Abstract

We propose a method for realizing a polarization-selective diffractive optical element by using of a single twisted-nematic liquid-crystal display (TN-LCD). We have demonstrated that two orthogonal polarization-encoding channels can be formed using a single TN-LCD operated in some special conditions. Based on the two orthogonal encoding channels, two orthogonal polarized components of a field with any complex amplitude can be holographically encoded and reconstructed and, hence, different output images with different polarization states could be obtained, or a vector beam with spatially inhomogeneous polarization distributions, as well as the desired complex amplitude distributions, could be combined.

© 2010 Optical Society of America

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  1. S. Sanyal, P. Bandyopadhyay, and A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592-599(1998).
    [CrossRef]
  2. P. C. Mogensen and J. Gluckstad, “A phase-based optical encryption system with polarisation encoding,” Opt. Commun. 173, 177-183 (2000).
    [CrossRef]
  3. F. Gori, “Measuring Stokes parameters by means of polarization grating,” Opt. Lett. 24, 584-586 (1999).
    [CrossRef]
  4. F. Xu, J. E. Ford, and Y. Fainman, “Polarization-selective computer-generated holograms: design, fabrication, and applications,” Appl. Opt. 34, 256-266 (1995)
    [CrossRef]
  5. A. V. Krishnamoorthy, F. Xu, J. E. Ford, and Y. Fainman, “Polarization-controlled multistage switch based on polarization-selective computer-generated holograms,” Appl. Opt. 36, 997-1010 (1997).
    [CrossRef]
  6. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27, 285-287(2002).
    [CrossRef]
  7. K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89, 251114 (2006).
    [CrossRef]
  8. X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32, 3549-3551 (2007).
    [CrossRef]
  9. M. A. Ahmed, A. Voss, M. M. Vogel, and T. Graf, “Multilayer polarizing grating mirror used for the generation of radial polarization inYb:YAG thin-disk lasers,” Opt. Lett. 32, 3272-3274 (2007).
    [CrossRef]
  10. B. C. Lim, P. B. Phua, W. J. Lai, and M. H. Hong, “Fast switchable electro-optic radial polarization retarder,” Opt. Lett. 33, 950-952 (2008).
    [CrossRef]
  11. G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radiallyand azimuthally-polarized beams,” Opt. Commun. 281, 732-738 (2008).
    [CrossRef]
  12. Qiwen Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1-57 (2009).
    [CrossRef]
  13. J. Ford, F. Xu, K. Urquhart, and Y. Fainman, “Polarization-selective computer-generated holograms,” Opt. Lett. 18, 456-458 (1993).
    [CrossRef]
  14. N. Nieuborg, A. Kirk, B. Morlion, H. Thienpont, and I. Veretennicoff, “Polarization-selective diffractive optical elements with an index-matching gap material,” Appl. Opt. 36, 4681-4685 (1997).
    [CrossRef]
  15. F. Xu, R.-C. Tyan, P.-C. Sun, Y. Fainman, C.-C. Cheng, and A. Scherer, “Form-birefringent computergenerated holograms,” Opt. Lett. 21, 1513-1515 (1996).
    [CrossRef]
  16. U. Zeitner, B. Schnabel, E. Kley, and F. Wyrowski, “Polarization multiplexing of diffractive elements with metal-stripe grating pixels,” Appl. Opt. 38, 2177-2181 (1999).
    [CrossRef]
  17. Z. Bomzon, V. Kleiner, and E. Hasman, “Computer-generated space-variant polarization elements with subwavelength metal stripes,” Opt. Lett. 26, 33-35 (2001).
    [CrossRef]
  18. W. Yu, T. Konishi, T. Hamamoto, H. Toyota, T. Yotsuya, and Y. Ichioka, “Polarization-multiplexed diffractive optical elements fabricated by subwavelength structures,” Appl. Opt. 41, 96-100 (2002).
    [CrossRef]
  19. S. H. Tao, X.-C. Yuan, W. C. Cheong, J. Bu, and V. Kudryashov, “Optimized polarization-selective computer-generated hologram with fewer phase combinations,” Opt. Express 11, 1252-1257 (2003).
  20. M. Mirotznik, D. Pustai, D. Prather, and J. Mait, “Design of two-dimensional polarization-selective diffractive optical elements with form-birefringent microstructures,” Appl. Opt. 43, 5947-5954 (2004).
    [CrossRef]
  21. W. Cai, A. R. Libertun, and R. Piestun, “Polarization selective computer-generated holograms realized in glass by femtosecond laser induced nanogratings,” Opt. Express 14, 3785-3791 (2006).
    [CrossRef]
  22. J. A. Davis, D. E. McNamara, D. M. Cottrell, and T. Sonehara, “Two dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator,” Appl. Opt. 39, 1549-1554 (2000).
    [CrossRef]
  23. J. A. Davis, J. Adachi, C. R. Fernandez-Pousa, and I. Moreno, “Polarization beam splitters using polarization diffraction gratings,” Opt. Lett. 26, 587-589 (2001).
    [CrossRef]
  24. C. R. Fernandez-Pousa, I. Moreno, J. A. Davis, and J. Adachi, “Polarizing diffraction-grating triplicators,” Opt. Lett. 26, 1651-1653 (2001).
    [CrossRef]
  25. Jeffrey A. Davis, Garrett H. Evans, and Ignacio Moreno, “Polarization-multiplexed diffractive optical elements with liquid-crystal displays,” Appl. Opt. 44, 4049-4052 (2005).
    [CrossRef]
  26. I. Moreno, J. L. Martínez, and J. A. Davis, “Two-dimensional polarization rotator using a twisted-nematic liquid-crystal display,” Appl. Opt. 46, 881-887 (2007).
    [CrossRef]
  27. J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937-945 (1998).
    [CrossRef]

