Abstract

A flexible approach is presented to generate vector beams with arbitrary polarization and complex amplitude by means of two cascaded transmissive liquid crystal spatial light modulators (LCSLMs). The configuration of the cascaded LCSLM system and its modulation characteristic are introduced. Theoretical analysis and experimental demonstration prove that the system in combination with a double-pass computer-generated hologram and a black-and-white pattern can generate vector beams with arbitrary polarization and complex amplitude by respectively controlling the complex amplitudes of two orthogonal polarization components of the beams. Using this system, we successfully generate radially polarized vector beams with helical phase distributions and vector Bessel beams with inhomogeneous amplitude distributions in experiments.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
    [CrossRef]
  2. F. Xu, J. E. Ford, Y. Fainman, “Polarization-selective computer-generated holograms: design, fabrication, and applications,” Appl. Opt. 34(2), 256–266 (1995).
    [CrossRef] [PubMed]
  3. H. W. Ren, Y. H. Lin, S. T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89(5), 051114 (2006).
    [CrossRef]
  4. A. Desyatnikov, T. A. Fadeyeva, V. G. Shvedov, Y. V. Izdebskaya, A. V. Volyar, E. Brasselet, D. N. Neshev, W. Krolikowski, Y. S. Kivshar, “Spatially engineered polarization states and optical vortices in uniaxial crystals,” Opt. Express 18(10), 10848–10863 (2010).
    [CrossRef] [PubMed]
  5. Z. Bomzon, V. Kleiner, E. Hasman, “Computer-generated space-variant polarization elements with subwavelength metal stripes,” Opt. Lett. 26(1), 33–35 (2001).
    [CrossRef] [PubMed]
  6. W. B. Chen, W. Han, D. C. Abeysinghe, R. L. Nelson, Q. Zhan, “Generating cylindrical vector beams with subwavelength concentric metallic gratings fabricated on optical fibers,” J. Opt. 13(1), 015003 (2011).
    [CrossRef]
  7. W. J. Cai, A. R. Libertun, R. Piestun, “Polarization selective computer-generated holograms realized in glass by femtosecond laser induced nanogratings,” Opt. Express 14(9), 3785–3791 (2006).
    [CrossRef] [PubMed]
  8. Q. Hu, Z. H. Tan, X. Y. Weng, H. M. Guo, Y. Wang, S. L. Zhuang, “Design of cylindrical vector beams based on the rotating Glan polarizing prism,” Opt. Express 21(6), 7343–7353 (2013).
    [CrossRef] [PubMed]
  9. S. C. Tidwell, D. H. Ford, W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29(15), 2234–2239 (1990).
    [CrossRef] [PubMed]
  10. K. C. Toussaint, S. Park, J. E. Jureller, N. F. Scherer, “Generation of optical vector beams with a diffractive optical element interferometer,” Opt. Lett. 30(21), 2846–2848 (2005).
    [CrossRef] [PubMed]
  11. V. G. Niziev, R. S. Chang, A. V. Nesterov, “Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer,” Appl. Opt. 45(33), 8393–8399 (2006).
    [CrossRef] [PubMed]
  12. C. Y. Han, R. S. Chang, H. F. Chen, “Solid-state interferometry of a pentaprism for generating cylindrical vector beam,” Opt. Rev. 20(2), 189–192 (2013).
    [CrossRef]
  13. O. Aharon, I. Abdulhalim, “Liquid crystal wavelength-independent continuous polarization rotator,” Opt. Eng. 49(3), 034002 (2010).
    [CrossRef]
  14. A. Safrani, I. Abdulhalim, “Liquid-crystal polarization rotator and a tunable polarizer,” Opt. Lett. 34(12), 1801–1803 (2009).
    [CrossRef] [PubMed]
  15. M. Bashkansky, D. Park, F. K. Fatemi, “Azimuthally and radially polarized light with a nematic SLM,” Opt. Express 18(1), 212–217 (2010).
    [CrossRef] [PubMed]
  16. S. Tripathi, K. C. Toussaint., “Versatile generation of optical vector fields and vector beams using a non-interferometric approach,” Opt. Express 20(10), 10788–10795 (2012).
    [CrossRef] [PubMed]
  17. D. Maluenda, I. Juvells, R. Martínez-Herrero, A. Carnicer, “Reconfigurable beams with arbitrary polarization and shape distributions at a given plane,” Opt. Express 21(5), 5432–5439 (2013).
    [CrossRef] [PubMed]
  18. X. L. Wang, J. P. Ding, W. J. Ni, C. S. Guo, H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32(24), 3549–3551 (2007).
    [CrossRef] [PubMed]
  19. H. Chen, J. J. Hao, B. F. Zhang, J. Xu, J. P. Ding, H. T. Wang, “Generation of vector beam with space-variant distribution of both polarization and phase,” Opt. Lett. 36(16), 3179–3181 (2011).
    [CrossRef] [PubMed]
  20. S. Liu, P. Li, T. Peng, J. L. Zhao, “Generation of arbitrary spatially variant polarization beams with a trapezoid Sagnac interferometer,” Opt. Express 20(19), 21715–21721 (2012).
    [CrossRef] [PubMed]
  21. C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
    [CrossRef]
  22. J. A. Davis, G. H. Evans, I. Moreno, “Polarization-multiplexed diffractive optical elements with liquid-crystal displays,” Appl. Opt. 44(19), 4049–4052 (2005).
    [CrossRef] [PubMed]
  23. I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express 20(1), 364–376 (2012).
    [CrossRef] [PubMed]
  24. J. H. Clegg, M. A. A. Neil, “Double pass, common path method for arbitrary polarization control using a ferroelectric liquid crystal spatial light modulator,” Opt. Lett. 38(7), 1043–1045 (2013).
    [CrossRef] [PubMed]
  25. P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley, 1999), Chap. 4.
  26. I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, F. Mateos, “Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display,” J. Appl. Phys. 94(6), 3697–3702 (2003).
    [CrossRef]

