Abstract

A convenient and accurate technique for measuring the birefringence of liquid crystals at discrete wavelengths or as a continuous function of wavelength in the ultraviolet, visible, or infrared spectral regions is described. The method is based on determination of the phase differences which occur when monochromatic polarized light propagates through a medium with an anisotropic refractive index. Birefringence measurements at 0.6328 μm for two liquid crystal materials, BDH-E7 and ZLI-1132, and a continuous birefringence spectrum of ZLI-1132 from 2 to 16 μm are reported. Additionally, a liquid crystal based phase retardation plate which can be voltage tuned and calibrated to provide any degree of phase shift from 0 to 2π over a wide wavelength range (0.4–16 μm) is discussed.

© 1984 Optical Society of America

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References

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  1. R. Chang, “Application of Polarimetry and Interferometry to Liquid Crystal-Film Research,” Mater. Res. Bull. 7, 267 (1972); “Orientational Order in MBBA from Optical Anisotropy Measurements,” Mol. Cryst. Liq. Cryst. 30, 155 (1975).
    [CrossRef]
  2. R. A. Soref, M. J. Rafuse, “Electrically Controlled Birefringence of Thin Nematic Films,” J. Appl. Phys. 43, 2029 (1972).
    [CrossRef]
  3. W. Haase, D. Potzsch, “Light Transmission Experiments with Nematic Liquid Crystals Showing Positive and Negative Dielectric Anisotropy,” Mol. Cryst. Liq. Cryst. 38, 77 (1977).
    [CrossRef]
  4. E. G. Hanson, Y. R. Shen, “Refractive Indices and Optical Anisotropy of Homologous Liquid Crystals,” Mol. Cryst. Liq. Cryst. 36, 193 (1976).
    [CrossRef]
  5. E. Miraldi, C. Oldano, L. Trossi, P. T. Valabrega, “Direct Measurement of the Two Principal Refractive Indexes of a Nematic Liquid Crystal Slab,” Appl. Opt. 21, 4163 (1982).
    [CrossRef] [PubMed]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 714.
  7. BDH Chemicals, Ltd., England.
  8. E. Merck Chemicals, Germany.
  9. H. J. Deuling, “Deformation of Nematic Liquid Crystals in an Electric Field,” Mol. Cryst. Liq. Cryst. 19, 123 (1972).
    [CrossRef]
  10. P. G. deGennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).
  11. S. T. Wu, U. Efron, L. D. Hess, “Infrared Birefringence of Liquid Crystals,” Appl. Phys. Lett. 44, 1033 (1984).
    [CrossRef]
  12. S. D. Jacobs, “Liquid Crystals as Large Aperture Waveplates and Circular Polarizer,” Proc. Soc. Photo-Opt. Instrum. Eng. 307, 98 (1981).
  13. S. T. Wu, L. D. Hess, “Nonlinear Birefringence of Liquid Crystals at 10.59 μm,” in Technical Digest, Conferenceon Lasers and Electrooptic Systems (Optical Society of America, Washington, D.C., 1984), paper F02.
  14. S. D. Durbin, S. M. Arakelian, Y. R. Shen, “Laser-Induced Diffraction Rings from a Nematic-Liquid-Crystal Film,” Opt. Lett. 6, 411 (1981).
    [PubMed]
  15. B. Ya Zeldovich, N. V. Tabiryan, “Theory of Optically Induced Fireedericksz Transition,” Sov. Phys. JETP 55, 656 (1982).

1984 (1)

S. T. Wu, U. Efron, L. D. Hess, “Infrared Birefringence of Liquid Crystals,” Appl. Phys. Lett. 44, 1033 (1984).
[CrossRef]

1982 (2)

1981 (2)

S. D. Jacobs, “Liquid Crystals as Large Aperture Waveplates and Circular Polarizer,” Proc. Soc. Photo-Opt. Instrum. Eng. 307, 98 (1981).

S. D. Durbin, S. M. Arakelian, Y. R. Shen, “Laser-Induced Diffraction Rings from a Nematic-Liquid-Crystal Film,” Opt. Lett. 6, 411 (1981).
[PubMed]

1977 (1)

W. Haase, D. Potzsch, “Light Transmission Experiments with Nematic Liquid Crystals Showing Positive and Negative Dielectric Anisotropy,” Mol. Cryst. Liq. Cryst. 38, 77 (1977).
[CrossRef]

1976 (1)

E. G. Hanson, Y. R. Shen, “Refractive Indices and Optical Anisotropy of Homologous Liquid Crystals,” Mol. Cryst. Liq. Cryst. 36, 193 (1976).
[CrossRef]

1972 (3)

R. Chang, “Application of Polarimetry and Interferometry to Liquid Crystal-Film Research,” Mater. Res. Bull. 7, 267 (1972); “Orientational Order in MBBA from Optical Anisotropy Measurements,” Mol. Cryst. Liq. Cryst. 30, 155 (1975).
[CrossRef]

R. A. Soref, M. J. Rafuse, “Electrically Controlled Birefringence of Thin Nematic Films,” J. Appl. Phys. 43, 2029 (1972).
[CrossRef]

H. J. Deuling, “Deformation of Nematic Liquid Crystals in an Electric Field,” Mol. Cryst. Liq. Cryst. 19, 123 (1972).
[CrossRef]

Arakelian, S. M.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 714.

