Abstract

We propose to study the conditions for implementation of complex amplitude modulation on standard liquid-crystal spatial light modulators when illuminated by polarized light. The spatial light modulators are used in a conventional configuration, i.e., the voltage is applied parallel to the wave-front propagation direction. The most commonly used liquid-crystal materials are compared and their usefulness in some general applications discussed. Their specificities with respect to different modulation types and application requirements are briefly described. Typical characteristics such as response time, modulation range, and wavelength insensitivity are also discussed. Finally, as an illustration, a first attempt at nomenclature is proposed for the case of a linearly polarized light.

© 1997 Optical Society of America

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    [CrossRef]
  3. P. Pellat-Finet, M. Le Doucen, “Polarization properties of birefringence gratings,” Optik (Stuttgart) 4, 159–166 (1995).
  4. Special issue on Spatial Light Modulators for Optical Information Processing, Appl. Opt. 28, 4715–4954 (1989).
  5. A. D. Fisher, “Spatial light modulators: functional capabilities, applications, and devices,” Int. J. Optoelectron. 5, 125–167 (1990).
  6. P. G. de Gennes, J. Prost, The Physics of Liquid Crystals (Oxford U. Press, Oxford, 1994).
  7. J.-C. Khoo, S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993).
    [CrossRef]
  8. A. Sneh, J.-Y. Liu, K. M. Johnson, “High-speed analog refractive-index modulator that uses a chiral smectic liquid crystal,” Opt. Lett. 19, 305–307 (1994).
    [CrossRef] [PubMed]
  9. H. Mailer, K. L. Likins, T. R. Taylor, J. L. Fergason, “Effects of ultrasound on a nematic liquid crystal,” Appl. Phys. Lett. 18, 105–107 (1971).
    [CrossRef]
  10. R. B. Meyer, L. Liébert, L. Strzelecki, P. Keller, “Ferroelectric liquid crystal,” J. Phys. (France) 36, 67–71 (1975).
  11. L. Dupont, M. Glogarova, J. P. Marcerou, H. T. Nguyen, C. Destrade, L. Lejcek, “Linear electroclinic coupling in ferroelectric liquid crystals,” J. Phys. II 1, 831–844 (1991).
  12. N. A. Clark, S. T. Lagerwall, Liquid Crystals of One or Two Dimensional Order (Springer-Verlag, Berlin, 1980), pp. 222–236
    [CrossRef]
  13. N. A. Clark, S. T. Lagerwall, “Submicrosecond bistable electro-optic switching in LC,” Appl. Phys. Lett. 36, 899–901 (1980).
    [CrossRef]
  14. M. Killinger, J. L. de Bougrenet de la Tocnaye, P. Cambon, R. C. Chittick, W. A. Crossland, “Bistability and nonlinearity in optically addressed ferroelectric spatial light modulators: applications to neurocomputing,” Appl. Opt. 31, 3930–3936 (1992).
    [CrossRef] [PubMed]
  15. L. Le Bourhis, C. Destrade, L. Dupont, “Alignment and switching properties of AFLC,” Ferroelectrics 173, 23–36 (1995).
    [CrossRef]
  16. V. Pertuis, J. S. Patel, “Twisted smectic structures for grey scale modulator,” Ferroelectrics 149, 193–205 (1993).
    [CrossRef]
  17. L. Le Bourhis, L. Dupont, J. Angelé, “Grey level optically addressed SLM using twisted SmC* LC,” Ferroelectrics 181, 161–170 (1996).
    [CrossRef]
  18. U. Efron, S. T. Wu, T. D. Bates, “Nematic liquid crystals for spatial light modulators: recent studies,” J. Opt. Soc. Am. B 3, 247–252 (1986).
    [CrossRef]
  19. J. A. Davis, G. M. Heissenberger, R. A. Lilly, D. M. Cotrell, M. F. Bromwell, “High-efficiency optical reconstruction of binary phase-only filters using the Hughes liquid crystal light valve,” Appl. Opt. 26, 929–933 (1987).
