Abstract

We present a method to generate complete arbitrary spatially variant polarization modulation of a light beam by means of a parallel aligned nematic liquid crystal spatial light modulator (SLM). We first analyze the polarization modulation properties in a transmission mode. We encode diffraction gratings onto the SLM and show how to achieve partial polarization control of the zero order transmitted light. We then extend the technique to a double modulation scheme, which is implemented using a single SLM divided in two areas in a reflective configuration. The polarization states of the transmitted beam from the first pass through the first area are rotated using two passes through a quarter wave plate. The beam then passes through the second area of the SLM where additional polarization information can be encoded. By combining previously reported techniques, we can achieve complete amplitude, phase and polarization control for the diffracted light that allows the creation of arbitrary diffractive optical elements including polarization control. Theoretical analysis based on the Jones matrix formalism, as well as excellent experimental results are presented.

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  1. J. E. Solomon, “Polarization imaging,” Appl. Opt. 20(9), 1537–1544 (1981).
    [CrossRef] [PubMed]
  2. J. A. Davis, G. H. Evans, and I. Moreno, “Polarization-multiplexed diffractive optical elements with liquid-crystal displays,” Appl. Opt. 44(19), 4049–4052 (2005).
    [CrossRef] [PubMed]
  3. Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett. 79(11), 1587–1589 (2001).
    [CrossRef]
  4. 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(10), 1549–1554 (2000).
    [CrossRef] [PubMed]
  5. 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(24), 3549–3551 (2007).
    [CrossRef] [PubMed]
  6. D. Preece, S. Keen, E. Botvinick, R. Bowman, M. Padgett, and J. Leach, “Independent polarisation control of multiple optical traps,” Opt. Express 16(20), 15897–15902 (2008).
    [CrossRef] [PubMed]
  7. C. Maurer, A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritch-Marte, “Tailoring of arbitrary optical vector beams,” New J. Phys. 9(3), 78 (2007).
    [CrossRef]
  8. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38(23), 5004–5013 (1999).
    [CrossRef] [PubMed]
  9. J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38(6), 1051–1057 (1999).
    [CrossRef]
  10. M. Taghi Tavassoly, I. Moaddel Haghighi, and K. Hassani, “Application of Fresnel diffraction from a phase step to the measurement of film thickness,” Appl. Opt. 48(29), 5497–5501 (2009).
    [CrossRef] [PubMed]
  11. J. A. Ferrari and J. L. Flores, “Nondirectional edge enhancement by contrast-reverted low-pass Fourier filtering,” Appl. Opt. 49(17), 3291–3296 (2010).
    [CrossRef] [PubMed]
  12. J. L. Horner and P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23(6), 812–816 (1984).
    [CrossRef] [PubMed]
  13. J. L. Horner and J. R. Leger, “Pattern recognition with binary phase-only filters,” Appl. Opt. 24(5), 609–611 (1985).
    [CrossRef] [PubMed]
  14. J. A. Davis, S. W. Flowers, D. M. Cottrell, and R. A. Lilly, “Smoothing of the edge-enhanced impulse response from binary phase-only filters using random binary patterns,” Appl. Opt. 28(15), 2987–2988 (1989).
    [CrossRef] [PubMed]
  15. C. Zhou and L. Liu, “Numerical study of Dammann array illuminators,” Appl. Opt. 34(26), 5961–5969 (1995).
    [CrossRef] [PubMed]
  16. I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X.-C. Yuan, “Encoding generalized phase functions on Dammann gratings,” Opt. Lett. 35(10), 1536–1538 (2010).
    [CrossRef] [PubMed]
  17. J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37(5), 937–945 (1998).
    [CrossRef] [PubMed]
  18. J. Nicolás and J. A. Davis, “Programmable wave plates using a twisted nematic liquid crystal display,” Opt. Eng. 41(12), 3004–3005 (2002).
    [CrossRef]
  19. J. Luis Martínez, I. Moreno, J. A. Davis, T. J. Hernandez, and K. P. McAuley, “Extended phase modulation depth in twisted nematic liquid crystal displays,” Appl. Opt. 49(30), 5929–5937 (2010).
    [CrossRef] [PubMed]

2010 (3)

2009 (1)

2008 (1)

2007 (2)

2005 (1)

2002 (1)

J. Nicolás and J. A. Davis, “Programmable wave plates using a twisted nematic liquid crystal display,” Opt. Eng. 41(12), 3004–3005 (2002).
[CrossRef]

2001 (1)

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett. 79(11), 1587–1589 (2001).
[CrossRef]

2000 (1)

1999 (2)

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38(6), 1051–1057 (1999).
[CrossRef]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38(23), 5004–5013 (1999).
[CrossRef] [PubMed]

1998 (1)

1995 (1)

1989 (1)

1985 (1)

1984 (1)

1981 (1)

Amako, J.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38(6), 1051–1057 (1999).
[CrossRef]

Bernet, S.