Chang, R.

R. Chang, “Application of Polarimetry and Interferometry to Liquid Crystal-Film Research,” Mater. Res. Bull. 7, 267 (1972); “Orientational Order in MBBA from Optical Anisotropy Measurements,” Mol. Cryst. Liq. Cryst. 30, 155 (1975).
[CrossRef]

deGennes, P. G.

P. G. deGennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).

Deuling, H. J.

H. J. Deuling, “Deformation of Nematic Liquid Crystals in an Electric Field,” Mol. Cryst. Liq. Cryst. 19, 123 (1972).
[CrossRef]

Durbin, S. D.

Efron, U.

S. T. Wu, U. Efron, L. D. Hess, “Infrared Birefringence of Liquid Crystals,” Appl. Phys. Lett. 44, 1033 (1984).
[CrossRef]

Haase, W.

W. Haase, D. Potzsch, “Light Transmission Experiments with Nematic Liquid Crystals Showing Positive and Negative Dielectric Anisotropy,” Mol. Cryst. Liq. Cryst. 38, 77 (1977).
[CrossRef]

Hanson, E. G.

E. G. Hanson, Y. R. Shen, “Refractive Indices and Optical Anisotropy of Homologous Liquid Crystals,” Mol. Cryst. Liq. Cryst. 36, 193 (1976).
[CrossRef]

Hess, L. D.

S. T. Wu, U. Efron, L. D. Hess, “Infrared Birefringence of Liquid Crystals,” Appl. Phys. Lett. 44, 1033 (1984).
[CrossRef]

S. T. Wu, L. D. Hess, “Nonlinear Birefringence of Liquid Crystals at 10.59 μm,” in Technical Digest, Conferenceon Lasers and Electrooptic Systems (Optical Society of America, Washington, D.C., 1984), paper F02.

Jacobs, S. D.

S. D. Jacobs, “Liquid Crystals as Large Aperture Waveplates and Circular Polarizer,” Proc. Soc. Photo-Opt. Instrum. Eng. 307, 98 (1981).

Miraldi, E.

Oldano, C.

Potzsch, D.

W. Haase, D. Potzsch, “Light Transmission Experiments with Nematic Liquid Crystals Showing Positive and Negative Dielectric Anisotropy,” Mol. Cryst. Liq. Cryst. 38, 77 (1977).
[CrossRef]

Rafuse, M. J.

R. A. Soref, M. J. Rafuse, “Electrically Controlled Birefringence of Thin Nematic Films,” J. Appl. Phys. 43, 2029 (1972).
[CrossRef]

Shen, Y. R.

S. D. Durbin, S. M. Arakelian, Y. R. Shen, “Laser-Induced Diffraction Rings from a Nematic-Liquid-Crystal Film,” Opt. Lett. 6, 411 (1981).
[PubMed]

E. G. Hanson, Y. R. Shen, “Refractive Indices and Optical Anisotropy of Homologous Liquid Crystals,” Mol. Cryst. Liq. Cryst. 36, 193 (1976).
[CrossRef]

Soref, R. A.

R. A. Soref, M. J. Rafuse, “Electrically Controlled Birefringence of Thin Nematic Films,” J. Appl. Phys. 43, 2029 (1972).
[CrossRef]

Tabiryan, N. V.

B. Ya Zeldovich, N. V. Tabiryan, “Theory of Optically Induced Fireedericksz Transition,” Sov. Phys. JETP 55, 656 (1982).

Trossi, L.

Valabrega, P. T.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 714.

Wu, S. T.

S. T. Wu, U. Efron, L. D. Hess, “Infrared Birefringence of Liquid Crystals,” Appl. Phys. Lett. 44, 1033 (1984).
[CrossRef]

S. T. Wu, L. D. Hess, “Nonlinear Birefringence of Liquid Crystals at 10.59 μm,” in Technical Digest, Conferenceon Lasers and Electrooptic Systems (Optical Society of America, Washington, D.C., 1984), paper F02.

Ya Zeldovich, B.