    [CrossRef] [PubMed]
  20. K. Lu, B. E. A. Saleh, “Complex amplitude reflectance of the liquid crystal light valve,” Appl. Opt. 30, 2354–2362 (1991).
    [CrossRef] [PubMed]
  21. L. Le Bourhis, “Structure et propriétés de quelques cristaux liquides ferroélectriques et antiferroélectriques: exemples d’applications,” Ph.D. dissertation (University of Bordeaux I, Bordeaux, France, October1995), No. 1304.
  22. D. C. O’Brien, R. Mears, T. D. Wilkinson, W. A. Crossland, “Dynamic holographic interconnects that use ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 33, 2795–2803 (1994).
    [CrossRef] [PubMed]
  23. P. Joffre, G. Illiaquer, J. P. Huignard, “Electro-optic properties of nematic liquid crystals for phase modulation in the infrared,” in Electro-Optic and Magneto-Optic Materials and Applications, J. P. Castera, ed., Proc. SPIE1126, 120–124 (1989).
  24. S. Sato, “Liquid crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18, 1679–1684 (1979).
    [CrossRef]
  25. G. Anderson, I. Dahl, W. Kuczynski, S. T. Lagerwall, K. Skarp, B. Stebler, “The soft mode ferroelectric effect,” Ferroelectrics 84, 285–315 (1988).
    [CrossRef]
  26. M. O. Freeman, T. A. Brown, D. M. Walba, “Quantized complex ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 31, 3917–3929 (1992).
    [CrossRef] [PubMed]
  27. S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, “Programmable multiple level phase modulation that uses ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 34, 6652–6665 (1995).
    [CrossRef] [PubMed]
  28. P. Berthelé, H. Hamam, J. L. de Bougrenet de la Tocnaye, “Programmable CGH using FLC SLM as phase modulators,” Ferroelectrics (to be published).
  29. J. W. Goodman, “Some effects of Fourier domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
    [CrossRef]
  30. H. Hamam, J. L. de Bougrenet, “Fractional Talbot four-level phase-only holograms using ferroelectric liquid-crystal spatial light modulators,” Opt. Lett. 19, 1654–1656 (1995).
    [CrossRef]
  31. B. V. K. Kumar, Z. Bahri, “Efficient algorithm for designing a ternary valued filter yielding maximum signal to noise ratio,” Appl. Opt. 28, 1919–1925 (1989).
    [CrossRef] [PubMed]
  32. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  33. N. Konforti, E. Marom, S.-T. Wu, “Phase-only modulation with twisted nematic liquid-crystal spatial light modulators,” Opt. Lett. 13, 251–253 (1988).
    [CrossRef] [PubMed]
  34. 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]
  35. 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]
  36. D. J. Mcknight, K. M. Johnson, R. A. Serati, “256 × 256 liquid-cridtal-on-silicon spatial light modulator,” App. Opt. 33, 2775–2784 (1994).
    [CrossRef]
  37. M. Guena, “Ferroelectric liquid crystals: memorization and grey levels,” Ph.D. from University of Bretagne Occidental, Brest, France, 1996.
  38. S. A. Serati, T. K. Ewing, R. A. Serati, K. M. Johnson, D. M. Simon, “Programmable 128 × 128 LCSLM compact correlator,” in Optical Pattern Recognition IV, D. P. Casesant, ed., Proc. SPIE1959, 55–68 (1993).
    [CrossRef]
  39. H. Hamam, J. L. de Bougrenet, “Programmable joint fractional Talbot computer-generated holograms,” J. Opt. Soc. Am. A 12, 314–324 (1995).
    [CrossRef]
  40. P. Réfrégier, V. Laude, “Spatial fluctuations of an optical field modulated with spatial light modulators and noisy input signal,” J. Opt. Soc. Am. A 12, 1338–1345 (1995).
    [CrossRef]

