Abstract

Propagation dynamics of optical vortices with anisotropic phase profiles, where the slope of the helical wave front is not uniform in the azimuthal direction, is studied in the linear and nonlinear regimes. Numerical results show that the rotation rate of optical vortices is proportional to the anisotropy and is in good agreement with the analytical approach.

© 2003 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  41. D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, “Motion control of ensembles of ordered optical vortices generated on finite extent background,” Opt. Commun. 151, 413-421 (1998).
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    [CrossRef] [PubMed]
  44. T. Ackemann, E. Kriege, and W. Lange, “Phase singularities via nonlinear beam propagation in sodium vapor,” Opt. Commun. 115, 339-346 (1995).
    [CrossRef]
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    [CrossRef] [PubMed]
  46. A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time-dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713-R1716 (1997).
    [CrossRef]
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    [CrossRef]
  48. B. Luther-Davies and X. Yang, “Steerable optical waveguides formed in self-defocusing media by using dark spatial solitons,” Opt. Lett. 17, 1755-1757 (1992).
    [CrossRef] [PubMed]
  49. I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247-264 (1993).
    [CrossRef]
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    [CrossRef]

2001 (3)

2000 (5)

1999 (1)

A. G. Truscott, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optically written waveguide in an atomic vapor,” Phys. Rev. Lett. 82, 1438-1441 (1999).
[CrossRef]

1998 (5)

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, “An array of phase singularities in a self-defocusing medium,” Opt. Commun. 147, 131-137 (1998).
[CrossRef]

G. H. Kim, J. H. Jeon, Y. C. Noh, J. H. Lee, J. S. Chang, K. H. Ko, and H. J. Moon, “Rotational characteristics of an array of optical vortices in a self-defocusing medium,” J. Korean Phys. Soc. 33, 308-314 (1998).

Y. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, and L. M. Pismen, “Dynamics of optical vortex solitons,” Opt. Commun. 152, 198-206 (1998).
[CrossRef]

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, “Motion control of ensembles of ordered optical vortices generated on finite extent background,” Opt. Commun. 151, 413-421 (1998).
[CrossRef]

J. P. Torres, J. M. Soto-Crespo, L. Torner, and D. V. Petrov, “Solitary-wave vortices in type II second-harmonic generation,” Opt. Commun. 149, 77-83 (1998).
[CrossRef]

1997 (5)

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

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time-dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713-R1716 (1997).
[CrossRef]

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Marker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948-2951 (1997).
[CrossRef]

I. Velchev, A. Dreischuh, D. Neshev, and S. Dinev, “Multiple-charged optical vortex solitons in bulk Kerr media,” Opt. Commun. 140, 77-82 (1997).
[CrossRef]

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

1996 (6)

K. T. Gahagan and G. A. Swartzlander, Jr., “Optical vortex trapping of particles,” Opt. Lett. 21, 827-829 (1996).
[CrossRef] [PubMed]

J. Christou, V. Tikhonenko, Y. S. Kivshar, and B. Luther-Davies, “Vortex soliton motion and steering,” Opt. Lett. 21, 1649-1651 (1996).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77, 4544-4547 (1996).
[CrossRef] [PubMed]

V. Tikhonenko and N. N. Akhmediev, “Excitation of vortex solitons in a Gaussian beam configuration,” Opt. Commun. 126, 108-112 (1996).
[CrossRef]

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).
[CrossRef]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593-1596 (1996).
[CrossRef] [PubMed]

1995 (5)

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604-612 (1995).
[CrossRef]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217-223 (1995).
[CrossRef]

T. Ackemann, E. Kriege, and W. Lange, “Phase singularities via nonlinear beam propagation in sodium vapor,” Opt. Commun. 115, 339-346 (1995).
[CrossRef]

F. S. Roux, “Dynamical behaviors of optical vortices,” J. Opt. Soc. Am. B 12, 1215-1221 (1995).
[CrossRef]

1994 (4)