B. Ya Zeldovich, N. V. Tabiryan, “Theory of Optically Induced Fireedericksz Transition,” Sov. Phys. JETP 55, 656 (1982).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. T. Wu, U. Efron, L. D. Hess, “Infrared Birefringence of Liquid Crystals,” Appl. Phys. Lett. 44, 1033 (1984).
[CrossRef]

J. Appl. Phys. (1)

R. A. Soref, M. J. Rafuse, “Electrically Controlled Birefringence of Thin Nematic Films,” J. Appl. Phys. 43, 2029 (1972).
[CrossRef]

Mater. Res. Bull. (1)

R. Chang, “Application of Polarimetry and Interferometry to Liquid Crystal-Film Research,” Mater. Res. Bull. 7, 267 (1972); “Orientational Order in MBBA from Optical Anisotropy Measurements,” Mol. Cryst. Liq. Cryst. 30, 155 (1975).
[CrossRef]

Mol. Cryst. Liq. Cryst. (3)

W. Haase, D. Potzsch, “Light Transmission Experiments with Nematic Liquid Crystals Showing Positive and Negative Dielectric Anisotropy,” Mol. Cryst. Liq. Cryst. 38, 77 (1977).
[CrossRef]

E. G. Hanson, Y. R. Shen, “Refractive Indices and Optical Anisotropy of Homologous Liquid Crystals,” Mol. Cryst. Liq. Cryst. 36, 193 (1976).
[CrossRef]

H. J. Deuling, “Deformation of Nematic Liquid Crystals in an Electric Field,” Mol. Cryst. Liq. Cryst. 19, 123 (1972).
[CrossRef]

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

S. D. Jacobs, “Liquid Crystals as Large Aperture Waveplates and Circular Polarizer,” Proc. Soc. Photo-Opt. Instrum. Eng. 307, 98 (1981).

Sov. Phys. JETP (1)

B. Ya Zeldovich, N. V. Tabiryan, “Theory of Optically Induced Fireedericksz Transition,” Sov. Phys. JETP 55, 656 (1982).

Other (5)

S. T. Wu, L. D. Hess, “Nonlinear Birefringence of Liquid Crystals at 10.59 μm,” in Technical Digest, Conferenceon Lasers and Electrooptic Systems (Optical Society of America, Washington, D.C., 1984), paper F02.

P. G. deGennes, The Physics of Liquid Crystals (Clarendon, Oxford, 1974).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), pp. 714.

BDH Chemicals, Ltd., England.

E. Merck Chemicals, Germany.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of experimental apparatus and optical configuration for liquid crystal birefringence measurements.

Fig. 2
Fig. 2

Voltage-dependent optical transmission of polarizer–LC cell–analyzer system for two analyzer orientations, perpendicular and parallel to the polarizer; λ = 0.6328 μm; LC cell excitation–sine wave, 1 kHz; T = 24°C; (a) BDH-E7 liquid crystal, d = 10.1 μm, (b) ZLI-1132 liquid crystal, d = 5.9 μm.

Fig. 3
Fig. 3

Voltage-dependent birefringence of BDH-E7 and ZLI-1132 liquid crystals; λ = 0.6328 μm; T = 24°C.

Fig. 4
Fig. 4

Measured transmission ratio I/I|| as a function of IR wavelength for the ZLI-1132 liquid crystal; cell thickness, 24 μm; no applied voltage.

Fig. 5
Fig. 5

Voltage-dependent optical transmission of polarizer–LC cell–analyzer system for two analyzer orientations, perpendicular and parallel to the polarizer; cell thickness, 24 μm; λ = 10.59 μm, ZLI-1132 liquid crystal; LC cell excitation–sine wave, 1 kHz; T 24°C.

Fig. 6
Fig. 6

Birefringence of the ZLI-1132 liquid crystal calculated from the data shown in Fig. 4; the dashed line is an extrapolation.

Tables (1)

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Table I Wavelength Tunable Lquid Crystal Phase Retardation Plate Characteristics

Equations (7)

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δ = 2 π d Δ n λ sin 2 θ ,
I = 1 4 I 0 sin 2 2 ϕ { exp ( - α o d ) + exp ( - α e d ) - 2 exp [ - ( α o + α e ) d / 2 ] cos δ } ,
I = I 0 ( { exp ( - α o d ) + exp ( - α e d ) - 2 exp [ - ( α o + α e ) d / 2 ] } cos 4 ϕ + { 2 exp [ - ( α o + α e ) d / 2 ] - 2 exp ( - α e d ) cos 2 ϕ + exp ( - α e d ) - exp [ - ( α o + α e ) d / 2 ] sin 2 2 ϕ sin 2 δ 2 ) ,
I = I 0 exp ( - α o d ) sin 2 δ 2 ,
I = I 0 exp ( - α o d ) cos 2 δ 2 ,
δ = N π + 2 tan - 1 I I ,             N = 0 , 2 , 4 , ,
δ = ( N + 1 ) π - 2 tan - 1 I I ,             N = 1 , 3 , 5 , .

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