Abstract

While a fundamental Gaussian light beam can form stably a spatial soliton in certain self-focusing medium, a single-wave topologically integer-n-charge vortex light beam cannot. It breaks up into 2n filaments due to symmetry breaking and azimuthal instability, in which every azimuthal section of a π phase range from a soliton and repels itself from its azimuthal neighboring soliton. Then what happens to the half-charge vortex light beam, which contains only one section of a π phase range? We investigate experimentally and theoretically the propagation and stability of a topologically half-charge vortex light beam in a self-focusing photorefractive medium. We observed that the light beam propagates unstably in a self-focusing medium and breaks up into three filaments. This result is confirmed by numerical simulation and perturbation analysis.

© 2014 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. T. F. Fric, A. Roshko, “Vortical structure in the wake of a transverse jet,” J. Fluid Mech. 279(-1), 1–47 (1994).
    [CrossRef]
  3. C. N. Weiler, T. W. Neely, D. R. Scherer, A. S. Bradley, M. J. Davis, B. P. Anderson, “Spontaneous vortices in the formation of Bose–Einstein condensates,” Nature 455(7215), 948–951 (2008).
    [CrossRef]
  4. A. Bandyopadhyay, R. P. Singh, “Wigner distribution of elliptical quantum optical vortex,” Opt. Commun. 284(1), 256–261 (2011).
    [CrossRef]
  5. J. Leach, E. Yao, M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
    [CrossRef]
  6. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
    [CrossRef] [PubMed]
  7. N. B. Simpson, K. Dholakia, L. Allen, M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: An optical spanner,” Opt. Lett. 22(1), 52–54 (1997).
    [CrossRef] [PubMed]
  8. Z. X. Wang, N. Zhang, X. C. Yuan, “High-volume optical vortex multiplexing and de-multiplexing for free-space optical communication,” Opt. Express 19(2), 482–492 (2011).
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    [CrossRef] [PubMed]
  11. Z. G. Chen, M. F. Shih, M. Segev, D. W. Wilson, R. E. Muller, P. D. Maker, “Steady-state vortex-screening solitons formed in biased photorefractive media,” Opt. Lett. 22(23), 1751–1753 (1997).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. W. J. Firth, D. V. Skryabin, “Optical solitons carrying orbital angular momentum,” Phys. Rev. Lett. 79(13), 2450–2453 (1997).
    [CrossRef]
  16. C. C. Jeng, M. F. Shih, K. Motzek, Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92(4), 043904 (2004).
    [CrossRef] [PubMed]
  17. S. Y. Chen, T. C. Lo, M. F. Shih, “Stabilization of optical vortices in noninstantaneous self-focusing medium by small rotating intensity modulation,” Opt. Express 15(21), 13689–13694 (2007).
    [CrossRef] [PubMed]
  18. M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6(2), 259–268 (2004).
    [CrossRef]
  19. I. V. Basistiy, V. A. Pas ko, V. V. Slyusar, M. S. Soskin, M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
    [CrossRef]
  20. I. V. Basistiy, M. S. Soskin, M. V. Vasnetsov, “Optical wave-front dislocations and their properties,” Opt. Commun. 119(5-6), 604–612 (1995).
    [CrossRef]
  21. J. B. Götte, S. Franke-Arnold, R. Zambrini, S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54(12), 1723–1738 (2007).
    [CrossRef]
  22. M. A. Molchan, E. V. Doktorov, R. A. Vlasov, “Propagation of fractional charge Laguerre-Gaussian light beams in moving defocusing media with thermal nonlinearity,” J. Opt. A: Pure Appl. Opt. 11(1), 015706 (2009).
    [CrossRef]
  23. M. Segev, M. F. Shih, G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13(4), 706–718 (1996).
    [CrossRef]
  24. B. Crosignani, P. DiPorto, A. Degasperis, M. Segev, S. Trillo, “Three-dimensional optical beam propagation and solitons in photorefractive crystals,” J. Opt. Soc. Am. B 14(11), 3078–3090 (1997).
    [CrossRef]
  25. Notice there is a small difference between the applied nonlinearity strength in the simulation and in the experiment. This is due to the possible imhomogeneity of electro-optic coefficient of the crystal, or not exactly the same light beam sizes in simulation and in experiment.
  26. A. V. Buryak, Y. S. Kivshar, M. F. Shih, M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82(1), 81–84 (1999).
    [CrossRef]
  27. M. F. Shih, M. Segev, G. Salamo, “Three-dimensional spiraling of interacting spatial solitons,” Phys. Rev. Lett. 78(13), 2551–2554 (1997).
    [CrossRef]