B. Luther-Davies, R. Powles, and V. Tikhonenko, “Nonlinear rotation of three-dimensional dark spatial solitons in a Gaussian laser beam,” Opt. Lett. 19, 1816-1818 (1994).
[CrossRef] [PubMed]

I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am. A 11, 1644–1652 (1994).
[CrossRef]

M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Pratti, A. J. Kent, G. L. Oppo, A. B. Coates, C. O. Weiss, C. Green, E. J. D’Angelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427-1451 (1994).
[CrossRef] [PubMed]

M. S. El Naschie, ed., “Special issue on nonlinear optical structures, patterns, chaos,” Chaos, Solitons Fractals 4(8/9), 1251-1844 (1994).

1993 (6)

Z. Jaroszewicz and A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102, 391-396 (1993).
[CrossRef]

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

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

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123-132 (1993).
[CrossRef]

G. A. Swartzlander, Jr., and C. T. Law, “The optical vortex soliton,” Opt. Photonics News 4(12), 10 (1993).
[CrossRef]

I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247-264 (1993).
[CrossRef]

1992 (3)

B. Luther-Davies and X. Yang, “Steerable optical waveguides formed in self-defocusing media by using dark spatial solitons,” Opt. Lett. 17, 1755-1757 (1992).
[CrossRef] [PubMed]

G. A. Swartzlander, Jr., and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503-2506 (1992).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

1991 (1)

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090-5113 (1991).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403-408 (1989).
[CrossRef]

1983 (1)

1981 (1)

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Philipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis'ma Zh. Eksp. Teor. Fiz. 33, 206-210 (1981)[JETP Lett. 33, 195-199 (1981)].

1979 (1)

J. M. Vaughan and D. V. Willetts, “Interference properties of a light beam having a helical wave surface,” Opt. Commun. 30, 263-267 (1979).
[CrossRef]

1974 (1)

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

Ackemann, T.

T. Ackemann, E. Kriege, and W. Lange, “Phase singularities via nonlinear beam propagation in sodium vapor,” Opt. Commun. 115, 339-346 (1995).
[CrossRef]

Akhmediev, N. N.

V. Tikhonenko and N. N. Akhmediev, “Excitation of vortex solitons in a Gaussian beam configuration,” Opt. Commun. 126, 108-112 (1996).
[CrossRef]

Alexander, T. J.

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123-132 (1993).
[CrossRef]

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).
[CrossRef] [PubMed]

Anderson, D.

Assa, M.

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, “Motion control of ensembles of ordered optical vortices generated on finite extent background,” Opt. Commun. 151, 413-421 (1998).
[CrossRef]

Baranova, N. B.

N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Philipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis'ma Zh. Eksp. Teor. Fiz. 33, 206-210 (1981)[JETP Lett. 33, 195-199 (1981)].

Basistiy, I. V.

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604-612 (1995).
[CrossRef]

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

Battipede, F.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090-5113 (1991).
[CrossRef] [PubMed]

Bazhenov, V. Yu.

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

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123-132 (1993).
[CrossRef]

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).
[CrossRef] [PubMed]

Berry, M. V.

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

Brambilla, M.

M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Pratti, A. J. Kent, G. L. Oppo, A. B. Coates, C. O. Weiss, C. Green, E. J. D’Angelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427-1451 (1994).
[CrossRef] [PubMed]

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090-5113 (1991).
[CrossRef] [PubMed]

Carlsson, A. H.

Cattaneo, M.

M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Pratti, A. J. Kent, G. L. Oppo, A. B. Coates, C. O. Weiss, C. Green, E. J. D’Angelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427-1451 (1994).
[CrossRef] [PubMed]

Chang, J. S.

G. H. Kim, J. H. Jeon, Y. C. Noh, J. H. Lee, J. S. Chang, K. H. Ko, and H. J. Moon, “Rotational characteristics of an array of optical vortices in a self-defocusing medium,” J. Korean Phys. Soc. 33, 308-314 (1998).

