Abstract

We study the modulation of programmable birefringent devices when they are illuminated by elliptically polarized light. We apply the theory to liquid-crystal display panels (LCDs). We consider the setups at the input and the output sides of the LCD as polarization-state generators (PSGs) or detectors (PSDs). We demonstrate that once the programmable birefringent device is described by a physical model, the amplitude and phase modulation depend only on the polarization state at the input of the device and on the output state detected behind it. This permits optimization of the modulation response only in terms of the input and the output states and the physical model of the device. The procedure to find the PSG and PSD configurations is detailed by using a geometrical interpretation of the states and the plates on the Poincaré sphere.

© 2002 Optical Society of America

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References

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  1. H. K. Liu, J. A. Davis, R. A. Lilly, “Optical data-processing properties of a liquid-crystal television spatial light modulator,” Opt. Lett. 10, 635–637 (1985).
    [CrossRef] [PubMed]
  2. F. T. S. Yu, S. Jutamulia, X. L. Huang, “Experimental application of low-cost liquid crystal TV to white-light optical signal processing,” Appl. Opt. 25, 3324–3326 (1986).
    [CrossRef] [PubMed]
  3. B. Javidi, T. Nomura, “Polarization encoding for optical security systems,” Opt. Eng. 39, 2439–2443 (2000).
    [CrossRef]
  4. G. Unnikrishnan, M. Pohit, K. Singh, “A polarization encoded optical encryption system using ferroelectric spatial light modulator,” Opt. Commun. 185, 25–31 (2000).
    [CrossRef]
  5. V. Laude, “Twisted-nematic liquid-crystal pixilated active lens,” Opt. Commun. 153, 134–152 (1998).
    [CrossRef]
  6. A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. Davis, M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator,” Appl. Opt. 40, 2316–2322 (2001).
    [CrossRef]
  7. R. C. Jones, “A new calculus for the treatment of optical systems. Description and discussion of the calculus,” J. Opt. Soc. Am. 31, 488–493 (1941).
    [CrossRef]
  8. C. R. Fernández-Pousa, I. Moreno, N. Bennis, C. Gómez-Reino, “Generalized formulation and symmetry properties of reciprocal nonabsorbing polarization devices: application to liquid-crystal displays,” J. Opt. Soc. Am. A 17, 2074–2080 (2000).
    [CrossRef]
  9. K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
    [CrossRef]
  10. J. A. Coy, M. Zaldarriaga, D. F. Grosz, O. E. Martinez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
    [CrossRef]
  11. A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
    [CrossRef]
  12. J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
    [CrossRef]
  13. I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 1–5 (1998).
  14. A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” Opt. Eng. 40, 2558–2564 (2001).
    [CrossRef]
  15. H. G. Jerrard, “Transmission of light through birefringent and optically active media: the Poincaré sphere,” J. Opt. Soc. Am. 44, 634–640 (1954).
    [CrossRef]
  16. D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25, 802–804 (2000).
    [CrossRef]
  17. R. M. A. Azzam, “Poincaré sphere representation of the fixed-polarizer rotating-retarder optical system,” J. Opt. Soc. Am. A 17, 2105–2107 (2000).
    [CrossRef]
  18. S. Huard, Polarisation de la Lumière (Masson, Paris, 1994).
  19. C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
    [CrossRef]
  20. J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
    [CrossRef]
  21. J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
    [CrossRef]

2001 (2)

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. Davis, M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator,” Appl. Opt. 40, 2316–2322 (2001).
[CrossRef]

2000 (6)

C. R. Fernández-Pousa, I. Moreno, N. Bennis, C. Gómez-Reino, “Generalized formulation and symmetry properties of reciprocal nonabsorbing polarization devices: application to liquid-crystal displays,” J. Opt. Soc. Am. A 17, 2074–2080 (2000).
[CrossRef]

R. M. A. Azzam, “Poincaré sphere representation of the fixed-polarizer rotating-retarder optical system,” J. Opt. Soc. Am. A 17, 2105–2107 (2000).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

B. Javidi, T. Nomura, “Polarization encoding for optical security systems,” Opt. Eng. 39, 2439–2443 (2000).
[CrossRef]

G. Unnikrishnan, M. Pohit, K. Singh, “A polarization encoded optical encryption system using ferroelectric spatial light modulator,” Opt. Commun. 185, 25–31 (2000).
[CrossRef]

D. S. Sabatke, M. R. Descour, E. L. Dereniak, W. C. Sweatt, S. A. Kemme, G. S. Phipps, “Optimization of retardance for a complete Stokes polarimeter,” Opt. Lett. 25, 802–804 (2000).
[CrossRef]

1999 (2)

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

1998 (3)

V. Laude, “Twisted-nematic liquid-crystal pixilated active lens,” Opt. Commun. 153, 134–152 (1998).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 1–5 (1998).