2013

2012

2011

H. Chen, J. J. Hao, B. F. Zhang, J. Xu, J. P. Ding, H. T. Wang, “Generation of vector beam with space-variant distribution of both polarization and phase,” Opt. Lett. 36(16), 3179–3181 (2011).
[CrossRef] [PubMed]

W. B. Chen, W. Han, D. C. Abeysinghe, R. L. Nelson, Q. Zhan, “Generating cylindrical vector beams with subwavelength concentric metallic gratings fabricated on optical fibers,” J. Opt. 13(1), 015003 (2011).
[CrossRef]

2010

2009

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[CrossRef]

A. Safrani, I. Abdulhalim, “Liquid-crystal polarization rotator and a tunable polarizer,” Opt. Lett. 34(12), 1801–1803 (2009).
[CrossRef] [PubMed]

2007

2006

2005

2003

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, F. Mateos, “Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display,” J. Appl. Phys. 94(6), 3697–3702 (2003).
[CrossRef]

2001

1995

1990

Abdulhalim, I.

O. Aharon, I. Abdulhalim, “Liquid crystal wavelength-independent continuous polarization rotator,” Opt. Eng. 49(3), 034002 (2010).
[CrossRef]

A. Safrani, I. Abdulhalim, “Liquid-crystal polarization rotator and a tunable polarizer,” Opt. Lett. 34(12), 1801–1803 (2009).
[CrossRef] [PubMed]

Abeysinghe, D. C.

W. B. Chen, W. Han, D. C. Abeysinghe, R. L. Nelson, Q. Zhan, “Generating cylindrical vector beams with subwavelength concentric metallic gratings fabricated on optical fibers,” J. Opt. 13(1), 015003 (2011).
[CrossRef]

Aharon, O.

O. Aharon, I. Abdulhalim, “Liquid crystal wavelength-independent continuous polarization rotator,” Opt. Eng. 49(3), 034002 (2010).
[CrossRef]

Bashkansky, M.