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, “An array of phase singularities in a self-defocusing medium,” Opt. Commun. 147, 131-137 (1998).
[CrossRef]

Chen, Z.

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Marker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948-2951 (1997).
[CrossRef]

Chinaglia, W.

P. D. Trapani, W. Chinaglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843-3846 (2000).
[CrossRef] [PubMed]

Christou, J.

Y. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, and L. M. Pismen, “Dynamics of optical vortex solitons,” Opt. Commun. 152, 198-206 (1998).
[CrossRef]

J. Christou, V. Tikhonenko, Y. S. Kivshar, and B. Luther-Davies, “Vortex soliton motion and steering,” Opt. Lett. 21, 1649-1651 (1996).
[CrossRef] [PubMed]

Coates, A. B.

M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Pratti, A. J. Kent, G. L. Oppo, A. B. Coates, C. O. Weiss, C. Green, E. J. D’Angelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427-1451 (1994).
[CrossRef] [PubMed]

Coullet, P.

P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403-408 (1989).
[CrossRef]

D’Angelo, E. J.

M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Pratti, A. J. Kent, G. L. Oppo, A. B. Coates, C. O. Weiss, C. Green, E. J. D’Angelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427-1451 (1994).
[CrossRef] [PubMed]

Dinev, S.

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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).
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M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593-1596 (1996).
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A. G. Truscott, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optically written waveguide in an atomic vapor,” Phys. Rev. Lett. 82, 1438-1441 (1999).
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M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Pratti, A. J. Kent, G. L. Oppo, A. B. Coates, C. O. Weiss, C. Green, E. J. D’Angelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427-1451 (1994).
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G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, “An array of phase singularities in a self-defocusing medium,” Opt. Commun. 147, 131-137 (1998).
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Lugiato, L. A.

M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Pratti, A. J. Kent, G. L. Oppo, A. B. Coates, C. O. Weiss, C. Green, E. J. D’Angelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427-1451 (1994).
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Malmberg, J. N.

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Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Marker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948-2951 (1997).
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Moon, H. J.

G. H. Kim, J. H. Jeon, Y. C. Noh, J. H. Lee, J. S. Chang, K. H. Ko, and H. J. Moon, “Rotational characteristics of an array of optical vortices in a self-defocusing medium,” J. Korean Phys. Soc. 33, 308-314 (1998).

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, “An array of phase singularities in a self-defocusing medium,” Opt. Commun. 147, 131-137 (1998).
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Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Marker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948-2951 (1997).
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D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, “Motion control of ensembles of ordered optical vortices generated on finite extent background,” Opt. Commun. 151, 413-421 (1998).
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I. Velchev, A. Dreischuh, D. Neshev, and S. Dinev, “Multiple-charged optical vortex solitons in bulk Kerr media,” Opt. Commun. 140, 77-82 (1997).
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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).
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G. H. Kim, J. H. Jeon, Y. C. Noh, J. H. Lee, J. S. Chang, K. H. Ko, and H. J. Moon, “Rotational characteristics of an array of optical vortices in a self-defocusing medium,” J. Korean Phys. Soc. 33, 308-314 (1998).

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, “An array of phase singularities in a self-defocusing medium,” Opt. Commun. 147, 131-137 (1998).
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M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090-5113 (1991).
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J. P. Torres, J. M. Soto-Crespo, L. Torner, and D. V. Petrov, “Solitary-wave vortices in type II second-harmonic generation,” Opt. Commun. 149, 77-83 (1998).
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N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Philipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis'ma Zh. Eksp. Teor. Fiz. 33, 206-210 (1981)[JETP Lett. 33, 195-199 (1981)].

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M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Pratti, A. J. Kent, G. L. Oppo, A. B. Coates, C. O. Weiss, C. Green, E. J. D’Angelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427-1451 (1994).
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Piskarskas, A.