2009 (1)

2008 (2)

B. C. Lim, P. B. Phua, W. J. Lai, and M. H. Hong, “Fast switchable electro-optic radial polarization retarder,” Opt. Lett. 33, 950-952 (2008).
[CrossRef]

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radiallyand azimuthally-polarized beams,” Opt. Commun. 281, 732-738 (2008).
[CrossRef]

2007 (3)

2006 (2)

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

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89, 251114 (2006).
[CrossRef]

2005 (1)

2004 (1)

2003 (1)

2002 (2)

2001 (3)

2000 (2)

1999 (2)

1998 (2)

S. Sanyal, P. Bandyopadhyay, and A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592-599(1998).
[CrossRef]

J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937-945 (1998).
[CrossRef]

1997 (2)

1996 (1)

1995 (1)

1993 (1)

Adachi, J.

Ahmed, M. A.

Bandyopadhyay, P.

S. Sanyal, P. Bandyopadhyay, and A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592-599(1998).
[CrossRef]

Biener, G.

Bomzon, Z.

Bu, J.

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89, 251114 (2006).
[CrossRef]

S. H. Tao, X.-C. Yuan, W. C. Cheong, J. Bu, and V. Kudryashov, “Optimized polarization-selective computer-generated hologram with fewer phase combinations,” Opt. Express 11, 1252-1257 (2003).

Burge, R. E.

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89, 251114 (2006).
[CrossRef]

Cai, W.

Cheng, C.-C.

Cheong, W. C.

Cottrell, D. M.

Davis, A.

Davis, J. A.

Ding, J.

Evans, Garrett H.

Fainman, Y.

Fernandez-Pousa, C. R.

Ford, J.

Ford, J. E.

Ghosh, A.

S. Sanyal, P. Bandyopadhyay, and A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592-599(1998).
[CrossRef]

Gluckstad, J.

P. C. Mogensen and J. Gluckstad, “A phase-based optical encryption system with polarisation encoding,” Opt. Commun. 173, 177-183 (2000).
[CrossRef]

Gori, F.

Graf, T.

Guo, C. S.

Hamamoto, T.

Hasman, E.

Hong, M. H.

Ichioka, Y.

Jackel, S.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radiallyand azimuthally-polarized beams,” Opt. Commun. 281, 732-738 (2008).
[CrossRef]

Kirk, A.

Kleiner, V.

Kley, E.

Konishi, T.

Krishnamoorthy, A. V.

Kudryashov, V.

Lai, W. J.

Libertun, A. R.

Lim, B. C.

Low, D. K. Y.

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89, 251114 (2006).
[CrossRef]

Lumer, Y.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radiallyand azimuthally-polarized beams,” Opt. Commun. 281, 732-738 (2008).
[CrossRef]

Machavariani, G.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radiallyand azimuthally-polarized beams,” Opt. Commun. 281, 732-738 (2008).
[CrossRef]

Mait, J.

Martínez, J. L.

