Abstract

We present simple methods to produce optical vortices on the axis of beam propagation with nonspiral phase plates. We show that a phase plate that provides linear phase retardation on one half of a laser beam produces optical vortices, which is demonstrated experimentally by use of a thickness-varying glass platelet. We also demonstrate and explain that mixed dislocations of a bent edge dislocation transform into a pair of vortices with opposing topological charges.

© 1997 Optical Society of America

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  1. G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
    [CrossRef]
  2. F. S. Roux, “Dynamical behavior of optical vortices,” J. Opt. Soc. Am. B 12, 1215–1221 (1995).
    [CrossRef]
  3. I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
    [CrossRef]
  4. I. V. Basistiy, M. S. Soskin, M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
    [CrossRef]
  5. C. O. Weiss, “Spatio-temporal structures. Part II. Vortices and defects in lasers,” Phys. Rep. 219, 311–338 (1992).
    [CrossRef]
  6. L. A. Lugiato, ed., Special Issues on Nonlinear Optical Structures, Patterns, Chaos, Chaos, Solitons, Fractals4, Nos. 6 and 7 (1994).
  7. A. W. Snyder, L. Poladian, D. J. Mitchell, “Stable black self-guided beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789–791 (1992).
    [CrossRef] [PubMed]
  8. G. A. Swartzlander, C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).
    [CrossRef] [PubMed]
  9. G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
    [CrossRef]
  10. Y. Chen, J. Atai, “Dynamics of optical-vortex solitons in perturbed nonlinear media,” J. Opt. Soc. Am. B 11, 2000–2003 (1994).
    [CrossRef]
  11. B Luther-Davies, R Powles, V Tikhonenko, “Nonlinear rotation of three-dimensional dark spatial solitons in a Gaussian laser beam,” Opt. Lett.19, 1816–1818 (1994); V. Tikhonenko, N. N. Akhmediev, “Excitation of vortex solitons in a Gaussian beam configuration,” Opt. Commun. 126, 108–112 (1996); J. Christou, V. Tikhonenko, Y. S. Kivshar, B. Luther-Davies, “Vortex soliton motion and steering,” Opt. Lett.21, 1649–1651 (1996).
  12. I. Velchev, A. Dreischuh, D. Neshev, S. Dinev, “Interactions of optical vortex solitons superimposed on different background beams,” Opt. Commun. 130, 385–392 (1996).
    [CrossRef]
  13. V Tikhonenko, J Christou, B Luther-Davies, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B12, 2046–2052 (1995); “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett.76, 2698–2701 (1996).
  14. A. V. Mamaev, M. Saffman, A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
    [CrossRef]
  15. G. R. Allan, S. R. Skinner, D. R. Andersen, A. L. Smirl, “Observation of fundamental dark spatial solitons in semiconductors using picosecond pulses,” Opt. Lett. 16, 156–158 (1991).
    [PubMed]
  16. J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
    [CrossRef]
  17. J. M. Vaughan, D. V. Willetts, “Temporal and interference fringe analysis of TEM01* laser modes,” J. Opt. Soc. Am. 73, 1018–1021 (1983).
    [CrossRef]
  18. F. T. Arecchi, G. Giacomelli, P. L. Ramazza, S. Residori, “Vortices and defect statistics in two-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991).
    [CrossRef] [PubMed]
  19. M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, C. O. Weiss, “Transverse laser patterns. I. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
    [CrossRef] [PubMed]
  20. J. Malos, M. Vaupel, K. Staliunas, C. O. Weiss, “Dynamical structures of a photorefractive oscillator,” Phys. Rev. A 53, 3559–3564 (1996).
    [CrossRef] [PubMed]
  21. N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, B. Ya. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. 73, 525–528 (1983).
    [CrossRef]
  22. N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
    [CrossRef] [PubMed]
  23. V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
    [CrossRef]
  24. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
    [CrossRef]
  25. S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
    [CrossRef]
  26. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
    [CrossRef]
  27. F Brownde Colstoun, G Khitrova, A. V. Fedorov, T. R. Nelson, C Lowry, T. M. Brennan, B. G. Hammons, P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos, Solitons, Fractals 4, 1575–1596 (1994).
  28. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993).
    [CrossRef]
  29. I Freund, N Shvartsman, V Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun.101, 247–264 (1993); I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am A 11, 1644–1652 (1994).
  30. Guang-Hoon Kim, Jin-Ho Jeon, Young-Chul Noh, Kwang-Hoon Ko, Hee-Jong Moon, Jai-Hyung Lee, Joon-Sung Chang, “Nonlinear propagation of an array of phase singularities through a self-defocusing medium,” Opt. Commun. (to be published).