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

Bomzon, Z.

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett. 79(11), 1587–1589 (2001).
[CrossRef]

Botvinick, E.

Bowman, R.

Campos, J.

Cottrell, D. M.

Davis, J. A.

I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X.-C. Yuan, “Encoding generalized phase functions on Dammann gratings,” Opt. Lett. 35(10), 1536–1538 (2010).
[CrossRef] [PubMed]

J. Luis Martínez, I. Moreno, J. A. Davis, T. J. Hernandez, and K. P. McAuley, “Extended phase modulation depth in twisted nematic liquid crystal displays,” Appl. Opt. 49(30), 5929–5937 (2010).
[CrossRef] [PubMed]

J. A. Davis, G. H. Evans, and I. Moreno, “Polarization-multiplexed diffractive optical elements with liquid-crystal displays,” Appl. Opt. 44(19), 4049–4052 (2005).
[CrossRef] [PubMed]

J. Nicolás and J. A. Davis, “Programmable wave plates using a twisted nematic liquid crystal display,” Opt. Eng. 41(12), 3004–3005 (2002).
[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(10), 1549–1554 (2000).
[CrossRef] [PubMed]

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38(6), 1051–1057 (1999).
[CrossRef]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38(23), 5004–5013 (1999).
[CrossRef] [PubMed]

J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37(5), 937–945 (1998).
[CrossRef] [PubMed]

J. A. Davis, S. W. Flowers, D. M. Cottrell, and R. A. Lilly, “Smoothing of the edge-enhanced impulse response from binary phase-only filters using random binary patterns,” Appl. Opt. 28(15), 2987–2988 (1989).
[CrossRef] [PubMed]

Ding, J.

Evans, G. H.

Ferrari, J. A.

Flores, J. L.

Flowers, S. W.

Fürhapter, S.

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

Gianino, P. D.

Guo, C.-S.

Hasman, E.

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett. 79(11), 1587–1589 (2001).
[CrossRef]

Hassani, K.

Hernandez, T. J.

Horner, J. L.

Jesacher, A.

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

Keen, S.

Kleiner, V.

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett. 79(11), 1587–1589 (2001).
[CrossRef]

Leach, J.

Leger, J. R.

Lilly, R. A.

Liu, L.

Luis Martínez, J.

Maurer, C.

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

McAuley, K. P.

McNamara, D. E.

Moaddel Haghighi, I.

Moreno, I.

Ni, W.-J.

Nicolás, J.

J. Nicolás and J. A. Davis, “Programmable wave plates using a twisted nematic liquid crystal display,” Opt. Eng. 41(12), 3004–3005 (2002).
[CrossRef]

Padgett, M.

Preece, D.

Ritch-Marte, M.

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

Solomon, J. E.

Sonehara, T.

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(10), 1549–1554 (2000).
[CrossRef] [PubMed]

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38(6), 1051–1057 (1999).
[CrossRef]

Taghi Tavassoly, M.

Tsai, P.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38(6), 1051–1057 (1999).
[CrossRef]

J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37(5), 937–945 (1998).
[CrossRef] [PubMed]

Wang, H.-T.

Wang, X.-L.

Yuan, X.-C.

Yzuel, M. J.

Zhang, N.

Zhou, C.

Appl. Opt. (12)

J. E. Solomon, “Polarization imaging,” Appl. Opt. 20(9), 1537–1544 (1981).
[CrossRef] [PubMed]

J. L. Horner and P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23(6), 812–816 (1984).
[CrossRef] [PubMed]

J. A. Davis, S. W. Flowers, D. M. Cottrell, and R. A. Lilly, “Smoothing of the edge-enhanced impulse response from binary phase-only filters using random binary patterns,” Appl. Opt. 28(15), 2987–2988 (1989).
[CrossRef] [PubMed]

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(10), 1549–1554 (2000).
[CrossRef] [PubMed]

C. Zhou and L. Liu, “Numerical study of Dammann array illuminators,” Appl. Opt. 34(26), 5961–5969 (1995).
[CrossRef] [PubMed]

J. A. Davis, I. Moreno, and P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37(5), 937–945 (1998).
[CrossRef] [PubMed]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38(23), 5004–5013 (1999).
[CrossRef] [PubMed]

J. A. Davis, G. H. Evans, and I. Moreno, “Polarization-multiplexed diffractive optical elements with liquid-crystal displays,” Appl. Opt. 44(19), 4049–4052 (2005).
[CrossRef] [PubMed]

J. L. Horner and J. R. Leger, “Pattern recognition with binary phase-only filters,” Appl. Opt. 24(5), 609–611 (1985).
[CrossRef] [PubMed]

M. Taghi Tavassoly, I. Moaddel Haghighi, and K. Hassani, “Application of Fresnel diffraction from a phase step to the measurement of film thickness,” Appl. Opt. 48(29), 5497–5501 (2009).
[CrossRef] [PubMed]