2011

2009

M. A. Molchan, E. V. Doktorov, R. A. Vlasov, “Propagation of fractional charge Laguerre-Gaussian light beams in moving defocusing media with thermal nonlinearity,” J. Opt. A: Pure Appl. Opt. 11(1), 015706 (2009).
[CrossRef]

2008

C. N. Weiler, T. W. Neely, D. R. Scherer, A. S. Bradley, M. J. Davis, B. P. Anderson, “Spontaneous vortices in the formation of Bose–Einstein condensates,” Nature 455(7215), 948–951 (2008).
[CrossRef]

2007

2005

2004

J. Leach, E. Yao, M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[CrossRef]

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6(2), 259–268 (2004).
[CrossRef]

I. V. Basistiy, V. A. Pas ko, V. V. Slyusar, M. S. Soskin, M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
[CrossRef]

C. C. Jeng, M. F. Shih, K. Motzek, Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92(4), 043904 (2004).
[CrossRef] [PubMed]

1999

A. V. Buryak, Y. S. Kivshar, M. F. Shih, M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82(1), 81–84 (1999).
[CrossRef]

1998

1997

1996

1995

1994

A. I. Larkin, V. M. Vinokur, “Quantum statistical mechanics of vortices in high-temperature superconductors,” Phys. Rev. B Condens. Matter 50(14), 10272–10286 (1994).
[CrossRef] [PubMed]

T. F. Fric, A. Roshko, “Vortical structure in the wake of a transverse jet,” J. Fluid Mech. 279(-1), 1–47 (1994).
[CrossRef]

1992

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

G. A. Swartzlander, C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69(17), 2503–2506 (1992).
[CrossRef] [PubMed]

Allen, L.

N. B. Simpson, K. Dholakia, L. Allen, M. J. Padgett, “Mechanical equivalence of spin and orbital angular momentum of light: An optical spanner,” Opt. Lett. 22(1), 52–54 (1997).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Anderson, B. P.

C. N. Weiler, T. W. Neely, D. R. Scherer, A. S. Bradley, M. J. Davis, B. P. Anderson, “Spontaneous vortices in the formation of Bose–Einstein condensates,” Nature 455(7215), 948–951 (2008).
[CrossRef]

Bandyopadhyay, A.

A. Bandyopadhyay, R. P. Singh, “Wigner distribution of elliptical quantum optical vortex,” Opt. Commun. 284(1), 256–261 (2011).
[CrossRef]

Barnett, S. M.

J. B. Götte, S. Franke-Arnold, R. Zambrini, S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54(12), 1723–1738 (2007).
[CrossRef]

Basistiy, I. V.

I. V. Basistiy, V. A. Pas ko, V. V. Slyusar, M. S. Soskin, M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
[CrossRef]

I. V. Basistiy, M. S. Soskin, M. V. Vasnetsov, “Optical wave-front dislocations and their properties,” Opt. Commun. 119(5-6), 604–612 (1995).
[CrossRef]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Bernet, S.

Berry, M. V.

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6(2), 259–268 (2004).
[CrossRef]

Bradley, A. S.

C. N. Weiler, T. W. Neely, D. R. Scherer, A. S. Bradley, M. J. Davis, B. P. Anderson, “Spontaneous vortices in the formation of Bose–Einstein condensates,” Nature 455(7215), 948–951 (2008).
[CrossRef]

Buryak, A. V.

A. V. Buryak, Y. S. Kivshar, M. F. Shih, M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82(1), 81–84 (1999).
[CrossRef]

Chen, S. Y.

Chen, Z. G.

Christou, J.

Crosignani, B.

Davis, M. J.

C. N. Weiler, T. W. Neely, D. R. Scherer, A. S. Bradley, M. J. Davis, B. P. Anderson, “Spontaneous vortices in the formation of Bose–Einstein condensates,” Nature 455(7215), 948–951 (2008).
[CrossRef]

Degasperis, A.

Dholakia, K.

DiPorto, P.

Doktorov, E. V.

