Abstract

We derive theoretical expressions for the eigenvalues and the eigenvectors for a twisted-nematic liquid-crystal display (LCD) as a function of the twist angle and the birefringence by use of the Jones-matrix formalism. These polarization eigenvectors are of particular interest for phase-only transmission because they propagate unchanged through the display. We find that the eigenvectors are elliptically polarized and that the ellipticity changes as a function of the birefringence of the LCD (which is proportional to the external voltage applied to the display). We can define an average eigenvector over a desired range for the applied voltage. We show, using Jones matrices, how this average eigenvector can be generated using a quarter-wave plate and a linear polarizer having appropriate orientation angles. Using this average eigenvector, we show that superior phase-only operation can be obtained over a given operating range for the LCD compared with other approaches.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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. D. A. Gregory, “Real-time pattern recognition using a modified liquid crystal television in a coherent optical correlator,” Appl. Opt. 25, 467–469 (1986).
    [CrossRef] [PubMed]
  3. 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]
  4. J. Amako, T. Sonehara, “Computer generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
    [CrossRef]
  5. N. Clark, C. M. Crancall, M. K. Giles, “Using liquid crystal TV’s in Vander Lugt optical correlators,” in Optical Information Processing Systems and Architectures III, Bahram Javidi, ed., Proc. SPIE1564, 439–451 (1991).
    [CrossRef]
  6. J. Amako, T. Sonehara, “Kinoform using an electrically controlled birefringent liquid-crystal spatial light modulator,” Appl. Opt. 30, 4622–4628 (1991).
    [CrossRef] [PubMed]
  7. T. H. Barnes, T. Eiju, K. Matsuda, N. Ooyama, “Phase-only modulation using a twisted nematic liquid crystal television,” Appl. Opt. 28, 4845–4852 (1989).
    [CrossRef] [PubMed]
  8. C. Soutar, S. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
    [CrossRef]
  9. C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
    [CrossRef]
  10. L. Neto, D. Roberge, Y. Sheng, “Programmable optical phase-mostly holograms with coupled-mode modulation liquid-crystal television,” Appl. Opt. 34, 1944–1950 (1995).
    [CrossRef] [PubMed]
  11. L. G. Neto, D. Roberge, Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35, 4567–4576 (1996).
    [CrossRef] [PubMed]
  12. J. L. Pezzaniti, R. A. Chipman, “Phase-only modulation of a twisted nematic liquid-crystal TV by use of the eigenpolarization states,” Opt. Lett. 18, 1567–1569 (1993).
    [CrossRef] [PubMed]
  13. C. Soutar, S. Monroe, “Selection of operating curves of twisted-nematic liquid crystal televisions,” in Advances in Optical Information Processing VI, Dennis R. Pape, ed., Proc. SPIE2240, 280–291 (1994).
    [CrossRef]
  14. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.
  15. 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]
  16. The analysis for the major axis direction and the ellipticity for elliptically polarized light is given in many textbooks. See, for example, R. Guenther , Modern Optics (Wiley, New York, 1990), Chap. 5.
  17. 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]

1996

L. G. Neto, D. Roberge, Y. Sheng, “Full-range, continuous, complex modulation by the use of two coupled-mode liquid-crystal televisions,” Appl. Opt. 35, 4567–4576 (1996).
[CrossRef] [PubMed]

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]

1995

1994

C. Soutar, S. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[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]

1993

1991

1990

J. Amako, T. Sonehara, “Computer generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
[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]

1989

1986

1985

Amako, J.

J. Amako, T. Sonehara, “Kinoform using an electrically controlled birefringent liquid-crystal spatial light modulator,” Appl. Opt. 30, 4622–4628 (1991).
[CrossRef] [PubMed]

J. Amako, T. Sonehara, “Computer generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
[CrossRef]

Barnes, T. H.

Chipman, R. A.

Clark, N.

N. Clark, C. M. Crancall, M. K. Giles, “Using liquid crystal TV’s in Vander Lugt optical correlators,” in Optical Information Processing Systems and Architectures III, Bahram Javidi, ed., Proc. SPIE1564, 439–451 (1991).
[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]

Crancall, C. M.

N. Clark, C. M. Crancall, M. K. Giles, “Using liquid crystal TV’s in Vander Lugt optical correlators,” in Optical Information Processing Systems and Architectures III, Bahram Javidi, ed., Proc. SPIE1564, 439–451 (1991).
[CrossRef]

Davis, J. A.

