. V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
  16. V. P. Lukin and V. V. Pokasov, “Optical wave phase fluctuations,” Appl. Opt. 20, 121–135 (1981).
  17. P. Coullet, L. Gill, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).
  18. C. T. Law and G. A. Swartzlander, Jr., “Optical vortex solitons and the stability of dark soliton stripes,” Opt. Lett. 18, 586–588 (1993).
  19. K. Staliunas, “Dynamics of optical vortices in a laser beam,” Opt. Commun. 90, 123–127 (1992).
  20. G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
  21. I. Freund, “Optical vortex trajectories,” Opt. Commun. 181, 19–33 (2000).
  22. I. Velchev, A. Dreischuh, D. Neshev, and S. Dinev, “Interaction of optical vortex solitons superimposed on different background beams,” Opt. Commun. 130, 385–392 (1996).
  23. L. V. Kreminskaya, M. S. Soskin, and A. I. Krizhnyak, “The Gaussian lenses give birth to optical vortices in laser beams,” Opt. Commun. 145, 377–384 (1998).
  24. D. Rozas, C. T. Law, and G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997).
  25. F. S. Roux, “Dynamical behavior of optical vortices,” J. Opt. Soc. Am. B 12, 1215–1221 (1995).
  26. D. Rozas, Z. S. Sacks, and G. A. Swartzlander, “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).
  27. L. C. Crasovan, G. Molina-Terriza, J. P. Torres, L. Torner, V. M. Perez-Garcia, and D. Mihalache, “Globally linked vortex clusters in trapped wave fields,” Phys. Rev. E 66, 036612 (2002).
  28. C. T. Law and G. A. Swartzlander, Jr., “Polarized optical vortex solitons: instabilities and dynamics in Kerr nonlinear media,” Chaos, Solitons Fractals 4, 1759–1766 (1994).
  29. H. J. Lugt, Vortex Flow in Nature and Technology (Wiley-Interscience, New York, 1983).

2002

D. Palacios, D. Rozas, and G. A. Swartzlander, “Observed scattering into a dark optical vortex core,” Phys. Rev. Lett. 88, 103902 (2002).

L. C. Crasovan, G. Molina-Terriza, J. P. Torres, L. Torner, V. M. Perez-Garcia, and D. Mihalache, “Globally linked vortex clusters in trapped wave fields,” Phys. Rev. E 66, 036612 (2002).

2001

2000

I. Freund, “Optical vortex trajectories,” Opt. Commun. 181, 19–33 (2000).

1999

1998

L. V. Kreminskaya, M. S. Soskin, and A. I. Krizhnyak, “The Gaussian lenses give birth to optical vortices in laser beams,” Opt. Commun. 145, 377–384 (1998).

1997

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

D. Rozas, C. T. Law, and G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997).

1996

I. Velchev, A. Dreischuh, D. Neshev, and S. Dinev, “Interaction of optical vortex solitons superimposed on different background beams,” Opt. Commun. 130, 385–392 (1996).

1995

1994

C. T. Law and G. A. Swartzlander, Jr., “Polarized optical vortex solitons: instabilities and dynamics in Kerr nonlinear media,” Chaos, Solitons Fractals 4, 1759–1766 (1994).

1993

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).

C. T. Law and G. A. Swartzlander, Jr., “Optical vortex solitons and the stability of dark soliton stripes,” Opt. Lett. 18, 586–588 (1993).

1992

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).

G. A. Swartlander, Jr. and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

A. W. Snyder, L. Poladian, and D. J. Michell, “Parallel spatial solitons,” Opt. Lett. 17, 789–791 (1992).

K. Staliunas, “Dynamics of optical vortices in a laser beam,” Opt. Commun. 90, 123–127 (1992).

1990

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis’ma Zh. Eks. Teor. Fiz. 52, 1037–1039 (1990) [JETP Lett. 52, 429–431 (1990)].

1989

P. Coullet, L. Gill, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).

1981

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetski, and V. V. Shkunov, “Speckle-inhomogeneous field wavefront dislocation,” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981)].

V. P. Lukin and V. V. Pokasov, “Optical wave phase fluctuations,” Appl. Opt. 20, 121–135 (1981).

1978

J. F. Nye, “Optical caustics in the near field from liquid drops,” Proc. R. Soc. London Ser. A 361, 21–41 (1978).

1974

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

Baranova, N. B.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetski, and V. V. Shkunov, “Speckle-inhomogeneous field wavefront dislocation,” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981)].

Basistiy, I. V.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).

Bazhenov, V. Y.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis’ma Zh. Eks. Teor. Fiz. 52, 1037–1039 (1990) [JETP Lett. 52, 429–431 (1990)].

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).

Coullet, P.

P. Coullet, L. Gill, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).

Crasovan, L. C.