McNamara, D. E.

Meir, A.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radiallyand azimuthally-polarized beams,” Opt. Commun. 281, 732-738 (2008).
[CrossRef]

Mirotznik, M.

Mogensen, P. C.

P. C. Mogensen and J. Gluckstad, “A phase-based optical encryption system with polarisation encoding,” Opt. Commun. 173, 177-183 (2000).
[CrossRef]

Moh, K. J.

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89, 251114 (2006).
[CrossRef]

Moreno, I.

Moreno, Ignacio

Morlion, B.

Moshe, I.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radiallyand azimuthally-polarized beams,” Opt. Commun. 281, 732-738 (2008).
[CrossRef]

Ni, W. J.

Nieuborg, N.

Phua, P. B.

Piestun, R.

Prather, D.

Pustai, D.

Sanyal, S.

S. Sanyal, P. Bandyopadhyay, and A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592-599(1998).
[CrossRef]

Scherer, A.

Schnabel, B.

Sonehara, T.

Sun, P.-C.

Tao, S. H.

Thienpont, H.

Toyota, H.

Tsai, P.

Tyan, R.-C.

Urquhart, K.

Veretennicoff, I.

Vogel, M. M.

Voss, A.

Wang, H. T.

Wang, X. L.

Wyrowski, F.

Xu, F.

Yotsuya, T.

Yu, W.

Yuan, X. C.

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89, 251114 (2006).
[CrossRef]

Yuan, X.-C.

Zeitner, U.

Zhan, Qiwen

Adv. Opt. Photon. (1)

Appl. Opt. (10)

M. Mirotznik, D. Pustai, D. Prather, and J. Mait, “Design of two-dimensional polarization-selective diffractive optical elements with form-birefringent microstructures,” Appl. Opt. 43, 5947-5954 (2004).
[CrossRef]

Jeffrey A. Davis, Garrett H. Evans, and Ignacio Moreno, “Polarization-multiplexed diffractive optical elements with liquid-crystal displays,” Appl. Opt. 44, 4049-4052 (2005).
[CrossRef]

I. Moreno, J. L. Martínez, and J. A. Davis, “Two-dimensional polarization rotator using a twisted-nematic liquid-crystal display,” Appl. Opt. 46, 881-887 (2007).
[CrossRef]

N. Nieuborg, A. Kirk, B. Morlion, H. Thienpont, and I. Veretennicoff, “Polarization-selective diffractive optical elements with an index-matching gap material,” Appl. Opt. 36, 4681-4685 (1997).
[CrossRef]

U. Zeitner, B. Schnabel, E. Kley, and F. Wyrowski, “Polarization multiplexing of diffractive elements with metal-stripe grating pixels,” Appl. Opt. 38, 2177-2181 (1999).
[CrossRef]

J. A. Davis, D. E. McNamara, D. M. Cottrell, and T. Sonehara, “Two dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator,” Appl. Opt. 39, 1549-1554 (2000).
[CrossRef]

F. Xu, J. E. Ford, and Y. Fainman, “Polarization-selective computer-generated holograms: design, fabrication, and applications,” Appl. Opt. 34, 256-266 (1995)
[CrossRef]

A. V. Krishnamoorthy, F. Xu, J. E. Ford, and Y. Fainman, “Polarization-controlled multistage switch based on polarization-selective computer-generated holograms,” Appl. Opt. 36, 997-1010 (1997).
[CrossRef]

J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937-945 (1998).
[CrossRef]

W. Yu, T. Konishi, T. Hamamoto, H. Toyota, T. Yotsuya, and Y. Ichioka, “Polarization-multiplexed diffractive optical elements fabricated by subwavelength structures,” Appl. Opt. 41, 96-100 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

K. J. Moh, X. C. Yuan, J. Bu, D. K. Y. Low, and R. E. Burge, “Direct noninterference cylindrical vector beam generation applied in the femtosecond regime,” Appl. Phys. Lett. 89, 251114 (2006).
[CrossRef]

Opt. Commun. (2)

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radiallyand azimuthally-polarized beams,” Opt. Commun. 281, 732-738 (2008).
[CrossRef]

P. C. Mogensen and J. Gluckstad, “A phase-based optical encryption system with polarisation encoding,” Opt. Commun. 173, 177-183 (2000).
[CrossRef]

Opt. Eng. (1)