1996 (1)

L. Le Bourhis, L. Dupont, J. Angelé, “Grey level optically addressed SLM using twisted SmC* LC,” Ferroelectrics 181, 161–170 (1996).
[CrossRef]

1995 (6)

1994 (3)

1993 (2)

1992 (2)

1991 (2)

K. Lu, B. E. A. Saleh, “Complex amplitude reflectance of the liquid crystal light valve,” Appl. Opt. 30, 2354–2362 (1991).
[CrossRef] [PubMed]

L. Dupont, M. Glogarova, J. P. Marcerou, H. T. Nguyen, C. Destrade, L. Lejcek, “Linear electroclinic coupling in ferroelectric liquid crystals,” J. Phys. II 1, 831–844 (1991).

1990 (1)

A. D. Fisher, “Spatial light modulators: functional capabilities, applications, and devices,” Int. J. Optoelectron. 5, 125–167 (1990).

1989 (3)

1988 (2)

N. Konforti, E. Marom, S.-T. Wu, “Phase-only modulation with twisted nematic liquid-crystal spatial light modulators,” Opt. Lett. 13, 251–253 (1988).
[CrossRef] [PubMed]

G. Anderson, I. Dahl, W. Kuczynski, S. T. Lagerwall, K. Skarp, B. Stebler, “The soft mode ferroelectric effect,” Ferroelectrics 84, 285–315 (1988).
[CrossRef]

1987 (1)

1986 (1)

1980 (1)

N. A. Clark, S. T. Lagerwall, “Submicrosecond bistable electro-optic switching in LC,” Appl. Phys. Lett. 36, 899–901 (1980).
[CrossRef]

1979 (1)

S. Sato, “Liquid crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18, 1679–1684 (1979).
[CrossRef]

1975 (1)

R. B. Meyer, L. Liébert, L. Strzelecki, P. Keller, “Ferroelectric liquid crystal,” J. Phys. (France) 36, 67–71 (1975).

1972 (1)

R. M. A. Azzam, N. M. Bashara, “Simplified approach to the propagation of polarized light in anisotropic media: application to liquid crystal,” J. Opt. Soc. Am. A 62, 1252–1257 (1972).
[CrossRef]

1971 (1)

H. Mailer, K. L. Likins, T. R. Taylor, J. L. Fergason, “Effects of ultrasound on a nematic liquid crystal,” Appl. Phys. Lett. 18, 105–107 (1971).
[CrossRef]

1970 (1)

J. W. Goodman, “Some effects of Fourier domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
[CrossRef]

Anderson, G.

G. Anderson, I. Dahl, W. Kuczynski, S. T. Lagerwall, K. Skarp, B. Stebler, “The soft mode ferroelectric effect,” Ferroelectrics 84, 285–315 (1988).
[CrossRef]

Angelé, J.

L. Le Bourhis, L. Dupont, J. Angelé, “Grey level optically addressed SLM using twisted SmC* LC,” Ferroelectrics 181, 161–170 (1996).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, “Simplified approach to the propagation of polarized light in anisotropic media: application to liquid crystal,” J. Opt. Soc. Am. A 62, 1252–1257 (1972).
[CrossRef]

Bahri, Z.

Barnes, T. H.

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, “Simplified approach to the propagation of polarized light in anisotropic media: application to liquid crystal,” J. Opt. Soc. Am. A 62, 1252–1257 (1972).
[CrossRef]

Bates, T. D.

Berthelé, P.

P. Berthelé, H. Hamam, J. L. de Bougrenet de la Tocnaye, “Programmable CGH using FLC SLM as phase modulators,” Ferroelectrics (to be published).

Bromwell, M. F.

Broomfield, S. E.

Brown, T. A.

Cambon, P.

Chipman, R. A.

Chittick, R. C.

Clark, N. A.

N. A. Clark, S. T. Lagerwall, “Submicrosecond bistable electro-optic switching in LC,” Appl. Phys. Lett. 36, 899–901 (1980).
[CrossRef]

N. A. Clark, S. T. Lagerwall, Liquid Crystals of One or Two Dimensional Order (Springer-Verlag, Berlin, 1980), pp. 222–236
[CrossRef]

Cotrell, D. M.

Crossland, W. A.

Dahl, I.

G. Anderson, I. Dahl, W. Kuczynski, S. T. Lagerwall, K. Skarp, B. Stebler, “The soft mode ferroelectric effect,” Ferroelectrics 84, 285–315 (1988).
[CrossRef]

Davis, J. A.

de Bougrenet, J. L.

de Bougrenet de la Tocnaye, J. L.

de Gennes, P. G.

P. G. de Gennes, J. Prost, The Physics of Liquid Crystals (Oxford U. Press, Oxford, 1994).

Destrade, C.

L. Le Bourhis, C. Destrade, L. Dupont, “Alignment and switching properties of AFLC,” Ferroelectrics 173, 23–36 (1995).
[CrossRef]

L. Dupont, M. Glogarova, J. P. Marcerou, H. T. Nguyen, C. Destrade, L. Lejcek, “Linear electroclinic coupling in ferroelectric liquid crystals,” J. Phys. II 1, 831–844 (1991).