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

1996 (1)

J. A. Coy, M. Zaldarriaga, D. F. Grosz, O. E. Martinez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

1994 (1)

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

1990 (1)

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

1986 (1)

1985 (1)

1954 (1)

1941 (1)

Allison, D. B.

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 1–5 (1998).

Azzam, R. M. A.

Bennis, N.

Campos, J.

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. Davis, M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator,” Appl. Opt. 40, 2316–2322 (2001).
[CrossRef]

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

Coy, J. A.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, O. E. Martinez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

D’Nelly, K. G.

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 1–5 (1998).

Davis, J. A.

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. Davis, M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator,” Appl. Opt. 40, 2316–2322 (2001).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 1–5 (1998).

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

H. K. Liu, J. A. Davis, R. A. Lilly, “Optical data-processing properties of a liquid-crystal television spatial light modulator,” Opt. Lett. 10, 635–637 (1985).
[CrossRef] [PubMed]

Dereniak, E. L.

Descour, M. R.

Escalera, J. C.

Fernández-Pousa, C. R.

Gómez-Reino, C.

Grosz, D. F.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, O. E. Martinez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

Huang, X. L.

Huard, S.

S. Huard, Polarisation de la Lumière (Masson, Paris, 1994).

Iemmi, C.

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. Davis, M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator,” Appl. Opt. 40, 2316–2322 (2001).
[CrossRef]

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

Javidi, B.

B. Javidi, T. Nomura, “Polarization encoding for optical security systems,” Opt. Eng. 39, 2439–2443 (2000).
[CrossRef]

Jerrard, H. G.

Jones, R. C.

Jutamulia, S.

Kemme, S. A.

Laude, V.

V. Laude, “Twisted-nematic liquid-crystal pixilated active lens,” Opt. Commun. 153, 134–152 (1998).
[CrossRef]

Ledesma, S.

Lilly, R. A.

Liu, H. K.

Lu, K.

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Márquez, A.

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. Davis, M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator,” Appl. Opt. 40, 2316–2322 (2001).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

Martinez, O. E.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, O. E. Martinez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

Moreno, A.

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

Moreno, I.

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

C. R. Fernández-Pousa, I. Moreno, N. Bennis, C. Gómez-Reino, “Generalized formulation and symmetry properties of reciprocal nonabsorbing polarization devices: application to liquid-crystal displays,” J. Opt. Soc. Am. A 17, 2074–2080 (2000).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 1–5 (1998).

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

Nomura, T.

B. Javidi, T. Nomura, “Polarization encoding for optical security systems,” Opt. Eng. 39, 2439–2443 (2000).
[CrossRef]

Phipps, G. S.

Pohit, M.

G. Unnikrishnan, M. Pohit, K. Singh, “A polarization encoded optical encryption system using ferroelectric spatial light modulator,” Opt. Commun. 185, 25–31 (2000).
[CrossRef]

Robert, A.

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

Sabatke, D. S.

Saleh, B. E. A.

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

Singh, K.

G. Unnikrishnan, M. Pohit, K. Singh, “A polarization encoded optical encryption system using ferroelectric spatial light modulator,” Opt. Commun. 185, 25–31 (2000).
[CrossRef]

Soutar, C.

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

Sweatt, W. C.

Tsai, P.

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

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

Unnikrishnan, G.

G. Unnikrishnan, M. Pohit, K. Singh, “A polarization encoded optical encryption system using ferroelectric spatial light modulator,” Opt. Commun. 185, 25–31 (2000).
[CrossRef]

Wilson, M. L.

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

Yu, F. T. S.

Yzuel, M. J.

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

A. Márquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. Davis, M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator,” Appl. Opt. 40, 2316–2322 (2001).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

Zaldarriaga, M.

J. A. Coy, M. Zaldarriaga, D. F. Grosz, O. E. Martinez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

G. Unnikrishnan, M. Pohit, K. Singh, “A polarization encoded optical encryption system using ferroelectric spatial light modulator,” Opt. Commun. 185, 25–31 (2000).
[CrossRef]

V. Laude, “Twisted-nematic liquid-crystal pixilated active lens,” Opt. Commun. 153, 134–152 (1998).
[CrossRef]

Opt. Eng. (9)

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 240–246 (1990).
[CrossRef]

J. A. Coy, M. Zaldarriaga, D. F. Grosz, O. E. Martinez, “Characterization of a liquid crystal television as a programmable spatial light modulator,” Opt. Eng. 35, 15–19 (1996).
[CrossRef]

A. Márquez, J. Campos, M. J. Yzuel, I. Moreno, J. A. Davis, C. Iemmi, A. Moreno, A. Robert, “Characterization of edge effects in twisted nematic liquid crystal displays,” Opt. Eng. 39, 3301–3307 (2000).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D’Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 37, 1–5 (1998).

