Abstract

We report the observation of optical vortices in a laser beam propagating through the stripe pattern of a cholesteric liquid crystal. The liquid crystal is confined in a cell with homogeneous boundary conditions and forms a diffraction phase grating. Optical vortices are produced by edge dislocations of the cholesteric grating. The vortices show up as spots of zero light intensity in the diffraction maxima. There is one spot in each +1 and -1 diffraction maximum and two spots in diffraction maxima +2 and -2.

© 2000 Optical Society of America

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References

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  1. I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
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    [CrossRef]
  4. G.-H. Kim, J.-H. Jeon, K.-H. Ko, H.-J. Moon, J.-H. Lee, and J.-S. Chang, Appl. Opt. 36, 8614 (1997).
    [CrossRef]
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    [CrossRef]
  6. P.-Y. Wang, M. Ye, J.-H. Dai, and H.-J. Zhang, Mol. Cryst. Liq. Cryst. 261, 143 (1995).
    [CrossRef]
  7. D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
    [CrossRef]
  8. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, 951 (1992).
    [CrossRef]
  9. M. Kleman, Points, Lines and Walls in Liquid Crystals, Magnetic Systems and Various Media (Wiley, New York, 1983).
  10. D. Subacius, S. Shiyanovskii, P. Bos, and O. Lavrentovich, Appl. Phys. Lett. 71, 3323 (1997).
    [CrossRef]
  11. P. G. de Gennes, Mol. Cryst. Liq. Cryst. 7, 325 (1969).

1997 (3)

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

D. Subacius, S. Shiyanovskii, P. Bos, and O. Lavrentovich, Appl. Phys. Lett. 71, 3323 (1997).
[CrossRef]

G.-H. Kim, J.-H. Jeon, K.-H. Ko, H.-J. Moon, J.-H. Lee, and J.-S. Chang, Appl. Opt. 36, 8614 (1997).
[CrossRef]

1996 (1)

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 465 (1996).
[CrossRef]

1995 (1)

P.-Y. Wang, M. Ye, J.-H. Dai, and H.-J. Zhang, Mol. Cryst. Liq. Cryst. 261, 143 (1995).
[CrossRef]

1994 (1)

M. W. Beijersbergen, R. Coerwinkel, M. Kristensen, and L. P. Werdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

1993 (1)

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

1992 (1)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, 951 (1992).
[CrossRef]

1990 (1)

1969 (1)

P. G. de Gennes, Mol. Cryst. Liq. Cryst. 7, 325 (1969).

Basistiy, I. V.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Bazhenov, V. Yu.

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, R. Coerwinkel, M. Kristensen, and L. P. Werdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Bos, P.

D. Subacius, S. Shiyanovskii, P. Bos, and O. Lavrentovich, Appl. Phys. Lett. 71, 3323 (1997).
[CrossRef]

Chang, J.-S.

Coerwinkel, R.

M. W. Beijersbergen, R. Coerwinkel, M. Kristensen, and L. P. Werdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Dai, J.-H.

P.-Y. Wang, M. Ye, J.-H. Dai, and H.-J. Zhang, Mol. Cryst. Liq. Cryst. 261, 143 (1995).
[CrossRef]

de Gennes, P. G.

P. G. de Gennes, Mol. Cryst. Liq. Cryst. 7, 325 (1969).

Heckenberg, N. R.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, 951 (1992).
[CrossRef]

Ilyenkov, A. V.

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 465 (1996).
[CrossRef]

Jeon, J.-H.

Khizhnyak, A. I.

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 465 (1996).
[CrossRef]

Kim, G.-H.

Kleman, M.

M. Kleman, Points, Lines and Walls in Liquid Crystals, Magnetic Systems and Various Media (Wiley, New York, 1983).

Ko, K.-H.

Kreminskaya, L. V.

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 465 (1996).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. Coerwinkel, M. Kristensen, and L. P. Werdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Lavrentovich, O.

D. Subacius, S. Shiyanovskii, P. Bos, and O. Lavrentovich, Appl. Phys. Lett. 71, 3323 (1997).
[CrossRef]

Lee, J.-H.