Dupont, L.

L. Le Bourhis, L. Dupont, J. Angelé, “Grey level optically addressed SLM using twisted SmC* LC,” Ferroelectrics 181, 161–170 (1996).
[CrossRef]

L. Le Bourhis, C. Destrade, L. Dupont, “Alignment and switching properties of AFLC,” Ferroelectrics 173, 23–36 (1995).
[CrossRef]

L. Dupont, M. Glogarova, J. P. Marcerou, H. T. Nguyen, C. Destrade, L. Lejcek, “Linear electroclinic coupling in ferroelectric liquid crystals,” J. Phys. II 1, 831–844 (1991).

Efron, U.

Eiju, T.

Ewing, T. K.

S. A. Serati, T. K. Ewing, R. A. Serati, K. M. Johnson, D. M. Simon, “Programmable 128 × 128 LCSLM compact correlator,” in Optical Pattern Recognition IV, D. P. Casesant, ed., Proc. SPIE1959, 55–68 (1993).
[CrossRef]

Fergason, J. L.

H. Mailer, K. L. Likins, T. R. Taylor, J. L. Fergason, “Effects of ultrasound on a nematic liquid crystal,” Appl. Phys. Lett. 18, 105–107 (1971).
[CrossRef]

Fisher, A. D.

A. D. Fisher, “Spatial light modulators: functional capabilities, applications, and devices,” Int. J. Optoelectron. 5, 125–167 (1990).

Freeman, M. O.

Glogarova, M.

L. Dupont, M. Glogarova, J. P. Marcerou, H. T. Nguyen, C. Destrade, L. Lejcek, “Linear electroclinic coupling in ferroelectric liquid crystals,” J. Phys. II 1, 831–844 (1991).

Goodman, J. W.

J. W. Goodman, “Some effects of Fourier domain phase quantization,” IBM J. Res. Dev. 14, 478–484 (1970).
[CrossRef]

Guena, M.

M. Guena, “Ferroelectric liquid crystals: memorization and grey levels,” Ph.D. from University of Bretagne Occidental, Brest, France, 1996.

Hamam, H.

Heissenberger, G. M.

Huignard, J. P.

P. Joffre, G. Illiaquer, J. P. Huignard, “Electro-optic properties of nematic liquid crystals for phase modulation in the infrared,” in Electro-Optic and Magneto-Optic Materials and Applications, J. P. Castera, ed., Proc. SPIE1126, 120–124 (1989).

Illiaquer, G.

P. Joffre, G. Illiaquer, J. P. Huignard, “Electro-optic properties of nematic liquid crystals for phase modulation in the infrared,” in Electro-Optic and Magneto-Optic Materials and Applications, J. P. Castera, ed., Proc. SPIE1126, 120–124 (1989).

Joffre, P.

P. Joffre, G. Illiaquer, J. P. Huignard, “Electro-optic properties of nematic liquid crystals for phase modulation in the infrared,” in Electro-Optic and Magneto-Optic Materials and Applications, J. P. Castera, ed., Proc. SPIE1126, 120–124 (1989).

Johnson, K. M.

A. Sneh, J.-Y. Liu, K. M. Johnson, “High-speed analog refractive-index modulator that uses a chiral smectic liquid crystal,” Opt. Lett. 19, 305–307 (1994).
[CrossRef] [PubMed]

D. J. Mcknight, K. M. Johnson, R. A. Serati, “256 × 256 liquid-cridtal-on-silicon spatial light modulator,” App. Opt. 33, 2775–2784 (1994).
[CrossRef]

S. A. Serati, T. K. Ewing, R. A. Serati, K. M. Johnson, D. M. Simon, “Programmable 128 × 128 LCSLM compact correlator,” in Optical Pattern Recognition IV, D. P. Casesant, ed., Proc. SPIE1959, 55–68 (1993).
[CrossRef]

Keller, P.

R. B. Meyer, L. Liébert, L. Strzelecki, P. Keller, “Ferroelectric liquid crystal,” J. Phys. (France) 36, 67–71 (1975).

Khoo, J.-C.

J.-C. Khoo, S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993).
[CrossRef]

Killinger, M.

Konforti, N.

Kuczynski, W.