1997 (1)

A. V. Mamaev, M. Saffman, A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

1996 (2)

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

J. Malos, M. Vaupel, K. Staliunas, C. O. Weiss, “Dynamical structures of a photorefractive oscillator,” Phys. Rev. A 53, 3559–3564 (1996).
[CrossRef] [PubMed]

1995 (3)

V Tikhonenko, J Christou, B Luther-Davies, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B12, 2046–2052 (1995); “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett.76, 2698–2701 (1996).

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

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

1994 (4)

Y. Chen, J. Atai, “Dynamics of optical-vortex solitons in perturbed nonlinear media,” J. Opt. Soc. Am. B 11, 2000–2003 (1994).
[CrossRef]

B Luther-Davies, R Powles, V Tikhonenko, “Nonlinear rotation of three-dimensional dark spatial solitons in a Gaussian laser beam,” Opt. Lett.19, 1816–1818 (1994); V. Tikhonenko, N. N. Akhmediev, “Excitation of vortex solitons in a Gaussian beam configuration,” Opt. Commun. 126, 108–112 (1996); J. Christou, V. Tikhonenko, Y. S. Kivshar, B. Luther-Davies, “Vortex soliton motion and steering,” Opt. Lett.21, 1649–1651 (1996).

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

F Brownde Colstoun, G Khitrova, A. V. Fedorov, T. R. Nelson, C Lowry, T. M. Brennan, B. G. Hammons, P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos, Solitons, Fractals 4, 1575–1596 (1994).

1993 (4)

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

I Freund, N Shvartsman, V Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun.101, 247–264 (1993); I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am A 11, 1644–1652 (1994).

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

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

1992 (8)

C. O. Weiss, “Spatio-temporal structures. Part II. Vortices and defects in lasers,” Phys. Rep. 219, 311–338 (1992).
[CrossRef]

A. W. Snyder, L. Poladian, D. J. Mitchell, “Stable black self-guided beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789–791 (1992).
[CrossRef] [PubMed]

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

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef] [PubMed]

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

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

1991 (3)

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, S. Residori, “Vortices and defect statistics in two-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991).
[CrossRef] [PubMed]

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

G. R. Allan, S. R. Skinner, D. R. Andersen, A. L. Smirl, “Observation of fundamental dark spatial solitons in semiconductors using picosecond pulses,” Opt. Lett. 16, 156–158 (1991).
[PubMed]

1983 (2)

1974 (1)

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

Allan, G. R.

Allen, L.

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

Andersen, D. R.

Arecchi, F. T.

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, S. Residori, “Vortices and defect statistics in two-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991).
[CrossRef] [PubMed]

Atai, J.

Baranova, N. B.

Basistiy, I. V.

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

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

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

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

Berry, M. V.

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

Brambilla, M.

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

Brennan, T. M.

F Brownde Colstoun, G Khitrova, A. V. Fedorov, T. R. Nelson, C Lowry, T. M. Brennan, B. G. Hammons, P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos, Solitons, Fractals 4, 1575–1596 (1994).

Brownde Colstoun, F

F Brownde Colstoun, G Khitrova, A. V. Fedorov, T. R. Nelson, C Lowry, T. M. Brennan, B. G. Hammons, P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos, Solitons, Fractals 4, 1575–1596 (1994).

Chang, Joon-Sung

Guang-Hoon Kim, Jin-Ho Jeon, Young-Chul Noh, Kwang-Hoon Ko, Hee-Jong Moon, Jai-Hyung Lee, Joon-Sung Chang, “Nonlinear propagation of an array of phase singularities through a self-defocusing medium,” Opt. Commun. (to be published).

Chen, Y.