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, I. Moreno, “Ambiguities in measuring the physical parameters for twisted-nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 705–709 (1999).
[CrossRef]

J. A. Davis, P. Tsai, K. G. D’Nelly, I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. 38, 929–932 (1999).
[CrossRef]

B. Javidi, T. Nomura, “Polarization encoding for optical security systems,” Opt. Eng. 39, 2439–2443 (2000).
[CrossRef]

Opt. Lett. (2)

Other (1)

S. Huard, Polarisation de la Lumière (Masson, Paris, 1994).

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Figures (8)

Fig. 1
Fig. 1

Elliptic PSG composed of a linear polarizer and a phase retarder.

Fig. 2
Fig. 2

Elliptic PSD. (a) An arbitrary state can be decomposed into two elliptical components orthogonal to each other. (b) The PSD transmits one and extinguishes the other.

Fig. 3
Fig. 3

Setup for modulation of light with elliptic polarization. The system is composed of a PSG, an addressable nonabsorbing polarizing device, LCD, and a PSD. LP’s are linear polarizers and WP’s are wave plates.

Fig. 4
Fig. 4

(a) Representation of a polarization state |χ, ϕ〉 in the Poincaré sphere. (b) Relation between the state and the parameters of the ellipse.

Fig. 5
Fig. 5

Spherical triangle on the Poincaré sphere. One of the vertices is the polarization state to be generated |χ, ϕ〉. The sides of the triangle represent the parameters of two different wave-plate-and-polarizer ensembles that generate the polarization state.

Fig. 6
Fig. 6

Representation of the states that can be reached by a wave plate with retardance Γ. “A” represents a state that can be reached with two different angle combinations. “B” represents a state that can be achieved with a unique combination for this wave plate and linear polarizer. “C” represents a state that cannot be reached with this wave plate.

Fig. 7
Fig. 7

Values of the LCD beta and delta used versus the displayed gray level.

Fig. 8
Fig. 8

Modulation obtained. (a) Phase modulation versus the displayed gray level, (b) amplitude transmission versus the gray level. Two different configurations (A and B in Table 1) and the corresponding theoretical prediction are represented.

Tables (1)

Tables Icon

Table 1 Angles θ and Retardance ϕ for the Polarizing Elements (Fig. 3) Used in Four Possible Configurations

Equations (32)

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

|A=I exp(iϕ1)cos χI exp(iϕ2)sin χ.
|χ, ϕ=cos χexp(iϕ)sin χ,
|χ, ϕ=sin χ-exp(iϕ)cos χ.
J|K=(JX*, JY*)KXKY,
|J=|χ, ϕχ, ϕ|J+|χ, ϕχ, ϕ|J,
|J=|χ, ϕA exp(iα)+|χ, ϕB exp(iβ).
|A=I exp(iϕ1)|χ, ϕ.
W(ϕ)|χ, 0=100exp(iϕ)cos χsin χ=cos χexp(iϕ)sin χ=|χ, ϕ,
W(ϕ)P(χ)=|χ, ϕ χ, 0|.
P(χ)W(-ϕ)|J=P(χ)W(-ϕ)|χ, ϕχ, ϕ|J+P(χ)W(-ϕ)|χ, ϕχ, ϕ|J.
P(χ)W(-ϕ)=|χ, 0χ, ϕ|.
W(θW, ϕ)P(χ+θW)=|χ, ϕχ, 0|,
P(χ+θW)W(θW,-ϕ)=|χ, 0χ, ϕ|,
MSLM=P(θP2)·W(θW2, ϕ2)·ULCD(V)·W(θW1, ϕ1)·P(θP1).
MSLM=|χout, 0χout, ϕout|ULCD(V)|χin, ϕinχin, 0|,
μ(V)=χout, ϕout|ULCD(V)|χin, ϕinχin, 0|Jχin, 0|J
=χout, ϕout|ULCD(V)|χin, ϕin,
μ(V)=i,j=x, yχout, ϕout|ij|χin, ϕinUij(V),
μ(V)=U11(V)cos χout cos χin+U12(V)cos χout exp(iϕin)sin χin+U21(V)exp(-iϕout)sin χout cos χin+U22(V)exp[i(ϕin-ϕout)]sin χout sin χin.
FPO[μ]=λ1(max[0, Vmax][arg μ]-min[0, Vmax][arg μ])+λ2E[μ*μ]+λ3(var[μ*μ])-1.
|χ, ϕ=R(θWP)|θLP-θWP, Γ,
sin 2ε=sin 2χ sin ϕ,
tan 2α=tan 2χ cos ϕ.
sin 2(θLP-θWP)=sin ϕ sin 2χsin Γ,
tan θWP=-cosϕ-Γ2cosϕ+Γ2tan(θLP-θWP).
ULCD(α, β(V), δ(V))=exp[-i(β+2δ)]R(-α-ψD)×X-iYZ-ZX+iYR(ψD),
X=cos γ cos 2δ-βγsin γ sin 2δ,
Y=cos γ sin 2δ+βγsin γ cos 2δ,
Z=αγsin γ cos 2δ,
γ2=α2+β2.
|χin, ϕin=|36.40°47.53°,
|χout, ϕout=|23.32°217.08°.

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