G. Anderson, I. Dahl, W. Kuczynski, S. T. Lagerwall, K. Skarp, B. Stebler, “The soft mode ferroelectric effect,” Ferroelectrics 84, 285–315 (1988).
[CrossRef]

Kumar, B. V. K.

Lagerwall, S. T.

G. Anderson, I. Dahl, W. Kuczynski, S. T. Lagerwall, K. Skarp, B. Stebler, “The soft mode ferroelectric effect,” Ferroelectrics 84, 285–315 (1988).
[CrossRef]

N. A. Clark, S. T. Lagerwall, “Submicrosecond bistable electro-optic switching in LC,” Appl. Phys. Lett. 36, 899–901 (1980).
[CrossRef]

N. A. Clark, S. T. Lagerwall, Liquid Crystals of One or Two Dimensional Order (Springer-Verlag, Berlin, 1980), pp. 222–236
[CrossRef]

Laude, V.

Le Bourhis, L.

L. Le Bourhis, L. Dupont, J. Angelé, “Grey level optically addressed SLM using twisted SmC* LC,” Ferroelectrics 181, 161–170 (1996).
[CrossRef]

L. Le Bourhis, C. Destrade, L. Dupont, “Alignment and switching properties of AFLC,” Ferroelectrics 173, 23–36 (1995).
[CrossRef]

L. Le Bourhis, “Structure et propriétés de quelques cristaux liquides ferroélectriques et antiferroélectriques: exemples d’applications,” Ph.D. dissertation (University of Bordeaux I, Bordeaux, France, October1995), No. 1304.

Le Doucen, M.

P. Pellat-Finet, M. Le Doucen, “Polarization properties of birefringence gratings,” Optik (Stuttgart) 4, 159–166 (1995).

Lejcek, L.

L. Dupont, M. Glogarova, J. P. Marcerou, H. T. Nguyen, C. Destrade, L. Lejcek, “Linear electroclinic coupling in ferroelectric liquid crystals,” J. Phys. II 1, 831–844 (1991).

Liébert, L.

R. B. Meyer, L. Liébert, L. Strzelecki, P. Keller, “Ferroelectric liquid crystal,” J. Phys. (France) 36, 67–71 (1975).

Likins, K. L.

H. Mailer, K. L. Likins, T. R. Taylor, J. L. Fergason, “Effects of ultrasound on a nematic liquid crystal,” Appl. Phys. Lett. 18, 105–107 (1971).
[CrossRef]

Lilly, R. A.

Liu, J.-Y.

Lu, K.

Mailer, H.

H. Mailer, K. L. Likins, T. R. Taylor, J. L. Fergason, “Effects of ultrasound on a nematic liquid crystal,” Appl. Phys. Lett. 18, 105–107 (1971).
[CrossRef]

Marcerou, J. P.

L. Dupont, M. Glogarova, J. P. Marcerou, H. T. Nguyen, C. Destrade, L. Lejcek, “Linear electroclinic coupling in ferroelectric liquid crystals,” J. Phys. II 1, 831–844 (1991).

Marom, E.

Matsuda, K.

Mcknight, D. J.

D. J. Mcknight, K. M. Johnson, R. A. Serati, “256 × 256 liquid-cridtal-on-silicon spatial light modulator,” App. Opt. 33, 2775–2784 (1994).
[CrossRef]

Mears, R.

Meyer, R. B.

R. B. Meyer, L. Liébert, L. Strzelecki, P. Keller, “Ferroelectric liquid crystal,” J. Phys. (France) 36, 67–71 (1975).

Neil, M. A. A.

Nguyen, H. T.

L. Dupont, M. Glogarova, J. P. Marcerou, H. T. Nguyen, C. Destrade, L. Lejcek, “Linear electroclinic coupling in ferroelectric liquid crystals,” J. Phys. II 1, 831–844 (1991).

O’Brien, D. C.

Ooyama, N.

Paige, E. G. S.

Patel, J. S.

V. Pertuis, J. S. Patel, “Twisted smectic structures for grey scale modulator,” Ferroelectrics 149, 193–205 (1993).
[CrossRef]

Pellat-Finet, P.

P. Pellat-Finet, M. Le Doucen, “Polarization properties of birefringence gratings,” Optik (Stuttgart) 4, 159–166 (1995).

Pertuis, V.

V. Pertuis, J. S. Patel, “Twisted smectic structures for grey scale modulator,” Ferroelectrics 149, 193–205 (1993).
[CrossRef]

Pezzaniti, J. L.

