Abstract

We show the opportunity of fabricating axially symmetric waveplates fine tuned to a desired wavelength. High quality waveplates are obtained using liquid crystal polymer layers on photoaligning substrates extending their functional range from UV to IR wavelengths. We characterize the effect of the waveplate on laser beams showing formation of a doughnut beam with over 240 times attenuation of intensity on the axis. We pay attention that the power density is strongly reduced on the doughnut ring as well and use this opportunity for taking charge coupled devices (CCDs) out of a deep saturation regime. Strong deformation of the beam profile is observed when the vortex axis is shifted towards the periferies of the beam. We demonstrate feasibility of using this phenomenon for shaping the profile of light beams with a set of waveplates.

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  1. R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28(Part 1), 1730–1731 (1989).
    [CrossRef]
  2. M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21(23), 1948–1950 (1996).
    [CrossRef]
  3. L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: Switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (1–3) (2006).
    [CrossRef]
  4. S. C. McEldowney, D. M. Shemo, R. A. Chipman, and P. K. Smith, “Creating vortex retarders using photoaligned liquid crystal polymers,” Opt. Lett. 33(2), 134–136 (2008).
    [CrossRef]
  5. H. Choi, J. H. Woo and J. W. Wu, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (1–3) (2007).
  6. R. Bhandari, “Polarization of light and topological phases,” Phys. Rep. 282(1), 1–64 (1997).
    [CrossRef]
  7. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002).
    [CrossRef]
  8. A. Jesacher, A. Schwaighofer, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Schwaighofer, S. Fuerhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Wavefront correction of spatial light modulators using an optical vortex image,” Opt. Express 15(9), 5801–5808 (2007).
    [CrossRef]
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    [CrossRef]
  11. A. V. Nesterov and V. G. Niziev, “Laser beams with axially symmetric polarization,” Phys. D: Appl. Phys. 33(15), 1817–1822 (2000).
    [CrossRef]
  12. J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75(6), 859–861 (1999).
    [CrossRef]
  13. G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, “Assembly of 3-dimensional structures using programmable holographic optical tweezers,” Opt. Express 12(22), 5475–5480 (2004).
    [CrossRef]
  14. S. C. Chapin, V. Germain, and E. R. Dufresne, “Automated trapping, assembly, and sorting with holographic optical tweezers,” Opt. Express 14(26), 13095–13100 (2006).
    [CrossRef]
  15. D. Ganic, X. Gan, M. Gu, M. Hain, S. Somalingam, S. Stankovic, and T. Tschudi, “Generation of doughnut laser beams by use of a liquid-crystal cell with a conversion efficiency near 100%,” Opt. Lett. 27(15), 1351–1353 (2002).
    [CrossRef]
  16. Q. Wang, X. W. Sun, P. Shum, and X. J. Yin, “Dynamic switching of optical vortices with dynamic gamma-correction liquid crystal spiral phase plate,” Opt. Express 13(25), 10285–10291 (2005).
    [CrossRef]
  17. H. Ren, Y.-H. Lin and S.-T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89, 051114 (1–3) (2006).
    [CrossRef]
  18. S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).
  19. Y. Y. Tzeng, S.-W. Ke, C.-L. Ting, A. Y.-G. Fuh, and T.-H. Lin, “Axially symmetric polarization converters based on photo-aligned liquid crystal films,” Opt. Express 16(6), 3768–3775 (2008).
    [CrossRef]
  20. S.-W. Ko, Y.-Y. Tzeng, C.-L. Ting, A. Y.-G. Fuh, and T.-H. Lin, “Axially symmetric liquid crystal devices based on double-side photo-alignment,” Opt. Express 16(24), 19643–19648 (2008).
    [CrossRef]
  21. S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
    [CrossRef]
  22. S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Reproduction of polarization gratings,” Appl. Opt. (Submitted to).
  23. V. V. Kotlyar, A. A. Kovalev, R. V. Skidanov, S. N. Khonina, O. Yu. Moiseev, and V. A. Soifer, “Simple optical vortices formed by a spiral phase plate,” J. Opt. Technol. 74, 686–693 (2007).
    [CrossRef]
  24. J. F. Nye and M. V. Berry, ““Dislocations in wave trains,” Proc. Roy. Soc. London, Ser,” A 336, 165–190 (1974).
  25. N. B. Baranova, B. Ya, and A. V. Zel’dovich, “Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

