Abstract

Influence of the anisotropic tensorial electro-optic effect of LiNbO 3:Fe photorefractive defocusing medium on propagation of a vortex beam is numerically and experimentally investigated. Characteristic behaviors are depicted by varying light polarization, sign of vortex angular momentum and propagation directions.

© 2008 Optical Society of America

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References

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  1. A. S. Desyatnikov, YuS.  Kivshar, and L. Torner, "Optical vortices and Vortex Solitons" in Progress in Optics, E. Wolf, ed., (Elsevier, Amsterdam, 2005) Vol. 47.
  2. Z. Jaroszewicz and A. Kolodziejczyk, "Zone plates performing generalized Hankel transforms and their metrological applications," Opt. Commun. 102, 391-396 (1993).
    [CrossRef]
  3. 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]
  4. 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]
  5. S. Minardi, G. Molina-Terriza, P. Di Trapani, J. P. Torres, and L. Torner, "Soliton algebra by vortex-beam splitting," Opt. Lett. 26, 1004-1006 (2001).
    [CrossRef]
  6. A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
    [CrossRef]
  7. Z. Chen, M. Feng Shih, M. Segev, D. W. Wilson, R. Muller, and P. D. Maker, "Steady-state vortex-screening solitons formed in biased photorefractive media," Opt. Lett. 22, 1751-1753 (1997).
    [CrossRef]
  8. M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
    [CrossRef] [PubMed]
  9. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, "Steady-State Spatial Screening Solitons in Photorefractive Materials with External Applied Field, " Phys. Rev. Lett. 73, 3211 - 3214 (1994).
    [CrossRef] [PubMed]
  10. A. V. Mamaev, M. Saffman, and A. A. Zozulya, "Time-dependent evolution of an optical vortex in photorefractive media," Phys. Rev. A 56, 1713-1716 (1997).
    [CrossRef]
  11. 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]
  12. I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, "Optical wavefront dislocations and their properties," Opt. Commun. 119, 604-612 (1995).
    [CrossRef]
  13. V. L. Vinetskii and N. V. Kukhtarev, "Wave front convolution in 4-wave interaction inmedia with nonlocal nonlinearity," Sovi. Phys. JETP Letters 30, 6 (1979).
  14. P. Yeh, Introduction to photorefractive nonlinear optics (Wiley-Interscience, New York, 1993).
  15. M. Simon, S. Wevering, K. Buse and E. Kratzig,"The bulk photovoltaic effect of photorefractive LiNbO3:Fe crystals at high light intensities," J. Phys. D 30, 144-149 (1997).
    [CrossRef]

2001 (1)

1999 (1)

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
[CrossRef]

1997 (3)

Z. Chen, M. Feng Shih, M. Segev, D. W. Wilson, R. Muller, and P. D. Maker, "Steady-state vortex-screening solitons formed in biased photorefractive media," Opt. Lett. 22, 1751-1753 (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, 1713-1716 (1997).
[CrossRef]

M. Simon, S. Wevering, K. Buse and E. Kratzig,"The bulk photovoltaic effect of photorefractive LiNbO3:Fe crystals at high light intensities," J. Phys. D 30, 144-149 (1997).
[CrossRef]

1996 (1)

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]

1995 (3)

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]

1994 (1)

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, "Steady-State Spatial Screening Solitons in Photorefractive Materials with External Applied Field, " Phys. Rev. Lett. 73, 3211 - 3214 (1994).
[CrossRef] [PubMed]

1993 (1)

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

1992 (1)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[CrossRef] [PubMed]

1979 (1)

V. L. Vinetskii and N. V. Kukhtarev, "Wave front convolution in 4-wave interaction inmedia with nonlocal nonlinearity," Sovi. Phys. JETP Letters 30, 6 (1979).

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]

Buse, K.

M. Simon, S. Wevering, K. Buse and E. Kratzig,"The bulk photovoltaic effect of photorefractive LiNbO3:Fe crystals at high light intensities," J. Phys. D 30, 144-149 (1997).
[CrossRef]

Chen, Z.

