Abstract

Liquid-crystal spiral phase plates with cell gaps of 7 and 20 μm have been used to generate doughnut-shaped beams (doughnut beams) with charges of 1 and 4, respectively. Stacking these liquid-crystal spiral phase plates yielded doughnut beams with charge numbers up to 8. High efficiency and flexibility are the advantages of generating doughnut beams by stacking liquid-crystal spiral phase plates. Interference of doughnut beams generated by liquid-crystal spiral phase plates and plane waves has been studied. Fingerlike interference patterns were obtained with a doughnut beam tilted from a Gaussian beam; spiral fanlike patterns were obtained with a doughnut beam and a Gaussian beam collimated coaxially. The experimental results are supported qualitatively by simulation. By rotating a glass slide in the path of the Gaussian beam, one can rotate the fanlike interference pattern in a controlled fashion. With the liquid-crystal display technology that we have developed and report here, these liquid-crystal spiral phase plates should find applications in optical tweezers.

© 2004 Optical Society of America

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References

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  1. 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, 8185–8189 (1992).
    [CrossRef] [PubMed]
  2. K. T. Gahagan, G. A. Swartzlander, “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996).
    [CrossRef] [PubMed]
  3. 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, 52–54 (1997).
    [CrossRef] [PubMed]
  4. L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
    [CrossRef] [PubMed]
  5. X. Xu, K. Kim, W. Jhe, N. Kwon, “Efficient optical guiding of trapped cold atoms by a hollow laser beam,” Phys. Rev. A 63, 340114 (2001).
    [CrossRef]
  6. 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]
  7. J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
    [CrossRef]
  8. M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
    [CrossRef]
  9. 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]
  10. N. R. Heckenberg, R. G. Mcduff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
    [CrossRef] [PubMed]
  11. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
    [CrossRef]
  12. K. Ganic, X. Gan, M. Gu, M. Hain, S. Somalingam, S. Stankovic, T. Tschudi, “Generation of doughnut laser beams by use of a liquid-crystal cell with a conversion efficiency near 100%,” Opt. Lett. 27, 1351–1353 (2002).
    [CrossRef]
  13. M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
    [CrossRef]
  14. S. Orlov, K. Regelskis, V. Smilgevicius, A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
    [CrossRef]
  15. Y. L. Zhang, P. J. Bos, D. B. Chung, “2-D modeling of the effect of electrode topography and interpixel gap on LCoS devices,” in Society for Information Display, International Symposium Digest of Technical Papers (Society for Information Display, San Jose, Calif., 2003), Vol. XXXIV, pp. 1382–1385.
    [CrossRef]

2002

2001

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

X. Xu, K. Kim, W. Jhe, N. Kwon, “Efficient optical guiding of trapped cold atoms by a hollow laser beam,” Phys. Rev. A 63, 340114 (2001).
[CrossRef]

1998

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[CrossRef]

1997

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

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, 52–54 (1997).
[CrossRef] [PubMed]

1996

1994

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

1993

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]

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, 8185–8189 (1992).
[CrossRef] [PubMed]

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]

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

Allen, L.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[CrossRef]

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, 52–54 (1997).
[CrossRef] [PubMed]

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]

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, 8185–8189 (1992).
[CrossRef] [PubMed]

Arlt, J.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” 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]

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, 8185–8189 (1992).
[CrossRef] [PubMed]

Bos, P. J.

Y. L. Zhang, P. J. Bos, D. B. Chung, “2-D modeling of the effect of electrode topography and interpixel gap on LCoS devices,” in Society for Information Display, International Symposium Digest of Technical Papers (Society for Information Display, San Jose, Calif., 2003), Vol. XXXIV, pp. 1382–1385.
[CrossRef]

Bryant, P. E.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

Chung, D. B.

Y. L. Zhang, P. J. Bos, D. B. Chung, “2-D modeling of the effect of electrode topography and interpixel gap on LCoS devices,” in Society for Information Display, International Symposium Digest of Technical Papers (Society for Information Display, San Jose, Calif., 2003), Vol. XXXIV, pp. 1382–1385.
[CrossRef]

Coerwinkel, R. P. C.

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

Courtial, J.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[CrossRef]

Dholakia, K.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[CrossRef]

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, 52–54 (1997).
[CrossRef] [PubMed]

Gahagan, K. T.

Gan, X.

Ganic, K.

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

Gu, M.

Hain, M.

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

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

Jhe, W.

X. Xu, K. Kim, W. Jhe, N. Kwon, “Efficient optical guiding of trapped cold atoms by a hollow laser beam,” Phys. Rev. A 63, 340114 (2001).
[CrossRef]

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, K.

X. Xu, K. Kim, W. Jhe, N. Kwon, “Efficient optical guiding of trapped cold atoms by a hollow laser beam,” Phys. Rev. A 63, 340114 (2001).
[CrossRef]

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 phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Kwon, N.