2009

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[CrossRef]

2008

2007

2006

2005

2004

2002

2001

2000

A. V. Nesterov and V. G. Niziev, “Laser beams with axially symmetric polarization,” Phys. D: Appl. Phys. 33(15), 1817–1822 (2000).
[CrossRef]

1999

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75(6), 859–861 (1999).
[CrossRef]

1997

R. Bhandari, “Polarization of light and topological phases,” Phys. Rep. 282(1), 1–64 (1997).
[CrossRef]

1996

S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21(23), 1948–1950 (1996).
[CrossRef]

1989

R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28(Part 1), 1730–1731 (1989).
[CrossRef]

1981

N. B. Baranova, B. Ya, and A. V. Zel’dovich, “Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

1974

J. F. Nye and M. V. Berry, ““Dislocations in wave trains,” Proc. Roy. Soc. London, Ser,” A 336, 165–190 (1974).

Baranova, N. B.

N. B. Baranova, B. Ya, and A. V. Zel’dovich, “Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Bernet, S.

Berry, M. V.

J. F. Nye and M. V. Berry, ““Dislocations in wave trains,” Proc. Roy. Soc. London, Ser,” A 336, 165–190 (1974).

Bhandari, R.

R. Bhandari, “Polarization of light and topological phases,” Phys. Rep. 282(1), 1–64 (1997).
[CrossRef]

Biener, G.

Bomzon, Z.

Chapin, S. C.

Chipman, R. A.

Cooper, J.

Courtial, J.

Dufresne, E. R.

Fuerhapter, S.

Fuh, A. Y.-G.

Fürhapter, S.

Gan, X.

Ganic, D.

Germain, V.

Gu, M.

Hain, M.

Hasman, E.

Jesacher, A.

Jordan, P.

Ke, S.-W.

Khonina, S. N.

Kim, H. R.

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75(6), 859–861 (1999).
[CrossRef]

Kimball, B. R.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[CrossRef]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Reproduction of polarization gratings,” Appl. Opt. (Submitted to).

Kleiner, V.

Ko, S.-W.

Kotlyar, V. V.

Kovalev, A. A.

Laczik, Z. J.

Lee, J. H.

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75(6), 859–861 (1999).
[CrossRef]

Lee, S. D.

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75(6), 859–861 (1999).
[CrossRef]

Lin, T.-H.

Masuda, S.

S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).

Maurer, C.

McEldowney, S. C.

Moiseev, O. Yu.

Nersisyan, S. R.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[CrossRef]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Reproduction of polarization gratings,” Appl. Opt. (Submitted to).

Nesterov, A. V.

A. V. Nesterov and V. G. Niziev, “Laser beams with axially symmetric polarization,” Phys. D: Appl. Phys. 33(15), 1817–1822 (2000).
[CrossRef]

Niziev, V. G.

A. V. Nesterov and V. G. Niziev, “Laser beams with axially symmetric polarization,” Phys. D: Appl. Phys. 33(15), 1817–1822 (2000).
[CrossRef]

Nose, T.

S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).

R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28(Part 1), 1730–1731 (1989).
[CrossRef]

Nye, J. F.

J. F. Nye and M. V. Berry, ““Dislocations in wave trains,” Proc. Roy. Soc. London, Ser,” A 336, 165–190 (1974).

Padgett, M.

Ritsch-Marte, M.

Sato, S.

S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).

R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28(Part 1), 1730–1731 (1989).
[CrossRef]

Schadt, M.

Schwaighofer, A.