Christou, J

V Tikhonenko, J Christou, B Luther-Davies, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B12, 2046–2052 (1995); “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett.76, 2698–2701 (1996).

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Dinev, S.

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

Dreischuh, A.

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

Fedorov, A. V.

F Brownde Colstoun, G Khitrova, A. V. Fedorov, T. R. Nelson, C Lowry, T. M. Brennan, B. G. Hammons, P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos, Solitons, Fractals 4, 1575–1596 (1994).

Firth, W. J.

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

Freilikher, V

I Freund, N Shvartsman, V Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun.101, 247–264 (1993); I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am A 11, 1644–1652 (1994).

Freund, I

I Freund, N Shvartsman, V Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun.101, 247–264 (1993); I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am A 11, 1644–1652 (1994).

Giacomelli, G.

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, S. Residori, “Vortices and defect statistics in two-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991).
[CrossRef] [PubMed]

Hammons, B. G.

F Brownde Colstoun, G Khitrova, A. V. Fedorov, T. R. Nelson, C Lowry, T. M. Brennan, B. G. Hammons, P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos, Solitons, Fractals 4, 1575–1596 (1994).

Heckenberg, N. R.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef] [PubMed]

Indebetouw, G.

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

Jeon, Jin-Ho

Guang-Hoon Kim, Jin-Ho Jeon, Young-Chul Noh, Kwang-Hoon Ko, Hee-Jong Moon, Jai-Hyung Lee, Joon-Sung Chang, “Nonlinear propagation of an array of phase singularities through a self-defocusing medium,” Opt. Commun. (to be published).

Khitrova, G

F Brownde Colstoun, G Khitrova, A. V. Fedorov, T. R. Nelson, C Lowry, T. M. Brennan, B. G. Hammons, P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos, Solitons, Fractals 4, 1575–1596 (1994).

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Kim, Guang-Hoon

Guang-Hoon Kim, Jin-Ho Jeon, Young-Chul Noh, Kwang-Hoon Ko, Hee-Jong Moon, Jai-Hyung Lee, Joon-Sung Chang, “Nonlinear propagation of an array of phase singularities through a self-defocusing medium,” Opt. Commun. (to be published).

Ko, Kwang-Hoon

Guang-Hoon Kim, Jin-Ho Jeon, Young-Chul Noh, Kwang-Hoon Ko, Hee-Jong Moon, Jai-Hyung Lee, Joon-Sung Chang, “Nonlinear propagation of an array of phase singularities through a self-defocusing medium,” Opt. Commun. (to be published).

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Law, C. T.

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

Lee, Jai-Hyung

Guang-Hoon Kim, Jin-Ho Jeon, Young-Chul Noh, Kwang-Hoon Ko, Hee-Jong Moon, Jai-Hyung Lee, Joon-Sung Chang, “Nonlinear propagation of an array of phase singularities through a self-defocusing medium,” Opt. Commun. (to be published).

Lowry, C

F Brownde Colstoun, G Khitrova, A. V. Fedorov, T. R. Nelson, C Lowry, T. M. Brennan, B. G. Hammons, P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos, Solitons, Fractals 4, 1575–1596 (1994).

Lugiato, L. A.

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

Luther-Davies, B

V Tikhonenko, J Christou, B Luther-Davies, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B12, 2046–2052 (1995); “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett.76, 2698–2701 (1996).

B Luther-Davies, R Powles, V Tikhonenko, “Nonlinear rotation of three-dimensional dark spatial solitons in a Gaussian laser beam,” Opt. Lett.19, 1816–1818 (1994); V. Tikhonenko, N. N. Akhmediev, “Excitation of vortex solitons in a Gaussian beam configuration,” Opt. Commun. 126, 108–112 (1996); J. Christou, V. Tikhonenko, Y. S. Kivshar, B. Luther-Davies, “Vortex soliton motion and steering,” Opt. Lett.21, 1649–1651 (1996).

Maker, P. D.

F Brownde Colstoun, G Khitrova, A. V. Fedorov, T. R. Nelson, C Lowry, T. M. Brennan, B. G. Hammons, P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos, Solitons, Fractals 4, 1575–1596 (1994).

Malos, J.