X. Xu, K. Kim, W. Jhe, N. Kwon, “Efficient optical guiding of trapped cold atoms by a hollow laser beam,” Phys. Rev. A 63, 340114 (2001).
[CrossRef]

MacDonald, M. P.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

Mcduff, R. G.

Orlov, S.

S. Orlov, K. Regelskis, V. Smilgevicius, A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[CrossRef]

Padgett, M. J.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[CrossRef]

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, 52–54 (1997).
[CrossRef] [PubMed]

Paterson, L.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

Regelskis, K.

S. Orlov, K. Regelskis, V. Smilgevicius, A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[CrossRef]

Robertson, D. A.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[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]

Sibbett, W.

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

Simpson, N. B.

Smilgevicius, V.

S. Orlov, K. Regelskis, V. Smilgevicius, A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[CrossRef]

Smith, C. P.

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]

Somalingam, S.

Soskin, M. S.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

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, 8185–8189 (1992).
[CrossRef] [PubMed]

Stabinis, A.

S. Orlov, K. Regelskis, V. Smilgevicius, A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[CrossRef]

Stankovic, S.

Swartzlander, G. A.

Tschudi, T.

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.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” 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]

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, 8185–8189 (1992).
[CrossRef] [PubMed]

Xu, X.

X. Xu, K. Kim, W. Jhe, N. Kwon, “Efficient optical guiding of trapped cold atoms by a hollow laser beam,” Phys. Rev. A 63, 340114 (2001).
[CrossRef]

Zhang, Y. L.

Y. L. Zhang, P. J. Bos, D. B. Chung, “2-D modeling of the effect of electrode topography and interpixel gap on LCoS devices,” in Society for Information Display, International Symposium Digest of Technical Papers (Society for Information Display, San Jose, Calif., 2003), Vol. XXXIV, pp. 1382–1385.
[CrossRef]

J. Mod. Opt.

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]

Opt. Commun.

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]

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

S. Orlov, K. Regelskis, V. Smilgevicius, A. Stabinis, “Propagation of Bessel beams carrying optical vortices,” Opt. Commun. 209, 155–165 (2002).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).
[CrossRef]

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, 8185–8189 (1992).
[CrossRef] [PubMed]

X. Xu, K. Kim, W. Jhe, N. Kwon, “Efficient optical guiding of trapped cold atoms by a hollow laser beam,” Phys. Rev. A 63, 340114 (2001).
[CrossRef]

Phys. Rev. Lett.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81, 4828–4830 (1998).
[CrossRef]

Science

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, K. Dholakia, “Controlled rotation of optically trapped microscopic particles,” Science 292, 912–914 (2001).
[CrossRef] [PubMed]

Other

Y. L. Zhang, P. J. Bos, D. B. Chung, “2-D modeling of the effect of electrode topography and interpixel gap on LCoS devices,” in Society for Information Display, International Symposium Digest of Technical Papers (Society for Information Display, San Jose, Calif., 2003), Vol. XXXIV, pp. 1382–1385.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Photograph of a LC spiral phase plate with a scale bar and the rubbing direction indicated. The 18 slices and the ITO resistors can be seen clearly with slanted illumination. (b) Schematic showing the stacking of the LC spiral phase plates. The rubbing angles of the LC spiral phase plates should be parallel and the polarization of the input laser beam should be parallel to the rubbing direction as well.

Fig. 2
Fig. 2

Retardation (Δnd/λ) versus driving voltage for the fabricated LC spiral phase plates with cell thicknesses of 7 and 20 μm.

Fig. 3
Fig. 3

Doughnut beams obtained in the experiment (top images) and the corresponding simulation results (bottom images): (a) with charge 1 generated with one 7-μm LC spiral phase plate, (b) with charge 2 generated by stacking of two 7-μm LC spiral phase plates, (c) with charge 3 generated by stacking of three 7-μm spiral phase plates.

Fig. 4
Fig. 4

Doughnut beams (a) with charges up to 4 (l = 1, 2, 3, 4) generated by one 20-μm-thick LC spiral phase plate and (b) with charges from 5 to 8 (l = 5, 6, 7, 8) generated by stacking of two 20-μm-thick LC spiral phase plates.

Fig. 5
Fig. 5

Experimental apparatus with which to study the interference of a doughnut beam and a plane wave.

Fig. 6
Fig. 6

(a) Interference patterns generated by doughnut beams of charges 3 (1) and 4 (2) with an inclined plane wave and 3 (3) and 4 (4) with a coaxial plane wave. The top images are experimental results, and the bottom images are simulations. (b) Rotating interference pattern generated by a doughnut beam of charge 3 and a coaxial plane wave. The bright dot at the left of each pattern was deliberately added as a reference to indicate the rotation.

Tables (1)

Tables Icon

Table 1 Gaussian-to-Doughnut Beam Conversion Efficiency of Single and Stacked LC Spiral Phase Platesa

Equations (2)

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

U=U0 expilθ,
U=U0 expil1θexpil2θ  expilnθ=U0 expiθ i li,

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