McDuff, R.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, 951 (1992).
[CrossRef]

Moon, H.-J.

Rozas, D.

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

Rubinstein-Dunlop, H.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, 951 (1992).
[CrossRef]

Sacks, Z. S.

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

Shiyanovskii, S.

D. Subacius, S. Shiyanovskii, P. Bos, and O. Lavrentovich, Appl. Phys. Lett. 71, 3323 (1997).
[CrossRef]

Smith, C. P.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, 951 (1992).
[CrossRef]

Soskin, M. S.

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 465 (1996).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Subacius, D.

D. Subacius, S. Shiyanovskii, P. Bos, and O. Lavrentovich, Appl. Phys. Lett. 71, 3323 (1997).
[CrossRef]

Swartzlander, G. A.

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

Tamm, C.

Vasnetsov, M. V.

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 465 (1996).
[CrossRef]

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

Wang, P.-Y.

P.-Y. Wang, M. Ye, J.-H. Dai, and H.-J. Zhang, Mol. Cryst. Liq. Cryst. 261, 143 (1995).
[CrossRef]

Wegener, M. J.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, 951 (1992).
[CrossRef]

Weiss, C. O.

Werdman, L. P.

M. W. Beijersbergen, R. Coerwinkel, M. Kristensen, and L. P. Werdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Ye, M.

P.-Y. Wang, M. Ye, J.-H. Dai, and H.-J. Zhang, Mol. Cryst. Liq. Cryst. 261, 143 (1995).
[CrossRef]

Zhang, H.-J.

P.-Y. Wang, M. Ye, J.-H. Dai, and H.-J. Zhang, Mol. Cryst. Liq. Cryst. 261, 143 (1995).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, Appl. Phys. B 62, 465 (1996).
[CrossRef]

Appl. Phys. Lett. (1)

D. Subacius, S. Shiyanovskii, P. Bos, and O. Lavrentovich, Appl. Phys. Lett. 71, 3323 (1997).
[CrossRef]

J. Opt. Soc. Am. B (1)

Mol. Cryst. Liq. Cryst. (2)

P. G. de Gennes, Mol. Cryst. Liq. Cryst. 7, 325 (1969).

P.-Y. Wang, M. Ye, J.-H. Dai, and H.-J. Zhang, Mol. Cryst. Liq. Cryst. 261, 143 (1995).
[CrossRef]

Opt. Commun. (2)

I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 103, 422 (1993).
[CrossRef]

M. W. Beijersbergen, R. Coerwinkel, M. Kristensen, and L. P. Werdman, Opt. Commun. 112, 321 (1994).
[CrossRef]

Opt. Quantum Electron. (1)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinstein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, 951 (1992).
[CrossRef]

Phys. Rev. Lett. (1)

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Phys. Rev. Lett. 79, 3399 (1997).
[CrossRef]

Other (1)

M. Kleman, Points, Lines and Walls in Liquid Crystals, Magnetic Systems and Various Media (Wiley, New York, 1983).

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Figures (4)

Fig. 1
Fig. 1

Fluorescent confocal microscope images of the edge dislocation in a cholesteric grating: (a) in the plane of the cell, (b)–(d) perpendicular to the plane of the cell.

Fig. 2
Fig. 2

Edge dislocation generated by Eq. (2).

Fig. 3
Fig. 3

Experimental diffraction patterns in the far-field zone: (a) 0, +1, +2 diffraction orders; (b) -1, 0, +1 diffraction orders.

Fig. 4
Fig. 4

Computer-generated diffraction pattern in the far-field zone with 0, ±1, and ±2 diffraction orders.

Equations (3)

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

nx=cos θy,  ny=0,  nz=sin θy,  θy=q0y+const.,
nˆ=cos φ,0,sin φ,  φ=s2 tan-12yx+q0y+const.
E˜ξ,η= exp-ikz+ξx+ηy×expi2πλnenozno2 sin2βx,y+ne2 cos2βx,y-1/2dxdy,

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