Abstract

In the present work, we propose a method to generate high-quality optical vortices with a reduced number of phase levels by using multilevel vortex-producing lenses (VPLs). The VPL is implemented in a liquid-crystal spatial light modulator with limited capacity to project phase levels. The proposed method significantly improves the quality of the optical vortex obtained by employing spiral phase plates with the same number of phase levels. Simulations and experimental results confirming the effectiveness of the method are presented.

© 2013 Optical Society of America

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References

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  1. M. Padgett, J. Courtial, and L. Allen, Phys. Today 57(5), 35 (2004).
    [CrossRef]
  2. A. M. Yao and M. J. Padgett, Adv. Opt. Photon. 3, 161 (2011).
    [CrossRef]
  3. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  4. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).
    [CrossRef]
  5. G. Swartzlander, Opt. Photon. News 17(11), 39 (2006).
    [CrossRef]
  6. J. A. Davis, D. E. McNamara, D. M. Cottrell, and J. Campos, Opt. Lett. 25, 99 (2000).
    [CrossRef]
  7. K. Crabtree, J. A. Davis, and I. Moreno, Appl. Opt. 43, 1360 (2004).
    [CrossRef]
  8. S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, Opt. Express 13, 689 (2005).
    [CrossRef]
  9. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
    [CrossRef]
  10. A. Arias, S. Etcheverry, P. Solano, J. P. Staforelli, M. J. Gallardo, H. Rubinsztein-Dunlop, and C. Saavedra, Opt. Express 21, 102 (2013).
    [CrossRef]
  11. X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
    [CrossRef]
  12. K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, Nano Lett. 12, 3645 (2012).
    [CrossRef]
  13. A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, Am. J. Phys. 76, 916 (2008).
    [CrossRef]
  14. V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1990).
  15. V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, J. Mod. Opt. 39, 985 (1992).
    [CrossRef]
  16. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
    [CrossRef]
  17. N. Zhang, J. A. Davis, I. Moreno, D. M. Cottrell, and X.-C. Yuan, Opt. Express 18, 25987 (2010).
    [CrossRef]
  18. J. F. Nye and M. V. Berry, Proc. R. Soc. London 336, 165 (1974).
    [CrossRef]
  19. C.-S. Guo, D.-M. Xue, Y.-J. Han, and J. Ding, Opt. Commun. 268, 235 (2006).
    [CrossRef]
  20. V. V. Kotlyar and A. A. Kovalev, Opt. Lett. 33, 189 (2008).
    [CrossRef]
  21. U. Levy, D. Mendlovic, and E. Marom, J. Opt. Soc. Am. A 18, 86 (2001).
    [CrossRef]
  22. E. Hecht, Optics4th ed. (Addison-Wesley, 2002), p. 246.
  23. P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley-VCH, 2000), p. 368.
  24. C.-S. Guo, Z.-Y. Rong, H.-T. Wang, Y. Wang, and L. Z. Ca, Appl. Opt. 42, 6975 (2003).
    [CrossRef]
  25. M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
    [CrossRef]
  26. A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 241, 237 (2004).
    [CrossRef]

2013

2012

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, Nano Lett. 12, 3645 (2012).
[CrossRef]

2011

2010

2008

A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, Am. J. Phys. 76, 916 (2008).
[CrossRef]

V. V. Kotlyar and A. A. Kovalev, Opt. Lett. 33, 189 (2008).
[CrossRef]

2006

C.-S. Guo, D.-M. Xue, Y.-J. Han, and J. Ding, Opt. Commun. 268, 235 (2006).
[CrossRef]

G. Swartzlander, Opt. Photon. News 17(11), 39 (2006).
[CrossRef]

2005

2004

2003

2001

2000

1997

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

1995

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

1992

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef]

1990

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1990).

1974

J. F. Nye and M. V. Berry, Proc. R. Soc. London 336, 165 (1974).
[CrossRef]

Allen, L.

M. Padgett, J. Courtial, and L. Allen, Phys. Today 57(5), 35 (2004).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Aoki, N.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, Nano Lett. 12, 3645 (2012).
[CrossRef]

Arias, A.