Shemo, D. M.

Shum, P.

Sinclair, G.

Skidanov, R. V.

Smith, P. K.

Soifer, V. A.

Somalingam, S.

Stalder, M.

Stankovic, S.

Steeves, D. M.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[CrossRef]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Reproduction of polarization gratings,” Appl. Opt. (Submitted to).

Sun, X. W.

Swartzlander, G. A.

Tabiryan, N. V.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[CrossRef]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Reproduction of polarization gratings,” Appl. Opt. (Submitted to).

Ting, C.-L.

Tschudi, T.

Tzeng, Y. Y.

Tzeng, Y.-Y.

Wang, Q.

Ya, B.

N. B. Baranova, B. Ya, and A. V. Zel’dovich, “Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Yamaguchi, R.

S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).

R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28(Part 1), 1730–1731 (1989).
[CrossRef]

Yin, X. J.

Zel’dovich, A. V.

N. B. Baranova, B. Ya, and A. V. Zel’dovich, “Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

A

J. F. Nye and M. V. Berry, ““Dislocations in wave trains,” Proc. Roy. Soc. London, Ser,” A 336, 165–190 (1974).

Appl. Opt.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Reproduction of polarization gratings,” Appl. Opt. (Submitted to).

Appl. Phys. Lett.

J. H. Lee, H. R. Kim, and S. D. Lee, “Polarization-insensitive wavelength selection in an axially symmetric liquid-crystal Fabry-Perot filter,” Appl. Phys. Lett. 75(6), 859–861 (1999).
[CrossRef]

J. Nonlinear Opt. Phys. Mater.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. Mater. 18(01), 1–47 (2009).
[CrossRef]

J. Opt. Technol.

JETP Lett.

N. B. Baranova, B. Ya, and A. V. Zel’dovich, “Mamayev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” JETP Lett. 33, 195–199 (1981).

Jpn. J. Appl. Phys.

R. Yamaguchi, T. Nose, and S. Sato, “Liquid crystal polarizers with axially symmetrical properties,” Jpn. J. Appl. Phys. 28(Part 1), 1730–1731 (1989).
[CrossRef]

Opt. Express

G. Sinclair, P. Jordan, J. Courtial, M. Padgett, J. Cooper, and Z. J. Laczik, “Assembly of 3-dimensional structures using programmable holographic optical tweezers,” Opt. Express 12(22), 5475–5480 (2004).
[CrossRef]

Q. Wang, X. W. Sun, P. Shum, and X. J. Yin, “Dynamic switching of optical vortices with dynamic gamma-correction liquid crystal spiral phase plate,” Opt. Express 13(25), 10285–10291 (2005).
[CrossRef]

S. Bernet, A. Jesacher, S. Fuerhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14(9), 3792–3805 (2006).
[CrossRef]

S. C. Chapin, V. Germain, and E. R. Dufresne, “Automated trapping, assembly, and sorting with holographic optical tweezers,” Opt. Express 14(26), 13095–13100 (2006).
[CrossRef]

A. Jesacher, A. Schwaighofer, S. Fürhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Schwaighofer, S. Fuerhapter, C. Maurer, S. Bernet, and M. Ritsch-Marte, “Wavefront correction of spatial light modulators using an optical vortex image,” Opt. Express 15(9), 5801–5808 (2007).
[CrossRef]

Y. Y. Tzeng, S.-W. Ke, C.-L. Ting, A. Y.-G. Fuh, and T.-H. Lin, “Axially symmetric polarization converters based on photo-aligned liquid crystal films,” Opt. Express 16(6), 3768–3775 (2008).
[CrossRef]

S.-W. Ko, Y.-Y. Tzeng, C.-L. Ting, A. Y.-G. Fuh, and T.-H. Lin, “Axially symmetric liquid crystal devices based on double-side photo-alignment,” Opt. Express 16(24), 19643–19648 (2008).
[CrossRef]

Opt. Lett.