Crosignani, B.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, "Steady-State Spatial Screening Solitons in Photorefractive Materials with External Applied Field, " Phys. Rev. Lett. 73, 3211 - 3214 (1994).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[CrossRef] [PubMed]

Di Trapani, P.

DiPorto, P.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, "Steady-State Spatial Screening Solitons in Photorefractive Materials with External Applied Field, " Phys. Rev. Lett. 73, 3211 - 3214 (1994).
[CrossRef] [PubMed]

Dreischuh, A.

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
[CrossRef]

Feng Shih, M.

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[CrossRef] [PubMed]

Friese, M. E. J.

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]

Grasbon, F.

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
[CrossRef]

He, H.

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]

Heckenberg, N. R.

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]

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]

Jaroszewicz, Z.

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

Kolodziejczyk, A.

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

Kratzig, E.

M. Simon, S. Wevering, K. Buse and E. Kratzig,"The bulk photovoltaic effect of photorefractive LiNbO3:Fe crystals at high light intensities," J. Phys. D 30, 144-149 (1997).
[CrossRef]

Kukhtarev, N. V.

V. L. Vinetskii and N. V. Kukhtarev, "Wave front convolution in 4-wave interaction inmedia with nonlocal nonlinearity," Sovi. Phys. JETP Letters 30, 6 (1979).

Maker, P. D.

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, "Time-dependent evolution of an optical vortex in photorefractive media," Phys. Rev. A 56, 1713-1716 (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]

Minardi, S.

Molina-Terriza, G.

Muller, R.

Paulus, G. G.

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
[CrossRef]

Rubinsztein-Dunlop, H.

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]

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]

Saffman, M.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, "Time-dependent evolution of an optical vortex in photorefractive media," Phys. Rev. A 56, 1713-1716 (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]

Segev, M.

Z. Chen, M. Feng Shih, M. Segev, D. W. Wilson, R. Muller, and P. D. Maker, "Steady-state vortex-screening solitons formed in biased photorefractive media," Opt. Lett. 22, 1751-1753 (1997).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, "Steady-State Spatial Screening Solitons in Photorefractive Materials with External Applied Field, " Phys. Rev. Lett. 73, 3211 - 3214 (1994).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[CrossRef] [PubMed]

Simon, M.

M. Simon, S. Wevering, K. Buse and E. Kratzig,"The bulk photovoltaic effect of photorefractive LiNbO3:Fe crystals at high light intensities," J. Phys. D 30, 144-149 (1997).
[CrossRef]

Soskin, M. S.

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

Torner, L.

Torres, J. P.

Valley, G. C.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, "Steady-State Spatial Screening Solitons in Photorefractive Materials with External Applied Field, " Phys. Rev. Lett. 73, 3211 - 3214 (1994).
[CrossRef] [PubMed]

Vasnetsov, M. V.

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

Vinetskii, V. L.

V. L. Vinetskii and N. V. Kukhtarev, "Wave front convolution in 4-wave interaction inmedia with nonlocal nonlinearity," Sovi. Phys. JETP Letters 30, 6 (1979).

Walther, H.

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
[CrossRef]

Wevering, S.

M. Simon, S. Wevering, K. Buse and E. Kratzig,"The bulk photovoltaic effect of photorefractive LiNbO3:Fe crystals at high light intensities," J. Phys. D 30, 144-149 (1997).
[CrossRef]

Wilson, D. W.

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, "Steady-State Spatial Screening Solitons in Photorefractive Materials with External Applied Field, " Phys. Rev. Lett. 73, 3211 - 3214 (1994).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[CrossRef] [PubMed]

Zacher, F.