Eiju, T.

Giles, M. K.

N. Clark, C. M. Crancall, M. K. Giles, “Using liquid crystal TV’s in Vander Lugt optical correlators,” in Optical Information Processing Systems and Architectures III, Bahram Javidi, ed., Proc. SPIE1564, 439–451 (1991).
[CrossRef]

Gregory, D. A.

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]

Guenther, R.

The analysis for the major axis direction and the ellipticity for elliptically polarized light is given in many textbooks. See, for example, R. Guenther , Modern Optics (Wiley, New York, 1990), Chap. 5.

Huang, X. L.

Jutamulia, S.

Knopp, J.

C. Soutar, S. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

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]

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]

Matsuda, K.

Monroe, S.

C. Soutar, S. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

C. Soutar, S. Monroe, “Selection of operating curves of twisted-nematic liquid crystal televisions,” in Advances in Optical Information Processing VI, Dennis R. Pape, ed., Proc. SPIE2240, 280–291 (1994).
[CrossRef]

Neto, L.

Neto, L. G.

Ooyama, N.

Pezzaniti, J. L.

Roberge, D.

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]

Sheng, Y.

Sonehara, T.

J. Amako, T. Sonehara, “Kinoform using an electrically controlled birefringent liquid-crystal spatial light modulator,” Appl. Opt. 30, 4622–4628 (1991).
[CrossRef] [PubMed]

J. Amako, T. Sonehara, “Computer generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
[CrossRef]

Soutar, C.

C. Soutar, S. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[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]

C. Soutar, S. Monroe, “Selection of operating curves of twisted-nematic liquid crystal televisions,” in Advances in Optical Information Processing VI, Dennis R. Pape, ed., Proc. SPIE2240, 280–291 (1994).
[CrossRef]

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.

Yu, F. T. S.

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.

Jpn. J. Appl. Phys.

J. Amako, T. Sonehara, “Computer generated hologram using TFT active matrix liquid crystal spatial light modulator (TFT-LCSLM),” Jpn. J. Appl. Phys. 29, L1533–L1535 (1990).
[CrossRef]

Opt. Eng.

C. Soutar, S. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[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]

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]

Opt. Lett.

Other

C. Soutar, S. Monroe, “Selection of operating curves of twisted-nematic liquid crystal televisions,” in Advances in Optical Information Processing VI, Dennis R. Pape, ed., Proc. SPIE2240, 280–291 (1994).
[CrossRef]

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 5.

The analysis for the major axis direction and the ellipticity for elliptically polarized light is given in many textbooks. See, for example, R. Guenther , Modern Optics (Wiley, New York, 1990), Chap. 5.

N. Clark, C. M. Crancall, M. K. Giles, “Using liquid crystal TV’s in Vander Lugt optical correlators,” in Optical Information Processing Systems and Architectures III, Bahram Javidi, ed., Proc. SPIE1564, 439–451 (1991).
[CrossRef]

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 (10)

Fig. 1
Fig. 1

Orientations of incident and transmitted elliptically polarized rotated eigenvectors relative to the entrance and the exit director axes for the LCD.

Fig. 2
Fig. 2

Ellipticity for the rotated eigenvectors for a LCD as a function of birefringence (assuming a twist angle of α = π/2 rad).

Fig. 3
Fig. 3

Phase shifts for the two rotated eigenvectors for a LCD as a function of birefringence (assuming a twist angle of α = π/2 rad).

Fig. 4
Fig. 4

Orientations of incident and transmitted elliptically polarized classic eigenvectors relative to the entrance and the exit director axes for the LCD.

Fig. 5
Fig. 5

Ellipticity for the classic eigenvectors for a LCD as a function of birefringence (with the assumption of a twist angle of α = π/2 rad).

Fig. 6
Fig. 6

Phase shifts for the two classic eigenvectors for a LCD as a function of birefringence (assuming a twist angle of α = π/2 rad).

Fig. 7
Fig. 7

Ellipticity for elliptically polarized light produced when linearly polarized light is incident at an angle ξ relative to the fast axis for a quarter-wave plate.

Fig. 8
Fig. 8

Transmitted light intensity as a function of birefringence with linear polarizers used at the entrance and at the exit for a LCD (with the assumption of a twist angle of α = π/2 rad). Two cases are shown: (a) a birefringence range from 0 to 3 rad, with polarizer angles ψ1 = -25° and ψ2 = -73°; (b) a birefringence range from 3 to 6 rad, with polarizer angles ψ1 = 0° and ψ2 = 90°.