P. D. Trapani, W. Chinaglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843-3846 (2000).
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Y. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, and L. M. Pismen, “Dynamics of optical vortex solitons,” Opt. Commun. 152, 198-206 (1998).
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Prati, F.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090-5113 (1991).
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M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Pratti, A. J. Kent, G. L. Oppo, A. B. Coates, C. O. Weiss, C. Green, E. J. D’Angelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427-1451 (1994).
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G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 87, 23902-23905 (2001).
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G. Molina-Terriza, J. Recolons, and L. Torner, “The curious arithmetic of optical vortices,” Opt. Lett. 25, 1135-1137 (2000).
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P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403-408 (1989).
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Rozas, D.

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A. G. Truscott, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optically written waveguide in an atomic vapor,” Phys. Rev. Lett. 82, 1438-1441 (1999).
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M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, “Optical angular-momentum transfer to trapped absorbing particles,” Phys. Rev. A 54, 1593-1596 (1996).
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H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high efficiency computer generated holograms,” J. Mod. Opt. 42, 217-223 (1995).
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A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time-dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713-R1716 (1997).
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A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77, 4544-4547 (1996).
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Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Marker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948-2951 (1997).
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N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Philipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis'ma Zh. Eksp. Teor. Fiz. 33, 206-210 (1981)[JETP Lett. 33, 195-199 (1981)].

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I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247-264 (1993).
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J. P. Torres, J. M. Soto-Crespo, L. Torner, and D. V. Petrov, “Solitary-wave vortices in type II second-harmonic generation,” Opt. Commun. 149, 77-83 (1998).
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Y. S. Kivshar, J. Christou, V. Tikhonenko, B. Luther-Davies, and L. M. Pismen, “Dynamics of optical vortex solitons,” Opt. Commun. 152, 198-206 (1998).
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G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 87, 23902-23905 (2001).
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G. Molina-Terriza, E. M. Wright, and L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26, 163-165 (2001).
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S. Minardi, G. Molina-Terriza, P. D. Trapani, J. P. Torres, and L. Torner, “Soliton algebra by vortex-beam splitting,” Opt. Lett. 26, 1004-1006 (2001).
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G. Molina-Terriza, J. Recolons, and L. Torner, “The curious arithmetic of optical vortices,” Opt. Lett. 25, 1135-1137 (2000).
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S. Minardi, G. Molina-Terriza, P. D. Trapani, J. P. Torres, and L. Torner, “Soliton algebra by vortex-beam splitting,” Opt. Lett. 26, 1004-1006 (2001).
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G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 87, 23902-23905 (2001).
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J. P. Torres, J. M. Soto-Crespo, L. Torner, and D. V. Petrov, “Solitary-wave vortices in type II second-harmonic generation,” Opt. Commun. 149, 77-83 (1998).
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S. Minardi, G. Molina-Terriza, P. D. Trapani, J. P. Torres, and L. Torner, “Soliton algebra by vortex-beam splitting,” Opt. Lett. 26, 1004-1006 (2001).
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P. D. Trapani, W. Chinaglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843-3846 (2000).
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M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Pratti, A. J. Kent, G. L. Oppo, A. B. Coates, C. O. Weiss, C. Green, E. J. D’Angelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427-1451 (1994).
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A. G. Truscott, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optically written waveguide in an atomic vapor,” Phys. Rev. Lett. 82, 1438-1441 (1999).
[CrossRef]

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P. D. Trapani, W. Chinaglia, S. Minardi, A. Piskarskas, and G. Valiulis, “Observation of quadratic optical vortex solitons,” Phys. Rev. Lett. 84, 3843-3846 (2000).
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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).
[CrossRef]

I. Velchev, A. Dreischuh, D. Neshev, and S. Dinev, “Multiple-charged optical vortex solitons in bulk Kerr media,” Opt. Commun. 140, 77-82 (1997).
[CrossRef]

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, “Motion control of ensembles of ordered optical vortices generated on finite extent background,” Opt. Commun. 151, 413-421 (1998).
[CrossRef]