M. A. Molchan, E. V. Doktorov, R. A. Vlasov, “Propagation of fractional charge Laguerre-Gaussian light beams in moving defocusing media with thermal nonlinearity,” J. Opt. A: Pure Appl. Opt. 11(1), 015706 (2009).
[CrossRef]

Firth, W. J.

W. J. Firth, D. V. Skryabin, “Optical solitons carrying orbital angular momentum,” Phys. Rev. Lett. 79(13), 2450–2453 (1997).
[CrossRef]

Franke-Arnold, S.

J. B. Götte, S. Franke-Arnold, R. Zambrini, S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54(12), 1723–1738 (2007).
[CrossRef]

Fric, T. F.

T. F. Fric, A. Roshko, “Vortical structure in the wake of a transverse jet,” J. Fluid Mech. 279(-1), 1–47 (1994).
[CrossRef]

Fürhapter, S.

Götte, J. B.

J. B. Götte, S. Franke-Arnold, R. Zambrini, S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54(12), 1723–1738 (2007).
[CrossRef]

Jeng, C. C.

C. C. Jeng, M. F. Shih, K. Motzek, Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92(4), 043904 (2004).
[CrossRef] [PubMed]

Jesacher, A.

Kartashov, Y. V.

Kivshar, Y.

C. C. Jeng, M. F. Shih, K. Motzek, Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92(4), 043904 (2004).
[CrossRef] [PubMed]

Kivshar, Y. S.

A. V. Buryak, Y. S. Kivshar, M. F. Shih, M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82(1), 81–84 (1999).
[CrossRef]

Larkin, A. I.

A. I. Larkin, V. M. Vinokur, “Quantum statistical mechanics of vortices in high-temperature superconductors,” Phys. Rev. B Condens. Matter 50(14), 10272–10286 (1994).
[CrossRef] [PubMed]

Law, C. T.

G. A. Swartzlander, C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69(17), 2503–2506 (1992).
[CrossRef] [PubMed]

Leach, J.

J. Leach, E. Yao, M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[CrossRef]

Lo, T. C.

Lutherdaves, B.

Maker, P. D.

Molchan, M. A.

M. A. Molchan, E. V. Doktorov, R. A. Vlasov, “Propagation of fractional charge Laguerre-Gaussian light beams in moving defocusing media with thermal nonlinearity,” J. Opt. A: Pure Appl. Opt. 11(1), 015706 (2009).
[CrossRef]

Motzek, K.

C. C. Jeng, M. F. Shih, K. Motzek, Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92(4), 043904 (2004).
[CrossRef] [PubMed]

Muller, R. E.

Neely, T. W.

C. N. Weiler, T. W. Neely, D. R. Scherer, A. S. Bradley, M. J. Davis, B. P. Anderson, “Spontaneous vortices in the formation of Bose–Einstein condensates,” Nature 455(7215), 948–951 (2008).
[CrossRef]

Padgett, M. J.

Pas ko, V. A.

I. V. Basistiy, V. A. Pas ko, V. V. Slyusar, M. S. Soskin, M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
[CrossRef]

Petrov, D. V.

Ritsch-Marte, M.

Roshko, A.

T. F. Fric, A. Roshko, “Vortical structure in the wake of a transverse jet,” J. Fluid Mech. 279(-1), 1–47 (1994).
[CrossRef]

Salamo, G.

M. F. Shih, M. Segev, G. Salamo, “Three-dimensional spiraling of interacting spatial solitons,” Phys. Rev. Lett. 78(13), 2551–2554 (1997).
[CrossRef]

Scherer, D. R.

C. N. Weiler, T. W. Neely, D. R. Scherer, A. S. Bradley, M. J. Davis, B. P. Anderson, “Spontaneous vortices in the formation of Bose–Einstein condensates,” Nature 455(7215), 948–951 (2008).
[CrossRef]

Segev, M.

Shih, M. F.