Prost, J.

P. G. de Gennes, J. Prost, The Physics of Liquid Crystals (Oxford U. Press, Oxford, 1994).

Réfrégier, P.

Saleh, B. E. A.

Sato, S.

S. Sato, “Liquid crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18, 1679–1684 (1979).
[CrossRef]

Serati, R. A.

D. J. Mcknight, K. M. Johnson, R. A. Serati, “256 × 256 liquid-cridtal-on-silicon spatial light modulator,” App. Opt. 33, 2775–2784 (1994).
[CrossRef]

S. A. Serati, T. K. Ewing, R. A. Serati, K. M. Johnson, D. M. Simon, “Programmable 128 × 128 LCSLM compact correlator,” in Optical Pattern Recognition IV, D. P. Casesant, ed., Proc. SPIE1959, 55–68 (1993).
[CrossRef]

Serati, S. A.

S. A. Serati, T. K. Ewing, R. A. Serati, K. M. Johnson, D. M. Simon, “Programmable 128 × 128 LCSLM compact correlator,” in Optical Pattern Recognition IV, D. P. Casesant, ed., Proc. SPIE1959, 55–68 (1993).
[CrossRef]

Simon, D. M.

S. A. Serati, T. K. Ewing, R. A. Serati, K. M. Johnson, D. M. Simon, “Programmable 128 × 128 LCSLM compact correlator,” in Optical Pattern Recognition IV, D. P. Casesant, ed., Proc. SPIE1959, 55–68 (1993).
[CrossRef]

Skarp, K.

G. Anderson, I. Dahl, W. Kuczynski, S. T. Lagerwall, K. Skarp, B. Stebler, “The soft mode ferroelectric effect,” Ferroelectrics 84, 285–315 (1988).
[CrossRef]

Sneh, A.

Stebler, B.

G. Anderson, I. Dahl, W. Kuczynski, S. T. Lagerwall, K. Skarp, B. Stebler, “The soft mode ferroelectric effect,” Ferroelectrics 84, 285–315 (1988).
[CrossRef]

Strzelecki, L.

R. B. Meyer, L. Liébert, L. Strzelecki, P. Keller, “Ferroelectric liquid crystal,” J. Phys. (France) 36, 67–71 (1975).

Taylor, T. R.

H. Mailer, K. L. Likins, T. R. Taylor, J. L. Fergason, “Effects of ultrasound on a nematic liquid crystal,” Appl. Phys. Lett. 18, 105–107 (1971).
[CrossRef]

Walba, D. M.

Wilkinson, T. D.

Wu, S. T.

Wu, S.-T.

Yariv, A.

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

Yeh, P.

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

App. Opt. (1)

D. J. Mcknight, K. M. Johnson, R. A. Serati, “256 × 256 liquid-cridtal-on-silicon spatial light modulator,” App. Opt. 33, 2775–2784 (1994).
[CrossRef]

Appl. Opt. (9)

J. A. Davis, G. M. Heissenberger, R. A. Lilly, D. M. Cotrell, M. F. Bromwell, “High-efficiency optical reconstruction of binary phase-only filters using the Hughes liquid crystal light valve,” Appl. Opt. 26, 929–933 (1987).
[CrossRef] [PubMed]

B. V. K. Kumar, Z. Bahri, “Efficient algorithm for designing a ternary valued filter yielding maximum signal to noise ratio,” Appl. Opt. 28, 1919–1925 (1989).
[CrossRef] [PubMed]

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]

K. Lu, B. E. A. Saleh, “Complex amplitude reflectance of the liquid crystal light valve,” Appl. Opt. 30, 2354–2362 (1991).
[CrossRef] [PubMed]

M. O. Freeman, T. A. Brown, D. M. Walba, “Quantized complex ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 31, 3917–3929 (1992).
[CrossRef] [PubMed]

M. Killinger, J. L. de Bougrenet de la Tocnaye, P. Cambon, R. C. Chittick, W. A. Crossland, “Bistability and nonlinearity in optically addressed ferroelectric spatial light modulators: applications to neurocomputing,” Appl. Opt. 31, 3930–3936 (1992).
[CrossRef] [PubMed]

D. C. O’Brien, R. Mears, T. D. Wilkinson, W. A. Crossland, “Dynamic holographic interconnects that use ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 33, 2795–2803 (1994).
[CrossRef] [PubMed]

S. E. Broomfield, M. A. A. Neil, E. G. S. Paige, “Programmable multiple level phase modulation that uses ferroelectric liquid-crystal spatial light modulators,” Appl. Opt. 34, 6652–6665 (1995).
[CrossRef] [PubMed]

Special issue on Spatial Light Modulators for Optical Information Processing, Appl. Opt. 28, 4715–4954 (1989).