Bernet, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[CrossRef]

Bomzon, Z.

Brasselet, E.

Cai, W. J.

Carnicer, A.

Chang, R. S.

C. Y. Han, R. S. Chang, H. F. Chen, “Solid-state interferometry of a pentaprism for generating cylindrical vector beam,” Opt. Rev. 20(2), 189–192 (2013).
[CrossRef]

V. G. Niziev, R. S. Chang, A. V. Nesterov, “Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer,” Appl. Opt. 45(33), 8393–8399 (2006).
[CrossRef] [PubMed]

Chen, H.

Chen, H. F.

C. Y. Han, R. S. Chang, H. F. Chen, “Solid-state interferometry of a pentaprism for generating cylindrical vector beam,” Opt. Rev. 20(2), 189–192 (2013).
[CrossRef]

Chen, W. B.

W. B. Chen, W. Han, D. C. Abeysinghe, R. L. Nelson, Q. Zhan, “Generating cylindrical vector beams with subwavelength concentric metallic gratings fabricated on optical fibers,” J. Opt. 13(1), 015003 (2011).
[CrossRef]

Clegg, J. H.

Cottrell, D. M.

Davis, J. A.

Desyatnikov, A.

Ding, J. P.

Evans, G. H.

Fadeyeva, T. A.

Fainman, Y.

Fatemi, F. K.

Fernández-Pousa, C. R.

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, F. Mateos, “Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display,” J. Appl. Phys. 94(6), 3697–3702 (2003).
[CrossRef]

Ford, D. H.

Ford, J. E.

Fürhapter, S.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[CrossRef]

Guo, C. S.

Guo, H. M.

Han, C. Y.

C. Y. Han, R. S. Chang, H. F. Chen, “Solid-state interferometry of a pentaprism for generating cylindrical vector beam,” Opt. Rev. 20(2), 189–192 (2013).
[CrossRef]

Han, W.

W. B. Chen, W. Han, D. C. Abeysinghe, R. L. Nelson, Q. Zhan, “Generating cylindrical vector beams with subwavelength concentric metallic gratings fabricated on optical fibers,” J. Opt. 13(1), 015003 (2011).
[CrossRef]

Hao, J. J.

Hasman, E.

Hernandez, T. M.

Hu, Q.

Izdebskaya, Y. V.

Jesacher, A.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[CrossRef]

Jureller, J. E.

Juvells, I.

Kimura, W. D.

Kivshar, Y. S.

Kleiner, V.

Krolikowski, W.

Li, P.

Libertun, A. R.

Lin, Y. H.

H. W. Ren, Y. H. Lin, S. T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89(5), 051114 (2006).
[CrossRef]

Liu, S.

Maluenda, D.

Martínez-Herrero, R.

Mateos, F.

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, F. Mateos, “Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display,” J. Appl. Phys. 94(6), 3697–3702 (2003).
[CrossRef]

Maurer, C.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[CrossRef]

Moreno, I.

Neil, M. A. A.

Nelson, R. L.

W. B. Chen, W. Han, D. C. Abeysinghe, R. L. Nelson, Q. Zhan, “Generating cylindrical vector beams with subwavelength concentric metallic gratings fabricated on optical fibers,” J. Opt. 13(1), 015003 (2011).
[CrossRef]

Neshev, D. N.

Nesterov, A. V.

Ni, W. J.

Niziev, V. G.

Park, D.

Park, S.

Peng, T.

Piestun, R.

Ren, H. W.

H. W. Ren, Y. H. Lin, S. T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89(5), 051114 (2006).
[CrossRef]

Ritsch-Marte, M.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[CrossRef]

Safrani, A.

Sánchez-López, M. M.

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, F. Mateos, “Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display,” J. Appl. Phys. 94(6), 3697–3702 (2003).
[CrossRef]

Sand, D.

Scherer, N. F.

Shvedov, V. G.

Tan, Z. H.

Tidwell, S. C.

Toussaint, K. C.

Tripathi, S.

Velásquez, P.