S. Y. Chen, T. C. Lo, M. F. Shih, “Stabilization of optical vortices in noninstantaneous self-focusing medium by small rotating intensity modulation,” Opt. Express 15(21), 13689–13694 (2007).
[CrossRef] [PubMed]

C. C. Jeng, M. F. Shih, K. Motzek, Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92(4), 043904 (2004).
[CrossRef] [PubMed]

A. V. Buryak, Y. S. Kivshar, M. F. Shih, M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82(1), 81–84 (1999).
[CrossRef]

M. F. Shih, M. Segev, G. Salamo, “Three-dimensional spiraling of interacting spatial solitons,” Phys. Rev. Lett. 78(13), 2551–2554 (1997).
[CrossRef]

Z. G. Chen, M. F. Shih, M. Segev, D. W. Wilson, R. E. Muller, P. D. Maker, “Steady-state vortex-screening solitons formed in biased photorefractive media,” Opt. Lett. 22(23), 1751–1753 (1997).
[CrossRef] [PubMed]

M. Segev, M. F. Shih, G. C. Valley, “Photorefractive screening solitons of high and low intensity,” J. Opt. Soc. Am. B 13(4), 706–718 (1996).
[CrossRef]

Simpson, N. B.

Singh, R. P.

A. Bandyopadhyay, R. P. Singh, “Wigner distribution of elliptical quantum optical vortex,” Opt. Commun. 284(1), 256–261 (2011).
[CrossRef]

Skryabin, D. V.

W. J. Firth, D. V. Skryabin, “Optical solitons carrying orbital angular momentum,” Phys. Rev. Lett. 79(13), 2450–2453 (1997).
[CrossRef]

Slyusar, V. V.

I. V. Basistiy, V. A. Pas ko, V. V. Slyusar, M. S. Soskin, M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
[CrossRef]

Soskin, M. S.

I. V. Basistiy, V. A. Pas ko, V. V. Slyusar, M. S. Soskin, M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
[CrossRef]

I. V. Basistiy, M. S. Soskin, M. V. Vasnetsov, “Optical wave-front dislocations and their properties,” Opt. Commun. 119(5-6), 604–612 (1995).
[CrossRef]

Soto-Crespo, J. M.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Swartzlander, G. A.

G. A. Swartzlander, C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69(17), 2503–2506 (1992).
[CrossRef] [PubMed]

Tikhonenko, V.

Torner, L.

Torres, J. P.

Trillo, S.

Valley, G. C.

Vasnetsov, M. V.

I. V. Basistiy, V. A. Pas ko, V. V. Slyusar, M. S. Soskin, M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
[CrossRef]

I. V. Basistiy, M. S. Soskin, M. V. Vasnetsov, “Optical wave-front dislocations and their properties,” Opt. Commun. 119(5-6), 604–612 (1995).
[CrossRef]

Vinokur, V. M.

A. I. Larkin, V. M. Vinokur, “Quantum statistical mechanics of vortices in high-temperature superconductors,” Phys. Rev. B Condens. Matter 50(14), 10272–10286 (1994).
[CrossRef] [PubMed]

Vlasov, R. A.

M. A. Molchan, E. V. Doktorov, R. A. Vlasov, “Propagation of fractional charge Laguerre-Gaussian light beams in moving defocusing media with thermal nonlinearity,” J. Opt. A: Pure Appl. Opt. 11(1), 015706 (2009).
[CrossRef]

Vysloukh, V. A.

Wang, Z. X.

Weiler, C. N.

C. N. Weiler, T. W. Neely, D. R. Scherer, A. S. Bradley, M. J. Davis, B. P. Anderson, “Spontaneous vortices in the formation of Bose–Einstein condensates,” Nature 455(7215), 948–951 (2008).
[CrossRef]

Wilson, D. W.

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Yao, E.

J. Leach, E. Yao, M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[CrossRef]

Yuan, X. C.

Zambrini, R.

J. B. Götte, S. Franke-Arnold, R. Zambrini, S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54(12), 1723–1738 (2007).
[CrossRef]

Zhang, N.

J. Fluid Mech.

T. F. Fric, A. Roshko, “Vortical structure in the wake of a transverse jet,” J. Fluid Mech. 279(-1), 1–47 (1994).
[CrossRef]

J. Mod. Opt.

J. B. Götte, S. Franke-Arnold, R. Zambrini, S. M. Barnett, “Quantum formulation of fractional orbital angular momentum,” J. Mod. Opt. 54(12), 1723–1738 (2007).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

I. V. Basistiy, V. A. Pas ko, V. V. Slyusar, M. S. Soskin, M. V. Vasnetsov, “Synthesis and analysis of optical vortices with fractional topological charges,” J. Opt. A, Pure Appl. Opt. 6(5), S166–S169 (2004).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

M. A. Molchan, E. V. Doktorov, R. A. Vlasov, “Propagation of fractional charge Laguerre-Gaussian light beams in moving defocusing media with thermal nonlinearity,” J. Opt. A: Pure Appl. Opt. 11(1), 015706 (2009).
[CrossRef]

M. V. Berry, “Optical vortices evolving from helicoidal integer and fractional phase steps,” J. Opt. A: Pure Appl. Opt. 6(2), 259–268 (2004).
[CrossRef]

J. Opt. Soc. Am. B

Nature

C. N. Weiler, T. W. Neely, D. R. Scherer, A. S. Bradley, M. J. Davis, B. P. Anderson, “Spontaneous vortices in the formation of Bose–Einstein condensates,” Nature 455(7215), 948–951 (2008).
[CrossRef]

New J. Phys.