Barnett, S. M.

Bazhenov, V. Y.

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1990).

Beijersbergen, M.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Bekshaev, A. Ya.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 241, 237 (2004).
[CrossRef]

Bernet, S.

Berry, M. V.

J. F. Nye and M. V. Berry, Proc. R. Soc. London 336, 165 (1974).
[CrossRef]

Ca, L. Z.

Cai, X.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Campos, J.

Carpentier, A. V.

A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, Am. J. Phys. 76, 916 (2008).
[CrossRef]

Cottrell, D. M.

Courtial, J.

Crabtree, K.

Davis, J. A.

Ding, J.

C.-S. Guo, D.-M. Xue, Y.-J. Han, and J. Ding, Opt. Commun. 268, 235 (2006).
[CrossRef]

Etcheverry, S.

Franke-Arnold, S.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

Fürhapter, S.

Gallardo, M. J.

Gibson, G.

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Guo, C.-S.

C.-S. Guo, D.-M. Xue, Y.-J. Han, and J. Ding, Opt. Commun. 268, 235 (2006).
[CrossRef]

C.-S. Guo, Z.-Y. Rong, H.-T. Wang, Y. Wang, and L. Z. Ca, Appl. Opt. 42, 6975 (2003).
[CrossRef]

Han, Y.-J.

C.-S. Guo, D.-M. Xue, Y.-J. Han, and J. Ding, Opt. Commun. 268, 235 (2006).
[CrossRef]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

Hecht, E.

E. Hecht, Optics4th ed. (Addison-Wesley, 2002), p. 246.

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef]

Jesacher, A.

Johnson-Morris, B.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Kotlyar, V. V.

Kovalev, A. A.

Levy, U.

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Marom, E.

McDuff, R.

McNamara, D. E.

Mendlovic, D.

Michinel, H.

A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, Am. J. Phys. 76, 916 (2008).
[CrossRef]

Miyamoto, K.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, Nano Lett. 12, 3645 (2012).
[CrossRef]

Moreno, I.

Morita, R.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, Nano Lett. 12, 3645 (2012).
[CrossRef]

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. London 336, 165 (1974).
[CrossRef]

O’Brien, J. L.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Olivieri, D.

A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, Am. J. Phys. 76, 916 (2008).
[CrossRef]

Omatsu, T.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, Nano Lett. 12, 3645 (2012).
[CrossRef]

Padgett, M.

M. Padgett, J. Courtial, and L. Allen, Phys. Today 57(5), 35 (2004).
[CrossRef]

Padgett, M. J.

Pas’ko, V.

Rastogi, P. K.

P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley-VCH, 2000), p. 368.

Ritsch-Marte, M.

Rong, Z.-Y.

Rubinsztein-Dunlop, H.

Saavedra, C.

Salgueiro, J. R.

A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, Am. J. Phys. 76, 916 (2008).
[CrossRef]

Smith, C. P.

Solano, P.

Sorel, M.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Soskin, M. S.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 241, 237 (2004).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1990).

Spreeuw, R.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Staforelli, J. P.

Strain, M. J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Swartzlander, G.

G. Swartzlander, Opt. Photon. News 17(11), 39 (2006).
[CrossRef]

Thompson, M. G.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Toyoda, K.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, Nano Lett. 12, 3645 (2012).
[CrossRef]

Vasnetsov, M.

Vasnetsov, M. V.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 241, 237 (2004).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1990).

Wang, H.-T.

Wang, J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Wang, Y.

White, A. G.

Woerdman, J.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Xue, D.-M.

C.-S. Guo, D.-M. Xue, Y.-J. Han, and J. Ding, Opt. Commun. 268, 235 (2006).
[CrossRef]

Yao, A. M.

Yu, S.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Yuan, X.-C.

Zhang, N.

Zhu, J.

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Adv. Opt. Photon.

Am. J. Phys.