J. Malos, M. Vaupel, K. Staliunas, C. O. Weiss, “Dynamical structures of a photorefractive oscillator,” Phys. Rev. A 53, 3559–3564 (1996).
[CrossRef] [PubMed]

Mamaev, A. V.

A. V. Mamaev, M. Saffman, A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

N. B. Baranova, A. V. Mamaev, N. F. Pilipetsky, V. V. Shkunov, B. Ya. Zel’dovich, “Wave-front dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. 73, 525–528 (1983).
[CrossRef]

McDonald, G. S.

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

McDuff, R.

N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

Mitchell, D. J.

Moon, Hee-Jong

Guang-Hoon Kim, Jin-Ho Jeon, Young-Chul Noh, Kwang-Hoon Ko, Hee-Jong Moon, Jai-Hyung Lee, Joon-Sung Chang, “Nonlinear propagation of an array of phase singularities through a self-defocusing medium,” Opt. Commun. (to be published).

Nelson, T. R.

F Brownde Colstoun, G Khitrova, A. V. Fedorov, T. R. Nelson, C Lowry, T. M. Brennan, B. G. Hammons, P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos, Solitons, Fractals 4, 1575–1596 (1994).

Neshev, D.

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

Noh, Young-Chul

Guang-Hoon Kim, Jin-Ho Jeon, Young-Chul Noh, Kwang-Hoon Ko, Hee-Jong Moon, Jai-Hyung Lee, Joon-Sung Chang, “Nonlinear propagation of an array of phase singularities through a self-defocusing medium,” Opt. Commun. (to be published).

Nye, J. F.

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

Penna, V.

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

Pilipetsky, N. F.

Poladian, L.

Powles, R

B Luther-Davies, R Powles, V Tikhonenko, “Nonlinear rotation of three-dimensional dark spatial solitons in a Gaussian laser beam,” Opt. Lett.19, 1816–1818 (1994); V. Tikhonenko, N. N. Akhmediev, “Excitation of vortex solitons in a Gaussian beam configuration,” Opt. Commun. 126, 108–112 (1996); J. Christou, V. Tikhonenko, Y. S. Kivshar, B. Luther-Davies, “Vortex soliton motion and steering,” Opt. Lett.21, 1649–1651 (1996).

Prati, F.

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

Ramazza, P. L.

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, S. Residori, “Vortices and defect statistics in two-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991).
[CrossRef] [PubMed]

Residori, S.

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, S. Residori, “Vortices and defect statistics in two-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991).
[CrossRef] [PubMed]

Roux, F. S.

Rubinsztein-Dunlop, H.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

Saffman, M.

A. V. Mamaev, M. Saffman, A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

Shinkaryev, M. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Shkunov, V. V.

Shvartsman, N

I Freund, N Shvartsman, V Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun.101, 247–264 (1993); I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am A 11, 1644–1652 (1994).

Skinner, S. R.

Smirl, A. L.

Smith, C. P.

N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

Snyder, A. W.

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Soskin, M. S.

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

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

Staliunas, K.

J. Malos, M. Vaupel, K. Staliunas, C. O. Weiss, “Dynamical structures of a photorefractive oscillator,” Phys. Rev. A 53, 3559–3564 (1996).
[CrossRef] [PubMed]

Swartzlander, G. A.

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

Syed, K. S.

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

Tamm, C.

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

Tikhonenko, V

V Tikhonenko, J Christou, B Luther-Davies, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B12, 2046–2052 (1995); “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett.76, 2698–2701 (1996).

B Luther-Davies, R Powles, V Tikhonenko, “Nonlinear rotation of three-dimensional dark spatial solitons in a Gaussian laser beam,” Opt. Lett.19, 1816–1818 (1994); V. Tikhonenko, N. N. Akhmediev, “Excitation of vortex solitons in a Gaussian beam configuration,” Opt. Commun. 126, 108–112 (1996); J. Christou, V. Tikhonenko, Y. S. Kivshar, B. Luther-Davies, “Vortex soliton motion and steering,” Opt. Lett.21, 1649–1651 (1996).

Uspleniev, G. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

van der Veen, H. E. L. O.

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

Vasnetsov, M. V.

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

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

Vaughan, J. M.

Vaupel, M.