L. C. Crasovan, G. Molina-Terriza, J. P. Torres, L. Torner, V. M. Perez-Garcia, and D. Mihalache, “Globally linked vortex clusters in trapped wave fields,” Phys. Rev. E 66, 036612 (2002).

Deykoon, A. M.

Dinev, S.

I. Velchev, A. Dreischuh, D. Neshev, and S. Dinev, “Interaction of optical vortex solitons superimposed on different background beams,” Opt. Commun. 130, 385–392 (1996).

Dreischuh, A.

I. Velchev, A. Dreischuh, D. Neshev, and S. Dinev, “Interaction of optical vortex solitons superimposed on different background beams,” Opt. Commun. 130, 385–392 (1996).

Freund, I.

I. Freund, “Optical vortex trajectories,” Opt. Commun. 181, 19–33 (2000).

Gill, L.

P. Coullet, L. Gill, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).

Indebetouw, G.

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).

Kreminskaya, L. V.

L. V. Kreminskaya, M. S. Soskin, and A. I. Krizhnyak, “The Gaussian lenses give birth to optical vortices in laser beams,” Opt. Commun. 145, 377–384 (1998).

Krizhnyak, A. I.

L. V. Kreminskaya, M. S. Soskin, and A. I. Krizhnyak, “The Gaussian lenses give birth to optical vortices in laser beams,” Opt. Commun. 145, 377–384 (1998).

Law, C. T.

D. Rozas, C. T. Law, and G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997).

C. T. Law and G. A. Swartzlander, Jr., “Polarized optical vortex solitons: instabilities and dynamics in Kerr nonlinear media,” Chaos, Solitons Fractals 4, 1759–1766 (1994).

C. T. Law and G. A. Swartzlander, Jr., “Optical vortex solitons and the stability of dark soliton stripes,” Opt. Lett. 18, 586–588 (1993).

G. A. Swartlander, Jr. and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).

Lukin, V. P.

Mamaev, A. V.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetski, and V. V. Shkunov, “Speckle-inhomogeneous field wavefront dislocation,” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981)].

Michell, D. J.

Mihalache, D.

L. C. Crasovan, G. Molina-Terriza, J. P. Torres, L. Torner, V. M. Perez-Garcia, and D. Mihalache, “Globally linked vortex clusters in trapped wave fields,” Phys. Rev. E 66, 036612 (2002).

Molina-Terriza, G.

L. C. Crasovan, G. Molina-Terriza, J. P. Torres, L. Torner, V. M. Perez-Garcia, and D. Mihalache, “Globally linked vortex clusters in trapped wave fields,” Phys. Rev. E 66, 036612 (2002).

Neshev, D.

I. Velchev, A. Dreischuh, D. Neshev, and S. Dinev, “Interaction of optical vortex solitons superimposed on different background beams,” Opt. Commun. 130, 385–392 (1996).

Nye, J. F.

J. F. Nye, “Optical caustics in the near field from liquid drops,” Proc. R. Soc. London Ser. A 361, 21–41 (1978).

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).

Palacios, D.

D. Palacios, D. Rozas, and G. A. Swartzlander, “Observed scattering into a dark optical vortex core,” Phys. Rev. Lett. 88, 103902 (2002).

Perez-Garcia, V. M.

L. C. Crasovan, G. Molina-Terriza, J. P. Torres, L. Torner, V. M. Perez-Garcia, and D. Mihalache, “Globally linked vortex clusters in trapped wave fields,” Phys. Rev. E 66, 036612 (2002).

Pilipetski, N. F.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetski, and V. V. Shkunov, “Speckle-inhomogeneous field wavefront dislocation,” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981)].

Pokasov, V. V.

Poladian, L.

Rocca, F.

P. Coullet, L. Gill, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).

Roux, F. S.

Rozas, D.

D. Palacios, D. Rozas, and G. A. Swartzlander, “Observed scattering into a dark optical vortex core,” Phys. Rev. Lett. 88, 103902 (2002).

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

D. Rozas, C. T. Law, and G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997).

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

Sacks, Z. S.

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

Shkunov, V. V.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetski, and V. V. Shkunov, “Speckle-inhomogeneous field wavefront dislocation,” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981)].

Snyder, A. W.

Soskin, M. S.

A. M. Deykoon, M. S. Soskin, and G. A. Swartzlander, Jr., “Nonlinear optical catastrophe from a smooth initial beam,” Opt. Lett. 24, 1224–1226 (1999).

L. V. Kreminskaya, M. S. Soskin, and A. I. Krizhnyak, “The Gaussian lenses give birth to optical vortices in laser beams,” Opt. Commun. 145, 377–384 (1998).

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis’ma Zh. Eks. Teor. Fiz. 52, 1037–1039 (1990) [JETP Lett. 52, 429–431 (1990)].