A. V. Carpentier, H. Michinel, J. R. Salgueiro, and D. Olivieri, Am. J. Phys. 76, 916 (2008).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, J. Mod. Opt. 39, 985 (1992).
[CrossRef]

J. Opt. Soc. Am. A

JETP Lett.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JETP Lett. 52, 429 (1990).

Nano Lett.

K. Toyoda, K. Miyamoto, N. Aoki, R. Morita, and T. Omatsu, Nano Lett. 12, 3645 (2012).
[CrossRef]

Opt. Commun.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 241, 237 (2004).
[CrossRef]

C.-S. Guo, D.-M. Xue, Y.-J. Han, and J. Ding, Opt. Commun. 268, 235 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Photon. News

G. Swartzlander, Opt. Photon. News 17(11), 39 (2006).
[CrossRef]

Phys. Rev. A

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Phys. Rev. Lett.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef]

Phys. Today

M. Padgett, J. Courtial, and L. Allen, Phys. Today 57(5), 35 (2004).
[CrossRef]

Proc. R. Soc. London

J. F. Nye and M. V. Berry, Proc. R. Soc. London 336, 165 (1974).
[CrossRef]

Science

X. Cai, J. Wang, M. J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J. L. O’Brien, M. G. Thompson, and S. Yu, Science 338, 363 (2012).
[CrossRef]

Other

E. Hecht, Optics4th ed. (Addison-Wesley, 2002), p. 246.

P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley-VCH, 2000), p. 368.

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Figures (9)

Fig. 1.
Fig. 1.

Simulation of a Gaussian beam diffracted by a multilevel SPP with m=1. First row: number of phase levels used to generate the SPP; second row: multilevel SPP; third row: intensity pattern in the physical lens back focal plane; fourth row: phase pattern in the physical lens back focal plane. SPP diameter DSPP=0.4mm, Gaussian beam waist w=0.13mm, f=12mm, λ=532nm. Red lines correspond to intensity contours.

Fig. 2.
Fig. 2.

MSE (measured with respect to the ideal case, N=256) of the intensity patterns obtained from the simulation of a Gaussian beam diffracted by a multilevel SPP with m=1. The intensity pattern of a multilevel SPP with N=1 corresponds to the MSE normalizing value. Simulation parameters are the same as in Fig. 1.

Fig. 3.
Fig. 3.

Intensity patterns obtained from SPPs for N=4: (first row) vortex topological charge; (second row) MSE with respect to the ideal case of N=256; (third row) SPP; (fourth row) intensity pattern in the physical lens back focal plane. Simulation parameters are the same as in Fig. 1.

Fig. 4.
Fig. 4.

VPL building procedure: (a) SPP with N=256 is computed. (b) Fresnel lens with N=256 is computed. (c) The SPP and the Fresnel lens are superimpose to generate a VPL with N=256. (d) The VPL is transformed into a multilevel VPL with N=4 and displayed on the LC-SLM. This example is for a VPL with m=1.

Fig. 5.
Fig. 5.

Basic optical setup for simulations and experiments.

Fig. 6.
Fig. 6.

Optical vortices generated by using multilevel VPLs with N=4: (first row) vortex topological charge; (second row) MSE with respect to the ideal case of N=256; (third row) VPL; (fourth row) intensity pattern at zopt. VPL diameter DVPL=0.4mm; w=0.13mm; f=12mm; fFR=12mm; λ=532nm.

Fig. 7.
Fig. 7.

OV quality (MSE) dependence with respect to the observation plane. Simulation parameters are the same as in Fig. 6. MSE>1 are due to the scaling phenomenon of the OV beam with respect to the ideal case. This example is for a VPL with m=1.

Fig. 8.
Fig. 8.

OV quality dependence with fFR/w. Simulation parameters are the same as in Fig. 6, except for fFR, which is varied.

Fig. 9.
Fig. 9.

Experimental results for OV beams generated by projecting VPLs in a four-phase levels transmission LC-SLM.

Equations (4)

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

η=[sin(πN)πN]2.
MSE(N)=i,j(I256(i.j)IN(i,j))2i,j(I256(i.j)I1(i,j))2,
t(r,θ)=eimθeiπr2λfFR,
zopt=f2fFR.

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