J. Malos, M. Vaupel, K. Staliunas, C. O. Weiss, “Dynamical structures of a photorefractive oscillator,” Phys. Rev. A 53, 3559–3564 (1996).
[CrossRef] [PubMed]

Velchev, I.

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

Wegener, M. J.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

Weiss, C. O.

J. Malos, M. Vaupel, K. Staliunas, C. O. Weiss, “Dynamical structures of a photorefractive oscillator,” Phys. Rev. A 53, 3559–3564 (1996).
[CrossRef] [PubMed]

C. O. Weiss, “Spatio-temporal structures. Part II. Vortices and defects in lasers,” Phys. Rep. 219, 311–338 (1992).
[CrossRef]

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

White, A. G.

Willetts, D. V.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

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

Zel’dovich, B. Ya.

Zozulya, A. A.

A. V. Mamaev, M. Saffman, A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

Chaos, Solitons, Fractals (1)

F Brownde Colstoun, G Khitrova, A. V. Fedorov, T. R. Nelson, C Lowry, T. M. Brennan, B. G. Hammons, P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos, Solitons, Fractals 4, 1575–1596 (1994).

J. Mod. Opt. (3)

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

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

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

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (3)

V Tikhonenko, J Christou, B Luther-Davies, “Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium,” J. Opt. Soc. Am. B12, 2046–2052 (1995); “Three-dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett.76, 2698–2701 (1996).

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

Y. Chen, J. Atai, “Dynamics of optical-vortex solitons in perturbed nonlinear media,” J. Opt. Soc. Am. B 11, 2000–2003 (1994).
[CrossRef]

Opt. Commun. (7)

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

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

G. S. McDonald, K. S. Syed, W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992).
[CrossRef]

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

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

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

I Freund, N Shvartsman, V Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun.101, 247–264 (1993); I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am A 11, 1644–1652 (1994).

Opt. Lett. (4)

N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef] [PubMed]

G. R. Allan, S. R. Skinner, D. R. Andersen, A. L. Smirl, “Observation of fundamental dark spatial solitons in semiconductors using picosecond pulses,” Opt. Lett. 16, 156–158 (1991).
[PubMed]

B Luther-Davies, R Powles, V Tikhonenko, “Nonlinear rotation of three-dimensional dark spatial solitons in a Gaussian laser beam,” Opt. Lett.19, 1816–1818 (1994); V. Tikhonenko, N. N. Akhmediev, “Excitation of vortex solitons in a Gaussian beam configuration,” Opt. Commun. 126, 108–112 (1996); J. Christou, V. Tikhonenko, Y. S. Kivshar, B. Luther-Davies, “Vortex soliton motion and steering,” Opt. Lett.21, 1649–1651 (1996).

A. W. Snyder, L. Poladian, D. J. Mitchell, “Stable black self-guided beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789–791 (1992).
[CrossRef] [PubMed]

Opt. Quantum Electron. (1)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

Phys. Rep. (1)

C. O. Weiss, “Spatio-temporal structures. Part II. Vortices and defects in lasers,” Phys. Rep. 219, 311–338 (1992).
[CrossRef]

Phys. Rev. A (2)

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

J. Malos, M. Vaupel, K. Staliunas, C. O. Weiss, “Dynamical structures of a photorefractive oscillator,” Phys. Rev. A 53, 3559–3564 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

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

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, S. Residori, “Vortices and defect statistics in two-dimensional optical chaos,” Phys. Rev. Lett. 67, 3749–3752 (1991).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, A. A. Zozulya, “Decay of high order optical vortices in anisotropic nonlinear optical media,” Phys. Rev. Lett. 78, 2108–2111 (1997).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

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

Other (2)

L. A. Lugiato, ed., Special Issues on Nonlinear Optical Structures, Patterns, Chaos, Chaos, Solitons, Fractals4, Nos. 6 and 7 (1994).

Guang-Hoon Kim, Jin-Ho Jeon, Young-Chul Noh, Kwang-Hoon Ko, Hee-Jong Moon, Jai-Hyung Lee, Joon-Sung Chang, “Nonlinear propagation of an array of phase singularities through a self-defocusing medium,” Opt. Commun. (to be published).