Phys. D: Appl. Phys.

A. V. Nesterov and V. G. Niziev, “Laser beams with axially symmetric polarization,” Phys. D: Appl. Phys. 33(15), 1817–1822 (2000).
[CrossRef]

Phys. Rep.

R. Bhandari, “Polarization of light and topological phases,” Phys. Rep. 282(1), 1–64 (1997).
[CrossRef]

Proc. SPIE

S. Masuda, T. Nose, R. Yamaguchi, and S. Sato, “Polarization converting devices using a UV curable liquid crystal,” Proc. SPIE 2873, 301–304 (1996).

Other

H. Ren, Y.-H. Lin and S.-T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89, 051114 (1–3) (2006).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, “Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: Switchable helical mode generation,” Appl. Phys. Lett. 88, 221102 (1–3) (2006).
[CrossRef]

H. Choi, J. H. Woo and J. W. Wu, “Holographic inscription of helical wavefronts in a liquid crystal polarization grating,” Appl. Phys. Lett. 91, 141112 (1–3) (2007).

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Figures (7)

Fig. 1.
Fig. 1.

(a) Axial waveplate between crossed polarizers illuminated with a white light. Photos of a He-Ne laser beam, λ=633 nm, propagated through an axial waveplate with half-waveplate condition at 458 nm. Photos are taken with no polarizers in the optical path (b), and between parallel (c) and orthogonal polarizers (d).

Fig. 2.
Fig. 2.

The patterns obtained for a circular polarized beam of a He-Ne laser propagated through a double-layer LCP axial waveplate as a result of interference with a reference plane wave, (a) and (b), and a reference beam of a spherical phase profile, (c) and (d). The patterns (a) and (c) switch to (b) and (d), respectively, when changing the sign of circular polarization.

Fig. 3.
Fig. 3.

The columns correspond to images of linear polarized laser beams of different wavelengths propagated through axial waveplates with no polarizers in the optical path (1st column) and between parallel (2nd column) and perpendicular polarizers (3rd column). (a)-(c) He-Cd laser beam propagated through an axial waveplate with half-wave condition at the wavelength λ=325 nm; (d)-(f) Ar+ laser beam, λ=458 nm, half-wave condition at 458 nm; (g)-(i) He-Ne laser beam and a double layer axial waveplate with half-wave condition at 633 nm; (j)-(l) IR laser beam, λ=1064 nm, and a three layer axial waveplate with half-wave condition at 1000 nm.

Fig. 4.
Fig. 4.

(a) One-dimensional intensity profiles of a He-Ne laser beam obtained without and with the axial waveplate. (b) 2-D and 3-D profiles of the doughnut beam obtained for a highly saturating gaussian beam; (c) 2-D and 3-D profiles of the beam at a power level saturating a CCD; (d) demonstrating the capability of the axial waveplate to remove the saturation of the CCD camera.

Fig. 5.
Fig. 5.

The effect of an axial waveplate on the profile of a He-Ne laser beam for different ratios of the separation distance between the axes of the waveplate and beam to the radius of the beam d/w: (a) >2; (b) 1; (c) 0.25; (d) 0; (e) -0.25; (f) -1; (g) -0.75; (h) <-2. The sign of the ratio refers to having the vortex on the opposite sides of the beam.

Fig. 6.
Fig. 6.

Beam shaping with axial waveplates. The profiles are obtained for a Gaussian He-Ne laser beam by shifting the centers of two radial waveplates positioned at 2 mm distance from each other with respect to the beam axis. The shifts are equal for both waveplates but are of opposite signs.

Fig. 7.
Fig. 7.

3×3 and 5×5 vortex arrays with single, (a) and (c), and double LCP layers, (b) and (d). The arrays (a), (c) and (b), (d) are designed for 458 nm and 633 nm wavelengths, correspondingly.

Equations (2)

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I=Ide(rrd)2wd2
IGId=πrdwd[1+erf(rdwd)]+e(rdwd)2

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