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
[CrossRef]

Zozulya, A. A.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, "Time-dependent evolution of an optical vortex in photorefractive media," Phys. Rev. A 56, 1713-1716 (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]

J. Mod. Opt. (1)

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]

J. Phys. D (1)

M. Simon, S. Wevering, K. Buse and E. Kratzig,"The bulk photovoltaic effect of photorefractive LiNbO3:Fe crystals at high light intensities," J. Phys. D 30, 144-149 (1997).
[CrossRef]

Opt. Commun. (2)

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

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

Opt. Lett. (2)

Phys. Rev. A (1)

A. V. Mamaev, M. Saffman, and A. A. Zozulya, "Time-dependent evolution of an optical vortex in photorefractive media," Phys. Rev. A 56, 1713-1716 (1997).
[CrossRef]

Phys. Rev. E (1)

A. Dreischuh, G. G. Paulus, F. Zacher, F. Grasbon, and H. Walther, "Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium," Phys. Rev. E 60, 6111-6117 (1999).
[CrossRef]

Phys. Rev. Lett. (4)

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]

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]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, "Spatial solitons in photorefractive media," Phys. Rev. Lett. 68, 923-926 (1992).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, "Steady-State Spatial Screening Solitons in Photorefractive Materials with External Applied Field, " Phys. Rev. Lett. 73, 3211 - 3214 (1994).
[CrossRef] [PubMed]

Sovi. Phys. JETP Letters (1)

V. L. Vinetskii and N. V. Kukhtarev, "Wave front convolution in 4-wave interaction inmedia with nonlocal nonlinearity," Sovi. Phys. JETP Letters 30, 6 (1979).

Other (2)

P. Yeh, Introduction to photorefractive nonlinear optics (Wiley-Interscience, New York, 1993).

A. S. Desyatnikov, YuS.  Kivshar, and L. Torner, "Optical vortices and Vortex Solitons" in Progress in Optics, E. Wolf, ed., (Elsevier, Amsterdam, 2005) Vol. 47.

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Figures (7)

Fig. 1.
Fig. 1.

Numerical results : Vortex intensity distribution at the crystal input (a) and output (b) in linear regime.

Fig. 2.
Fig. 2.

Numerical results : Vortex intensity distribution at the crystal output for extraordinary polarization with topological charges m=+1 (a) and m=-1 (b) and corresponding refractive index modulations (c, d). Arrows indicate sense of rotation of light.

Fig. 3.
Fig. 3.

Vortex intensity for ordinary polarization and propagation along X-axis: charge m=+1 (a) and m=-1 (c) and corresponding refractive index modulations (b, d).

Fig. 4.
Fig. 4.

Vortex intensity for ordinary polarization and propagation along Y-axis: charge m=+1 (a) and m=-1 (c) and corresponding refractive index modulations (b, d).

Fig. 5.
Fig. 5.

Experimental setup.

Fig. 6.
Fig. 6.

Experimental results : Vortex intensity distribution at the input (a) and at the output (b) before nonlinearity occurs. The insert shows the interferogram of the vortex. Vortex intensity distribution for extraordinary polarization at the output of a 9mm long LiNbO 3:Fe sample for topological charges m=+1 (c) and m=-1 (d) at t=1000 s for propagation along X axis.

Fig. 7.
Fig. 7.

Experimental vortex intensity for charges m=1 (a, b) and m=-1 (c, d) for ordinary polarization and for propagation along Y axis (a, c) and X axis (b, d).

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

U em ( r ) = A ( r , z ) exp ( i ( ω t kz ) ) exp ( im θ )
N D + t = s ( I + I d ) ( N D N D + ) γ N e N D +
· { [ ε ] E } = ρ
ρ = e ( N D + N A N e )
J = e μ N e E + μ k B T N e + β ph ( N D N D + ) I c
ρ t = · J .
N ˜ e = ξ ( I + I d ) ( N ˜ D N ˜ D + ) N ˜ D +
ρ ˜ t = μ { [ N ˜ e ] · E + N ˜ e · E + k B T e Δ N ˜ e
+ ξ E ph [ ( N ˜ D N ˜ D + ) I ] c }
E ( r ) = 1 4 π [ ε ] V ρ ( r ) r r r r 3 d V
Δ n Y 1 2 n o 3 ( r 22 E Y + r 13 E Z )
Δ n Z 1 2 n e 3 r 33 E Z
Δ n X 1 2 n o 3 r 13 E Z

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