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, F. Mateos, “Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display,” J. Appl. Phys. 94(6), 3697–3702 (2003).
[CrossRef]

Volyar, A. V.

Wang, H. T.

Wang, X. L.

Wang, Y.

Weng, X. Y.

Wu, S. T.

H. W. Ren, Y. H. Lin, S. T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89(5), 051114 (2006).
[CrossRef]

Xu, F.

Xu, J.

Zhan, Q.

W. B. Chen, W. Han, D. C. Abeysinghe, R. L. Nelson, Q. Zhan, “Generating cylindrical vector beams with subwavelength concentric metallic gratings fabricated on optical fibers,” J. Opt. 13(1), 015003 (2011).
[CrossRef]

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[CrossRef]

Zhang, B. F.

Zhao, J. L.

Zhuang, S. L.

Adv. Opt. Photonics

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

H. W. Ren, Y. H. Lin, S. T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89(5), 051114 (2006).
[CrossRef]

J. Appl. Phys.

I. Moreno, P. Velásquez, C. R. Fernández-Pousa, M. M. Sánchez-López, F. Mateos, “Jones matrix method for predicting and optimizing the optical modulation properties of a liquid-crystal display,” J. Appl. Phys. 94(6), 3697–3702 (2003).
[CrossRef]

J. Opt.

W. B. Chen, W. Han, D. C. Abeysinghe, R. L. Nelson, Q. Zhan, “Generating cylindrical vector beams with subwavelength concentric metallic gratings fabricated on optical fibers,” J. Opt. 13(1), 015003 (2011).
[CrossRef]

New J. Phys.

C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, M. Ritsch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
[CrossRef]

Opt. Eng.

O. Aharon, I. Abdulhalim, “Liquid crystal wavelength-independent continuous polarization rotator,” Opt. Eng. 49(3), 034002 (2010).
[CrossRef]

Opt. Express

M. Bashkansky, D. Park, F. K. Fatemi, “Azimuthally and radially polarized light with a nematic SLM,” Opt. Express 18(1), 212–217 (2010).
[CrossRef] [PubMed]

A. Desyatnikov, T. A. Fadeyeva, V. G. Shvedov, Y. V. Izdebskaya, A. V. Volyar, E. Brasselet, D. N. Neshev, W. Krolikowski, Y. S. Kivshar, “Spatially engineered polarization states and optical vortices in uniaxial crystals,” Opt. Express 18(10), 10848–10863 (2010).
[CrossRef] [PubMed]

I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express 20(1), 364–376 (2012).
[CrossRef] [PubMed]

S. Tripathi, K. C. Toussaint., “Versatile generation of optical vector fields and vector beams using a non-interferometric approach,” Opt. Express 20(10), 10788–10795 (2012).
[CrossRef] [PubMed]

S. Liu, P. Li, T. Peng, J. L. Zhao, “Generation of arbitrary spatially variant polarization beams with a trapezoid Sagnac interferometer,” Opt. Express 20(19), 21715–21721 (2012).
[CrossRef] [PubMed]

D. Maluenda, I. Juvells, R. Martínez-Herrero, A. Carnicer, “Reconfigurable beams with arbitrary polarization and shape distributions at a given plane,” Opt. Express 21(5), 5432–5439 (2013).
[CrossRef] [PubMed]

Q. Hu, Z. H. Tan, X. Y. Weng, H. M. Guo, Y. Wang, S. L. Zhuang, “Design of cylindrical vector beams based on the rotating Glan polarizing prism,” Opt. Express 21(6), 7343–7353 (2013).
[CrossRef] [PubMed]

W. J. Cai, A. R. Libertun, R. Piestun, “Polarization selective computer-generated holograms realized in glass by femtosecond laser induced nanogratings,” Opt. Express 14(9), 3785–3791 (2006).
[CrossRef] [PubMed]

Opt. Lett.

Opt. Rev.

C. Y. Han, R. S. Chang, H. F. Chen, “Solid-state interferometry of a pentaprism for generating cylindrical vector beam,” Opt. Rev. 20(2), 189–192 (2013).
[CrossRef]

Other

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley, 1999), Chap. 4.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Architecture of the experiment setup.