J. P. Torres, J. M. Soto-Crespo, L. Torner, and D. V. Petrov, “Solitary-wave vortices in type II second-harmonic generation,” Opt. Commun. 149, 77-83 (1998).
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T. Ackemann, E. Kriege, and W. Lange, “Phase singularities via nonlinear beam propagation in sodium vapor,” Opt. Commun. 115, 339-346 (1995).
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Opt. Lett. (10)

B. Luther-Davies and X. Yang, “Steerable optical waveguides formed in self-defocusing media by using dark spatial solitons,” Opt. Lett. 17, 1755-1757 (1992).
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G. Molina-Terriza, J. Recolons, and L. Torner, “The curious arithmetic of optical vortices,” Opt. Lett. 25, 1135-1137 (2000).
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S. Minardi, G. Molina-Terriza, P. D. Trapani, J. P. Torres, and L. Torner, “Soliton algebra by vortex-beam splitting,” Opt. Lett. 26, 1004-1006 (2001).
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G. Molina-Terriza, E. M. Wright, and L. Torner, “Propagation and control of noncanonical optical vortices,” Opt. Lett. 26, 163-165 (2001).
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D. Rozas and G. A. Swartzlander, Jr., “Observed rotational enhancement of nonlinear optical vortices,” Opt. Lett. 25, 126-128 (2000).
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C. T. Law, X. Zhang, and G. A. Swartzlander, Jr., “Waveguiding properties of optical vortex solitons,” Opt. Lett. 25, 55-57 (2000).
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B. Luther-Davies, R. Powles, and V. Tikhonenko, “Nonlinear rotation of three-dimensional dark spatial solitons in a Gaussian laser beam,” Opt. Lett. 19, 1816-1818 (1994).
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Opt. Photonics News (1)

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Phys. Rev. A (5)

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[CrossRef] [PubMed]

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090-5113 (1991).
[CrossRef] [PubMed]

M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Pratti, A. J. Kent, G. L. Oppo, A. B. Coates, C. O. Weiss, C. Green, E. J. D’Angelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427-1451 (1994).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Time-dependent evolution of an optical vortex in photorefractive media,” Phys. Rev. A 56, R1713-R1716 (1997).
[CrossRef]

Phys. Rev. Lett. (8)

Z. Chen, M. Segev, D. W. Wilson, R. E. Muller, and P. D. Marker, “Self-trapping of an optical vortex by use of the bulk photovoltaic effect,” Phys. Rev. Lett. 78, 2948-2951 (1997).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Vortex evolution and bound pair formation in anisotropic nonlinear optical media,” Phys. Rev. Lett. 77, 4544-4547 (1996).
[CrossRef] [PubMed]

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G. A. Swartzlander, Jr., and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503-2506 (1992).
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G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 87, 23902-23905 (2001).
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N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Philipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis'ma Zh. Eksp. Teor. Fiz. 33, 206-210 (1981)[JETP Lett. 33, 195-199 (1981)].

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Figures (12)

Fig. 1
Fig. 1

(a) Typical form of a helicoidal wave-front structure of an optical vortex. The plotting range of r is from 0 to 10 with an interval of Δr=2, and that of kz is from -π/2 to 6π with an interval of kΔz=2π/40. (b) Gray-scale contour plot of the transverse phase distribution. The phase is contoured with the interval of Δθ=2π/10, and black (white) corresponds to a phase value of -π (+π).

Fig. 2
Fig. 2

(a) Typical form of a helicoidal wave-front structure of an anisotropic optical vortex with an anisotropy of σ=2. The plotting range of r is from 0 to 10 with an interval of Δr=2, and that of kz is from -π/2 to 6π with an interval of kΔz=2π/40. (b) Gray-scale contour plot of transverse phase distribution. The phase is contoured with the interval of ΔΦ=2π/10, and black (white) corresponds to a phase value of -π (+π).