Fig. 9
Fig. 9

Transmitted light intensity as a function of birefringence for a LCD (assuming a twist angle of α = π/2 rad) when an average elliptically polarized eigenvector is generated and detected. Two cases are shown: (a) birefringence range from 0 to 3 rad, polarizer angles at ξ = ±35° relative to the fast axes for the quarter-wave plates; (b) birefringence range from 3 to 6 rad, polarizer angles ξ = ±10.1° relative to the fast axes for the quarter-wave plates.

Fig. 10
Fig. 10

Transmitted light intensity as a function of birefringence for a LCD (assuming a twist angle of α = π/2 rad) when an average elliptically polarized eigenvector is generated and only a linearly polarized component is detected. Two cases are shown: (a) birefringence range from 0 to 3 rad, incident polarizer angle at ξ = 45° relative to the fast axis for the quarter-wave plate, output polarizer aligned along the direction of the output director axis; (b) birefringence range from 3 to 6 rad, incident polarizer angle at ξ = 10° relative to the fast axis for the quarter-wave plate, output polarizer aligned along the direction of the output director axis.

Equations (35)

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

M LCD = exp - i β R - α M α ,   β .
R θ = cos   θ - sin   θ       sin   θ       cos   θ .
M α ,   β = cos   γ - i β   sin   γ / γ - α   sin   γ / γ α   sin   γ / γ cos   γ + i β   sin   γ / γ .
E T = T   exp - i δ .
M α ,   β E λ = λ E λ .
R - α M α ,   β E λ = λ R - α E λ .
cos   γ - i β   sin   γ / γ - λ - α   sin   γ / γ α   sin   γ / γ cos   γ + i β   sin   γ / γ - λ = 0 .
λ ± = exp - i β exp ± i γ .
cos   γ - i β   sin   γ / γ - λ ± - α   sin   γ / γ α   sin   γ / γ cos   γ + i β   sin   γ / γ - λ ± E λ ± x E λ ± y = 0 .
E λ ( + ) = [ α ( 2 γ 2 + 2 β γ ) 1 / 2 i ( β + γ ) ( 2 γ 2 + 2 β γ ) 1 / 2 ] ,
E λ ( - ) = [ ( β + γ ) ( 2 γ 2 + 2 β γ ) 1 / 2 - i α ( 2 γ 2 + 2 β γ ) 1 / 2 ] .
E m E M = α β + γ ,
δ = β - ± γ .
E λ ( + ) = 0 1 ,
E λ ( ) = 1 0 .
π   sin   γ / 2 γ - χ cos   γ + i β   sin   γ / γ - cos   γ + i β   sin   γ / γ π   sin   γ / 2 γ - χ = 0 .
χ ± = exp - i β exp ± i .
tan   = 2 γ 2 cos 2   γ + β 2 sin 2   γ 1 / 2 π   sin   γ .
E χ + = 1 2 - i   exp i θ 1 ,
E χ ( - ) = 1 2 i   exp i θ 1 ,
tan   θ = β   tan   γ γ .
E m E M = - cos   θ 1 + sin   θ ,
δ = β - ± .
E = W π / 2 ,   0 E i .
E i = cos   ξ sin   ξ .
W π / 2 ,   0 = exp + i π / 4 0 0 exp - i π / 4 .
E = cos   ξ sin   ξ exp + i π / 4 exp - i π / 4 .
E m / E M = tan   ξ ,
E = P 0 R ψ 2 R - α M α ,   β R - ψ 1 E 0 .
P 0 = 1 0 0 0 .
T = cos   γ cos ψ 1 - ψ 2 + α + α γ sin   γ ×   sin ψ 1 - ψ 2 + α 2 + β γ sin   γ   cos ψ 1 + ψ 2 - α 2 .
E = P 0 R - ξ + α R - α W π / 2 ,   0 R α × R - α M α ,   β W π / 2 ,   0 R - ξ E 0 .
T = cos 2   γ + β   sin   γ   cos   2 ξ / γ + α   sin   γ   sin   2 ξ / γ 2 .
E = P 0 R α R - α M α ,   β W π / 2 ,   0 R - ξ E 0 .
T = cos 2   γ   cos 2   ξ + β   cos   ξ + α   sin   ξ 2 sin 2   γ / γ 2 .

Metrics