Fig. 2
Fig. 2

Scheme for design of the double-pass computer generated hologram (DPCGH). (a) and (b) are computer generated holograms (CGHs) of the complex function u and v respectively. (c) and (d) are enlarged parts of the CGHs shown in (a) and (b). (e) and (f) are enlarged parts of the complementary sampling masks (MASK-1 and MASK-2). (g) and (h) are enlarged parts of the sampling results of CGH-1 and CGH-2. (i) is the final DPCGH combined by sampling CGH-1 and CGH-2. (j) is an enlarged part of the DPCGH. The colors in the figures are only used to distinguish the x-component and the y-component.

Fig. 3
Fig. 3

Experimental results. (a) is the distribution of the spatial spectrum. (b)-(h) are the intensity distributions of the output cylindrical vector beams when parameter δ is taken as θ, θ + π/2, 4θ, 2πr/r0, 2πr/r0 + π/4, 4πr/r0, and 2θ + 2πr/r0 + π/4 respectively.

Fig. 4
Fig. 4

Intensity distributions of the radially polarized vector beams with a helical phase profile and their interference patterns after superimposing a plane wave.

Fig. 5
Fig. 5

Intensity distributions of the vector Bessel beams. (a-d) show the intensity distributions of the vector Bessel beams with different analyzer orientations. (e-h) show the recorded results after further diffracting a distance of about 100mm. (i-l) show the intensity profiles along the analyzer orientations on the two record planes, the solid lines and dashed lines corresponding to the cases before and after diffracting the distance of 100mm.

Equations (16)

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

E o = J SLM-2 J P J SLM-1 E i ,
E o = J SLM-2 [ 1 0 0 0 ] J SLM-1 [ E ix 0 ]= E ix A g,1 [ A g,2 C g,2 ],
E o = E ix [ A w,2 A g,1 comb( yd 2d ) C b,2 A g,1 comb( y 2d ) ],
E=( u( r ) v( r ) )=( tx( r )exp[i ϕ x ( r )] ty( r )exp[i ϕ y ( r )] ),
Hx(x,y)= [1+txcos(2π f 0 x+ ϕ x )] /2 ,
Hy(x,y)= [1+tycos(2π f 0 x+ ϕ y )] /2 ,
H SDPCGH (x,y)=Hxcomb( yd 2d )+Hycomb( y 2d ).
E o = A w,2 E ix [ Hxcomb( yd 2d ) exp(iΔβ)Hycomb( y 2d ) ].
G x (ξ,η)=F{Hxcomb( yd 2d )}=[ 1 2 δ(ξ,η)+ 1 4 T x (ξ f 0 ,η)+ 1 4 T x * (ξ f 0 ,η)] *[ n=N+1 N δ(η n 2d ) exp(i2πηd)],
G y (ξ,η)=F{Hycomb( y 2d )}=[ 1 2 δ(ξ,η)+ 1 4 T y (ξ f 0 ,η)+ 1 4 T y * (ξ f 0 ,η)] *[ n=N+1 N δ(η n 2d ) ].
F +1 G x (ξ,η) n=0 = 1 4 T x (ξ f 0 ,η)*δ(η)= 1 4 T x (ξ f 0 ,η),
F +1 G y (ξ,η) n=0 = 1 4 T y (ξ f 0 ,η)*δ(η)= 1 4 T y (ξ f 0 ,η).
F -1 { F +1 G x (ξ,η) n=0 }=txexp(i ϕ x )exp(i2π f 0 x),
F -1 { F +1 G y (ξ,η) n=0 }=tyexp(i ϕ y )exp(i2π f 0 x).
U CCD (x,y)= A w,2 E ix exp(i2π f 0 x)[ txexp(i ϕ x ) exp(iΔβ)tyexp(i ϕ y ) ].
E=( u( r ) v( r ) )=( cosδ sinδ ),

Metrics