J. A. Ferrari and J. L. Flores, “Nondirectional edge enhancement by contrast-reverted low-pass Fourier filtering,” Appl. Opt. 49(17), 3291–3296 (2010).
[CrossRef] [PubMed]

J. Luis Martínez, I. Moreno, J. A. Davis, T. J. Hernandez, and K. P. McAuley, “Extended phase modulation depth in twisted nematic liquid crystal displays,” Appl. Opt. 49(30), 5929–5937 (2010).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings,” Appl. Phys. Lett. 79(11), 1587–1589 (2001).
[CrossRef]

New J. Phys. (1)

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

Opt. Eng. (2)

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38(6), 1051–1057 (1999).
[CrossRef]

J. Nicolás and J. A. Davis, “Programmable wave plates using a twisted nematic liquid crystal display,” Opt. Eng. 41(12), 3004–3005 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

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Figures (9)

Fig. 1
Fig. 1

Figure shows how (a) vertical and (b) horizontal polarization components of light are affected after passing through the LC-SLM that is encoded with a diffraction grating. Only the vertical polarization component is affected.

Fig. 2
Fig. 2

(a) Blazed grating with variable depth of phase MA and (b) corresponding intensity of the first and zero diffraction order versus MA. (c) the diffracted light efficiency can vary spatially by applying a spatially variant blazed grating. (d) application of a phase bias φA to the blazed grating.

Fig. 3
Fig. 3

Experimental configuration for the single pass experiment.

Fig. 4
Fig. 4

(a) Grating mask. (b) Output images are shown using a linear polarizer analyzer oriented at 0°, 45°, 90°, 135° and with right and left circularly polarizer analyzers.

Fig. 5
Fig. 5

Figure shows how (a) horizontal and (b) vertical polarization components of light are affected after passing a second time through a different part of the LC-SLM that is encoded with a different diffraction grating. The polarization states of Fig. 1 have been rotated by 90°. Again, only the vertical polarization component (which was the previous horizontal polarization component in the first pass) is affected.

Fig. 6
Fig. 6

Experimental configuration for the double pass experiment.

Fig. 7
Fig. 7

Mask and experimental results from the double modulation polarization control when encoding two polarization sensitive diffractive elements. (a)-(d) the Fourier transform computer generated holograms reproducing letters “SDSU” and “UMH”; (e)-(h) 2D Dammann gratings with 4x4 and 5x5 diffraction orders. The analyzer polarizer is oriented horizontally in (b) and (f), at 45° from the vertical axis in (c) and (g) and vertically in (d) and (h).

Fig. 8
Fig. 8

Experimental results when the same pattern “SDSU” is encoded on both sides of the SLM, but a phase bias φB is added on one side with respect to the other (corresponding to the different rows). In each column an analyzer polarizer is placed before the CCD, linear at 0°, 45°, 90° and 135°, and circular right and left.

Fig. 9
Fig. 9

(a) Central detail of the phase mask displayed on the SLM. (b) Experimental results when the same amplitude and phase pattern designed to generate a rectangle is encoded on both sides of the SLM, but with a phase bias φB added on one side relative to the other. In each column an analyzer polarizer is placed before the CCD, linear at 0°, 45°, 90° and 135°, and circular right and left.

Equations (7)

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

E A ( x )=( cos( θ ) A 0 e i ϕ A sin( θ ) )+( cos( θ ) A 1 e i ϕ A 0 ) e i2πx/ d A ,
E=( sin( θ ) A 0 cos( θ ) e i ϕ A )+( 0 A 1 cos( θ ) e i ϕ A e i2πx/ d A ).
E B ( x )=( B 0 sin( θ ) e i ϕ B A 0 cos( θ ) e i ϕ A )+( sin( θ ) e i ϕ B B 1 cos( θ ) e i ϕ A A 1 ) e i2πx/ d 0 ,
E B ( x,y )= 1 2 ( e iϕ g B ( x,y ) e i2πx/ d 0 e iϕ g A ( x,y ) e i2πx/ d 0 )= e iϕ g B ( x,y ) e i2πx/ d 0 2 ( 1 0 )+ e iϕ g A ( x,y ) e +i2πx/ d 0 2 ( 0 1 ),
E B ( p,q )= 1 2 ( δ( pγ )G ' B ( p,q ) )( 1 0 )+ 1 2 ( δ( p+γ )G ' A ( p,q ) )( 0 1 ).
E B ( x,y )= 1 2 ( e i ϕ g ( x,y ) e i ϕ B e +i2πx/ d 0 e i ϕ g ( x,y ) e +i2πx/ d 0 )= e i ϕ g ( x,y ) e +i2πx/ d 0 2 ( e i ϕ B 1 ),
E B ( p,q )=[ δ( pγ )G'( p,q ) ] 1 2 ( e i ϕ B 1 ).

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