J. Leach, E. Yao, M. J. Padgett, “Observation of the vortex structure of a non-integer vortex beam,” New J. Phys. 6, 71 (2004).
[CrossRef]

Opt. Commun.

A. Bandyopadhyay, R. P. Singh, “Wigner distribution of elliptical quantum optical vortex,” Opt. Commun. 284(1), 256–261 (2011).
[CrossRef]

I. V. Basistiy, M. S. Soskin, M. V. Vasnetsov, “Optical wave-front dislocations and their properties,” Opt. Commun. 119(5-6), 604–612 (1995).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Phys. Rev. B Condens. Matter

A. I. Larkin, V. M. Vinokur, “Quantum statistical mechanics of vortices in high-temperature superconductors,” Phys. Rev. B Condens. Matter 50(14), 10272–10286 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett.

G. A. Swartzlander, C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69(17), 2503–2506 (1992).
[CrossRef] [PubMed]

W. J. Firth, D. V. Skryabin, “Optical solitons carrying orbital angular momentum,” Phys. Rev. Lett. 79(13), 2450–2453 (1997).
[CrossRef]

C. C. Jeng, M. F. Shih, K. Motzek, Y. Kivshar, “Partially incoherent optical vortices in self-focusing nonlinear media,” Phys. Rev. Lett. 92(4), 043904 (2004).
[CrossRef] [PubMed]

A. V. Buryak, Y. S. Kivshar, M. F. Shih, M. Segev, “Induced coherence and stable soliton spiraling,” Phys. Rev. Lett. 82(1), 81–84 (1999).
[CrossRef]

M. F. Shih, M. Segev, G. Salamo, “Three-dimensional spiraling of interacting spatial solitons,” Phys. Rev. Lett. 78(13), 2551–2554 (1997).
[CrossRef]

Other

Notice there is a small difference between the applied nonlinearity strength in the simulation and in the experiment. This is due to the possible imhomogeneity of electro-optic coefficient of the crystal, or not exactly the same light beam sizes in simulation and in experiment.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup

Fig. 2
Fig. 2

The half-charge vortex light beam: (a) shows the intensity at the input face, (b) at the output face, (c) shows the interference at the output face without nonlinearity, (d) and (e) are intensity and interference images at the output face with a biasing voltage 2.1 kV.

Fig. 3
Fig. 3

Computer simulation results: (a)(e) are intensity and interference images at the input face; (b)(f) are intensity and interference images at the output face without nonlinearity, (c)(g) are intensity and interference images at the output face with nonlinearity 3.0 × 10−4. (d) is 3D plot of (c) and (h) shows the phase structure.

Fig. 4
Fig. 4

Normalized amplitudes of different azimuthal modes in the self-focusing photorefractive medium; Inset: field difference between perturbed vortex beam and unperturbed original beam.

Fig. 5
Fig. 5

Half-charge vortex light beam: Upper row are experimental intensity images (a) at the input face of the crystal and at the output face with the biasing voltage (b) at zero and (c) 2.85 kV. Lower row are simulation result (d) at the input face of the crystal and at the output face (e) without nonlinearity and (f) with nonlinearity 9.0 × 10−4. The light beam breaks up into three after 3 mm of propagation (g).

Equations (2)

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u α ( r )= A 0 exp( r 2 w 0 2 ) exp{ i( z+πα ) }sin(πα) π exp( inϕ ) P n ( ρ ) αn
( i ζ + 2 )u= 1 1+ | u | 2 ( 1+ 1 2 ln( 1+ | u | 2 ) )u+ u 2π 1 1+ | u | 2 dρdθ ρ cos( 2θ ) ln( 1+ | u( ξ+ρcos(θ),η+ρsin(θ) ) | 2 )

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