S. Sanyal, P. Bandyopadhyay, and A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592-599(1998).
[CrossRef]

Opt. Express (2)

Opt. Lett. (10)

M. A. Ahmed, A. Voss, M. M. Vogel, and T. Graf, “Multilayer polarizing grating mirror used for the generation of radial polarization inYb:YAG thin-disk lasers,” Opt. Lett. 32, 3272-3274 (2007).
[CrossRef]

X. L. Wang, J. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement,” Opt. Lett. 32, 3549-3551 (2007).
[CrossRef]

B. C. Lim, P. B. Phua, W. J. Lai, and M. H. Hong, “Fast switchable electro-optic radial polarization retarder,” Opt. Lett. 33, 950-952 (2008).
[CrossRef]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27, 285-287(2002).
[CrossRef]

Z. Bomzon, V. Kleiner, and E. Hasman, “Computer-generated space-variant polarization elements with subwavelength metal stripes,” Opt. Lett. 26, 33-35 (2001).
[CrossRef]

J. A. Davis, J. Adachi, C. R. Fernandez-Pousa, and I. Moreno, “Polarization beam splitters using polarization diffraction gratings,” Opt. Lett. 26, 587-589 (2001).
[CrossRef]

C. R. Fernandez-Pousa, I. Moreno, J. A. Davis, and J. Adachi, “Polarizing diffraction-grating triplicators,” Opt. Lett. 26, 1651-1653 (2001).
[CrossRef]

J. Ford, F. Xu, K. Urquhart, and Y. Fainman, “Polarization-selective computer-generated holograms,” Opt. Lett. 18, 456-458 (1993).
[CrossRef]

F. Gori, “Measuring Stokes parameters by means of polarization grating,” Opt. Lett. 24, 584-586 (1999).
[CrossRef]

F. Xu, R.-C. Tyan, P.-C. Sun, Y. Fainman, C.-C. Cheng, and A. Scherer, “Form-birefringent computergenerated holograms,” Opt. Lett. 21, 1513-1515 (1996).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Relationship between the intensity penetrated through the TN-LCD and the gray level displayed on the TN-LCD.

Fig. 2
Fig. 2

Measured phase modulations of the TN-LCD when the gray level is limited in (a) region A and (b) region B.

Fig. 3
Fig. 3

Example of the PSDOE designed according to the two orthogonal polarized encoding channels.

Fig. 4
Fig. 4

Schematic of the experimental setup.

Fig. 5
Fig. 5

Reconstructed image using the PSDOE when the output polarizer is (a) at 0 ° (vertical), (b) at 45 ° , and (c) at 90 ° .

Equations (15)

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α ( z ) = α 0 d z ,
Γ = 2 π λ ( n e n o ) d ,
= exp ( i ϕ ) R ( α 0 ) ( cos X i Γ sin X 2 X α 0 sin X X α 0 sin X X cos X + i Γ sin X 2 X ) ,
R ( α 0 ) = ( cos α 0 sin α 0 sin α 0 cos α 0 ) .
M V = exp ( i ϕ V ) m = 1 N R ( α m ) M m R ( α m ) = exp ( i ϕ V ) ( A V B V C V D V ) ,
ϕ V = π n o λ 0 d [ 1 + n e n e 2 sin 2 θ ( z ) + n o 2 cos 2 θ ( z ) ] d z ,
M m = ( exp ( i Γ m / 2 ) 0 0 exp ( i Γ m / 2 ) ) .
( E x o E y o ) = exp ( i ϕ V ) ( A V B V C V D V ) ( E x i E y i ) = exp ( i ϕ V ) ( A V E x i + B V E y i C V E x i + D V E y i ) .
( E x o E y o ) = exp ( i ϕ V ) ( A V E x i + B V E y i 0 ) ( when     V VR 1 ) ,
( E x o E y o ) = exp ( i ϕ V ) ( 0 C V E x i + D V E y i ) ( when     V VR 2 ) .
H x = 0.5 [ 1 + A x cos ( 2 π ξ R x + ϕ x ) ] ,
H y = 0.5 [ 1 + A y cos ( 2 π ξ R x + ϕ y ) ] ,
g x = T x 0 + T x 1 H x , [ V ( g x ) VR 1 ] ,
g y = T y 0 + T y 1 H y , [ V ( g y ) VR 2 ] ,
g = g x comb ( y 2 Δ ) + g y comb ( y Δ 2 Δ ) ,

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