Fig. 3
Fig. 3

Phase gradient as a function of the azimuthal angle for different anisotropy values of σ=1/2, 1, and 2.

Fig. 4
Fig. 4

Initial field distribution of a tanh-vortex beam: (a) transverse beam pattern and (b) intensity profile along the x axis. The background beam width is taken to be w0=30 wv, and the separation distance of two optical vortices is taken to be d=2 wv.

Fig. 5
Fig. 5

Typical phase distribution of a vortex pair for different anisotropy values: (a) σ=1/2 and (b) σ=2. The transverse coordinates extend from -3 to 3, and the phase is contoured by ten levels with the interval of 2π/10.

Fig. 6
Fig. 6

Gray-scale images: (a), (c), and (e) intensity patterns and (b), (d), and (f) corresponding contoured phase distributions after the initial optical vortices propagate to the distance of Z=20 in the linear regime when (a) and (b) σ=0.6, (c) and (d) σ=1.0, and (e) and (f) σ=1.4. The images are plotted in the range of transverse coordinates, X and Y, from -15 to 15. The intensity patterns are plotted in the logarithmic scale, whereas the phase distributions are contoured linearly with the interval of 2π/10.

Fig. 7
Fig. 7

Projection of the vortex trajectories for different anisotropy values of σ=0.6, 1.0, and 1.4 in the linear regime onto the transverse plane up to the propagation distance of Z=20, where each symbol is marked by the propagation interval of ΔZ=2.

Fig. 8
Fig. 8

Rotation angle as a function of the propagation distance in the linear regime for different anisotropy values of σ=0.6, 1.0, and 1.4.

Fig. 9
Fig. 9

Gray-scale images: (a), (c), and (e) intensity patterns and (b), (d), and (f) corresponding contoured phase distributions after the initial optical vortices propagate to the distance of Z=20 in the nonlinear regime when (a) and (b) σ=0.6, (c) and (d) σ=1.0, and (e) and (f) σ=1.4. The images are plotted in the range of transverse coordinates, X and Y, from -15 to 15. The intensity patterns are plotted in the logarithmic scale, whereas the phase distributions are contoured linearly with the interval of 2π/10.

Fig. 10
Fig. 10

Projection of the vortex trajectories for different anisotropy values of σ=0.6, 1.0, and 1.4 in the nonlinear regime onto the transverse plane up to the propagation distance of Z=20, where each symbol is marked by the propagation interval of ΔZ=2.

Fig. 11
Fig. 11

Rotation angle as a function of the propagation distance in the nonlinear regime for different anisotropy values of σ=0.6, 1.0, and 1.4. The inset shows the variation of rotation angle in a short distance up to Z=2.

Fig. 12
Fig. 12

Rotation rate as a function of the anisotropy value. Filled (empty) square symbols represent the initial rotation rates obtained numerically in the linear (nonlinear) regime. The solid line represents the rotation rate obtained when the intensity gradient by both the background beam and the nearby vortex are included [see Eq. (8)]. The dashed line represents the rotation rate obtained when the contribution of the background beam is excluded. The dotted line represents the rotation rate when only the phase gradient by the other vortex is considered. Error bars correspond to the uncertainty of the polynomial fit in the nonlinear regime, and those in the linear regime are nearly the same.

Equations (8)

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Φ(x, y)=tan-1σ yx=tan-1σ sin θcos θ,
dΦdθ=σcos2 θ+σ2sin2 θ.
Φ(r, θ)=tan-1σ y1x1+tan-1σ y2x2=tan-1σ sin θ1cos θ1+tan-1σ sin θ2cos θ2,
Φ|x10,y10=θ^2σd,
Ωz=0=dΦdzz=0=-2σkd2.
i AZ=2X2+2Y2A-2|A|2A,
A(X, Y, Z=0)=BG(X, Y)tanh(R1/wv)×tanh(R2/wv)exp[i(Φ1+Φ2)],
dΦdzz=0=-2kσd2+1w02-2 cosh(2d/wv)dwv,

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