Appl. Phys. Lett. (2)

H. Mailer, K. L. Likins, T. R. Taylor, J. L. Fergason, “Effects of ultrasound on a nematic liquid crystal,” Appl. Phys. Lett. 18, 105–107 (1971).
[CrossRef]

N. A. Clark, S. T. Lagerwall, “Submicrosecond bistable electro-optic switching in LC,” Appl. Phys. Lett. 36, 899–901 (1980).
[CrossRef]

Ferroelectrics (4)

L. Le Bourhis, C. Destrade, L. Dupont, “Alignment and switching properties of AFLC,” Ferroelectrics 173, 23–36 (1995).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Geometry of the uniform nematic structure in a planar configuration.

Fig. 2
Fig. 2

Smectic cone. The director n is tilted with respect to the normal of the layer (oz) by an angle θ. Its position on the cone is given by the azimuthal angle ϕ.

Fig. 3
Fig. 3

SmA* structure in a homeotropic configuration.

Fig. 4
Fig. 4

SSFLC structure. Both steady-state positions have polarizations along the ox axis.

Fig. 5
Fig. 5

Double-loop hysteresis curve of the AFLC. u.a., arbitrary units.

Fig. 6
Fig. 6

Twisted nematic with and without an applied electric field.

Fig. 7
Fig. 7

Angular position of the director on the SmC cone.

Fig. 8
Fig. 8

Angular position of the director, polarizer, and analyzer for the smectic case.

Fig. 9
Fig. 9

LC classification notation for the case of linear polarization. P, polarizer; A, analyzer; I, intensity; V, voltage.

Equations (32)

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Δnne-n0cos2 θ,
1/n2z=cos2 θzne2+sin2 θzn02.
Δneff=1/d0dnzdz-n0.
θsin θ=Ω.
Ω=μTE,
P=νΩ,
τγθ/ϖT-Tc, T>Tc,
τγφ/PE,
θ=0V<Vcπ2-2 tan-1exp-V-Vc/V0V>Vc,
ϕ=πz/d.
τdecay=η/Kd2, τrise=η/ΔεE2/4π-Kπ/d2,
ϕ=πx/d.
sin θ=sin θ cos ϕ, sin θ=sin θ sin ϕ,
βeff=2πλ0dnθdz-n0d, Ψ=πdneθ+n0/λ=Ψ0+β, β=2πdneθ-n0/λ, with θ=θz,
d2θ/dz2+ΔεV2fθKd2=0, fθ=sin θ cos θ1+Δεsin2 θ/ε0,
I=Ip sin22δsin22βeff,
Jπα+sθ=expjΨ×cos2α0+2sθsin2α0+2sθsin2α0+2sθ-cos2α0+2sθ,
Pout=Jπα+sθ 1j=K exp2jsθ 1-j,
Pout=expjΨcos2θ+α2 cos α1sin α1,
Jπα0+sπ/4=s expjΨ -sin2α0cos2α0cos2α0sin2α0.
Pouts=expjΨcos2sθ+α2cos α1sin α1.
Jπsθ=expjΨ cos2sθsin2sθsin2sθ-cos2sθ.
Pouts=expjΨsin2sθ01.
JTN=expjΨRαX-jYZZX+jY,
JTN=expjΨRαexp-jβ00expjβ.
JTN=exp-2jβX-jYjZjZX+jY,
X=α/γ2+β/γ2cos2γ, Y=β/γ sin2γ, Z=αβ/γ21-cos2γ.
Λ=X±jZ2+Y21/2,
R=R1/2 exp-jδ,
R=A2+B2, δ=2β-tan-1B/A,
A=α/γ2+β/γ2cos2γcosΨ1-Ψ2, B=αβ/γ21-cos2γsinΨ1+Ψ2-β/γ sin2γcosΨ1+Ψ2.
S=1/Nn=0NSeigen,n

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