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Figures (8)

Fig. 1
Fig. 1

(a) Phase distribution in a gray-scale image when a Gaussian beam passes a phase plate having a hyperbolic arc tangent phase shift Φ(y) = 2 tan−1 (y/y0) + π in Eq. (1) with y0 = 0.8, where black and white represent −π and π, respectively. The circle represents the trace of Gaussian beam radius in e−2 intensity. (b) Amplitude distribution in the far-field region obtained by a two-dimensional Fourier transform. The size of the near-field and far-field images is 6 × 6.

Fig. 2
Fig. 2

(a) Phase distribution in a gray scale image when a Gaussian beam passes a phase plate having a hyperbolic arc tangent phase shift Φ(y) = 2 tan−1 (y/y0) + π in Eq. (1) with y0 = 0.01, where black and white represent −π and π, respectively. The circle represents the trace of Gaussian beam radius in e−2 intensity. (b) Amplitude distribution in the far-field region obtained by a two-dimensional Fourier transform. The size of the near-field and far-field images is 6 × 6.

Fig. 3
Fig. 3

(a) Phase distribution in a gray-scale image when a Gaussian beam passes a phase plate having a linear phase shift Φ(y) = π(ay + 1) in Eq. (1) with a = 0.8, where black and white represent −π and π, respectively. The circle represents the trace of Gaussian beam radius in e−2 intensity. (b) Amplitude distribution in the far-field region obtained by a two-dimensional Fourier transform and (c) its intensity profiles across the dark core along the x (horizontal) and y (vertical) axes. The size of the near-field and far-field images is 6 × 6.

Fig. 4
Fig. 4

(a) Phase distribution in a gray-scale image when a pure edge dislocation is bent at a right angle, where black and white represent −π and π, respectively. The circle represents the trace of Gaussian beam radius in e−2 intensity. The first quarter of a Gaussian beam is shifted in phase by π. (b) Amplitude distribution in the far-field region obtained by a two-dimensional Fourier transform. The size of the near-field and far-field images is 6 × 6.

Fig. 5
Fig. 5

Schematic of the experimental arrangement to produce an optical vortex. A curved thin glass platelet with large radius of curvature is used to give linear phase retardation on one half of an input Gaussian beam. Near-field and far-field beam patterns and their interferograms are viewed by two-dimensional charge-coupled devices (CCD’s) and captured by a frame grabber system. The modified phase distribution is sketched in the phase diagram.

Fig. 6
Fig. 6

(a) Near-field intensity distribution and (b) its interferogram. (c) Far-field intensity distribution and (d) its interferogram when a curved glass platelet is adjusted to give the phase variation as shown in Fig. 3(a). (e) Far-field intensity profiles across the dark core along the x (horizontal) and y (vertical) axes. The scale is 0.5 mm for the near-field images and 0.35 mrad for the far-field images.

Fig. 7
Fig. 7

(a) Near-field intensity distribution and (b) its interferogram. (c) Far-field intensity distribution when several phase singularities are given to the input beam by a curved glass platelet. The scale is 2.5 mm for the near-field images and 0.35 mrad for the far-field images.

Fig. 8
Fig. 8

(a) Near-field intensity distribution and (b) its interferogram. (c) Far-field intensity distribution and (d) its interferogram when a rectangular corner of a thin flat glass platelet is used to give the phase variation of a bent edge dislocation as shown in Fig. 2(a). The scale is 2.5 mm for the near-field images and 0.35 mrad for the far-field images.

Equations (3)

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t ( x , y ) = { exp [ i Φ ( y ) ] , x > 0 1 , x < 0 .
E ( ρ , ϕ ) = ρ α sin ( ϕ / 2 ) sin [ ( ϕ - ϕ 0 ) / 2 ] × exp [ - ( ρ 2 / α 2 ) ] exp [ - ( i k ρ 2 / 2 R ) ] ,
E ( ρ , ϕ ) = - ( ρ / 4 α ) { exp [ i ( ϕ - ϕ 0 / 2 ) ] + exp [ - i ( ϕ - ϕ 0 / 2 ) ] - 2 cos ( ϕ 0 / 2 } × exp [ - ( ρ 2 / α 2 ) ] exp [ - ( i k ρ 2 / 2 R ) ] ,

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