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

Staliunas, K.

K. Staliunas, “Dynamics of optical vortices in a laser beam,” Opt. Commun. 90, 123–127 (1992).

Swartlander Jr., G. A.

G. A. Swartlander, Jr., “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26, 497–499 (2001).

G. A. Swartlander, Jr. and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).

Swartzlander, G. A.

D. Palacios, D. Rozas, and G. A. Swartzlander, “Observed scattering into a dark optical vortex core,” Phys. Rev. Lett. 88, 103902 (2002).

D. Rozas, C. T. Law, and G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997).

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

Swartzlander Jr., G. A.

A. M. Deykoon, M. S. Soskin, and G. A. Swartzlander, Jr., “Nonlinear optical catastrophe from a smooth initial beam,” Opt. Lett. 24, 1224–1226 (1999).

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

C. T. Law and G. A. Swartzlander, Jr., “Polarized optical vortex solitons: instabilities and dynamics in Kerr nonlinear media,” Chaos, Solitons Fractals 4, 1759–1766 (1994).

C. T. Law and G. A. Swartzlander, Jr., “Optical vortex solitons and the stability of dark soliton stripes,” Opt. Lett. 18, 586–588 (1993).

Torner, L.

L. C. Crasovan, G. Molina-Terriza, J. P. Torres, L. Torner, V. M. Perez-Garcia, and D. Mihalache, “Globally linked vortex clusters in trapped wave fields,” Phys. Rev. E 66, 036612 (2002).

Torres, J. P.

L. C. Crasovan, G. Molina-Terriza, J. P. Torres, L. Torner, V. M. Perez-Garcia, and D. Mihalache, “Globally linked vortex clusters in trapped wave fields,” Phys. Rev. E 66, 036612 (2002).

Vasnetsov, M. V.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis’ma Zh. Eks. Teor. Fiz. 52, 1037–1039 (1990) [JETP Lett. 52, 429–431 (1990)].

Velchev, I.

I. Velchev, A. Dreischuh, D. Neshev, and S. Dinev, “Interaction of optical vortex solitons superimposed on different background beams,” Opt. Commun. 130, 385–392 (1996).

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

Zel’dovich, B. Ya.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetski, and V. V. Shkunov, “Speckle-inhomogeneous field wavefront dislocation,” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981)].

Appl. Opt.

Chaos, Solitons Fractals

C. T. Law and G. A. Swartzlander, Jr., “Polarized optical vortex solitons: instabilities and dynamics in Kerr nonlinear media,” Chaos, Solitons Fractals 4, 1759–1766 (1994).

J. Mod. Opt.

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).

J. Opt. Soc. Am. B

JETP Lett.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis’ma Zh. Eks. Teor. Fiz. 52, 1037–1039 (1990) [JETP Lett. 52, 429–431 (1990)].

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetski, and V. V. Shkunov, “Speckle-inhomogeneous field wavefront dislocation,” Pis’ma Zh. Eks. Teor. Fiz. 33, 206–210 (1981) [JETP Lett. 33, 195–199 (1981)].

Opt. Commun.

I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).

I. Freund, “Optical vortex trajectories,” Opt. Commun. 181, 19–33 (2000).

I. Velchev, A. Dreischuh, D. Neshev, and S. Dinev, “Interaction of optical vortex solitons superimposed on different background beams,” Opt. Commun. 130, 385–392 (1996).

L. V. Kreminskaya, M. S. Soskin, and A. I. Krizhnyak, “The Gaussian lenses give birth to optical vortices in laser beams,” Opt. Commun. 145, 377–384 (1998).

P. Coullet, L. Gill, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989).

K. Staliunas, “Dynamics of optical vortices in a laser beam,” Opt. Commun. 90, 123–127 (1992).

Opt. Lett.

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).

Phys. Rev. E

L. C. Crasovan, G. Molina-Terriza, J. P. Torres, L. Torner, V. M. Perez-Garcia, and D. Mihalache, “Globally linked vortex clusters in trapped wave fields,” Phys. Rev. E 66, 036612 (2002).

Phys. Rev. Lett.

D. Palacios, D. Rozas, and G. A. Swartzlander, “Observed scattering into a dark optical vortex core,” Phys. Rev. Lett. 88, 103902 (2002).

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

G. A. Swartlander, Jr. and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).

Proc. R. Soc. London Ser. A

J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).

J. F. Nye, “Optical caustics in the near field from liquid drops,” Proc. R. Soc. London Ser. A 361, 21–41 (1978).

Other

M. Vasnetsov and K. Staliunas, eds., Optical Vortices, Vol. 228 in Horizons in World Physics (Nova Science, Huntington, N.Y., 1999).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

H. J. Lugt, Vortex Flow in Nature and Technology (Wiley-Interscience, New York, 1983).

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