Abstract

A new technique to measure the principal refractive indexes of a nematic liquid crystal is presented. The method is based on an indirect measurement of the refraction angle by determining the direction of a magnetic field which minimizes the light scattering. With this technique one can perform different light scattering experiments, which require a knowledge of the refractive indexes, on the same crystal slab. The accuracy is better than ±0.15%. A discussion about the systematic error due to the distortion of the director profile near the holder edges and the relative correction is given.

© 1982 Optical Society of America

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  1. P. Chatelain, Bull. Soc. Fr. Mineral. Cristallogr. 50, 280 (1937).
  2. P. Chatelain, Bull. Soc. Fr. Mineral Cristallogr. 78, 262 (1955).
  3. M. B. Germain, C. R. Acad. Sci. Ser. B 271, 1075 (1970).
  4. D. A. Balzarini, Phys. Rev. Lett. 25, 914 (1970).
    [CrossRef]
  5. I. Haller, H. A. Huggings, M. J. Freiser, Mol. Cryst. Liq. Cryst. 16, 53 (1972).
    [CrossRef]
  6. W. Kuczynski, B. Stryla, Mol. Cryst. Liq. Cryst. 31, 267 (1975).
    [CrossRef]
  7. R. Chang, Mol. Cryst. Liq. Cryst. 30, 155 (1975).
    [CrossRef]
  8. M. Laurent, R. Journeaux, Mol. Cryst. Liq. Cryst. 36, 171 (1976).
    [CrossRef]
  9. E. G. Hanson, Y. R. Shen, Mol. Cryst. Liq. Cryst. 36, 193 (1976).
    [CrossRef]
  10. R. K. Sarna, B. Bahadur, V. Bhide, Mol. Cryst. Liq. Cryst. 51, 117 (1979).
    [CrossRef]
  11. F. Scudieri, Appl. Opt. 18, 1455 (1979).
    [CrossRef] [PubMed]
  12. H. Mada, S. Kobayashi, Appl. Phys. Lett. 35, 4 (1979).
    [CrossRef]
  13. T. Akahane, T. Tako, S. Masubuchi, Opt. Acta 26, 943 (1979).
    [CrossRef]
  14. K. C. Chu, C. K. Chen, Y. R. Sheu, Mol. Cryst. Liq. Cryst. 59, 97 (1980).
    [CrossRef]
  15. G. Jungk, Appl. Opt. 19, 508 (1980).
    [CrossRef] [PubMed]
  16. E. Miraldi, C. Oldano, L. Trossi, P. T. Valabrega: Nuovo Cimento B 60, 165 (1980).
    [CrossRef]

1980 (3)

K. C. Chu, C. K. Chen, Y. R. Sheu, Mol. Cryst. Liq. Cryst. 59, 97 (1980).
[CrossRef]

E. Miraldi, C. Oldano, L. Trossi, P. T. Valabrega: Nuovo Cimento B 60, 165 (1980).
[CrossRef]

G. Jungk, Appl. Opt. 19, 508 (1980).
[CrossRef] [PubMed]

1979 (4)

F. Scudieri, Appl. Opt. 18, 1455 (1979).
[CrossRef] [PubMed]

R. K. Sarna, B. Bahadur, V. Bhide, Mol. Cryst. Liq. Cryst. 51, 117 (1979).
[CrossRef]

H. Mada, S. Kobayashi, Appl. Phys. Lett. 35, 4 (1979).
[CrossRef]

T. Akahane, T. Tako, S. Masubuchi, Opt. Acta 26, 943 (1979).
[CrossRef]

1976 (2)

M. Laurent, R. Journeaux, Mol. Cryst. Liq. Cryst. 36, 171 (1976).
[CrossRef]

E. G. Hanson, Y. R. Shen, Mol. Cryst. Liq. Cryst. 36, 193 (1976).
[CrossRef]

1975 (2)

W. Kuczynski, B. Stryla, Mol. Cryst. Liq. Cryst. 31, 267 (1975).
[CrossRef]

R. Chang, Mol. Cryst. Liq. Cryst. 30, 155 (1975).
[CrossRef]

1972 (1)

I. Haller, H. A. Huggings, M. J. Freiser, Mol. Cryst. Liq. Cryst. 16, 53 (1972).
[CrossRef]

1970 (2)

M. B. Germain, C. R. Acad. Sci. Ser. B 271, 1075 (1970).

D. A. Balzarini, Phys. Rev. Lett. 25, 914 (1970).
[CrossRef]

1955 (1)

P. Chatelain, Bull. Soc. Fr. Mineral Cristallogr. 78, 262 (1955).

1937 (1)

P. Chatelain, Bull. Soc. Fr. Mineral. Cristallogr. 50, 280 (1937).

Akahane, T.

T. Akahane, T. Tako, S. Masubuchi, Opt. Acta 26, 943 (1979).
[CrossRef]

Bahadur, B.

R. K. Sarna, B. Bahadur, V. Bhide, Mol. Cryst. Liq. Cryst. 51, 117 (1979).
[CrossRef]

Balzarini, D. A.

D. A. Balzarini, Phys. Rev. Lett. 25, 914 (1970).
[CrossRef]

Bhide, V.

R. K. Sarna, B. Bahadur, V. Bhide, Mol. Cryst. Liq. Cryst. 51, 117 (1979).
[CrossRef]

Chang, R.

R. Chang, Mol. Cryst. Liq. Cryst. 30, 155 (1975).
[CrossRef]

Chatelain, P.

P. Chatelain, Bull. Soc. Fr. Mineral Cristallogr. 78, 262 (1955).

P. Chatelain, Bull. Soc. Fr. Mineral. Cristallogr. 50, 280 (1937).

Chen, C. K.

K. C. Chu, C. K. Chen, Y. R. Sheu, Mol. Cryst. Liq. Cryst. 59, 97 (1980).
[CrossRef]

Chu, K. C.

K. C. Chu, C. K. Chen, Y. R. Sheu, Mol. Cryst. Liq. Cryst. 59, 97 (1980).
[CrossRef]

Freiser, M. J.

I. Haller, H. A. Huggings, M. J. Freiser, Mol. Cryst. Liq. Cryst. 16, 53 (1972).
[CrossRef]

Germain, M. B.

M. B. Germain, C. R. Acad. Sci. Ser. B 271, 1075 (1970).

Haller, I.

I. Haller, H. A. Huggings, M. J. Freiser, Mol. Cryst. Liq. Cryst. 16, 53 (1972).
[CrossRef]

Hanson, E. G.

E. G. Hanson, Y. R. Shen, Mol. Cryst. Liq. Cryst. 36, 193 (1976).
[CrossRef]

Huggings, H. A.

I. Haller, H. A. Huggings, M. J. Freiser, Mol. Cryst. Liq. Cryst. 16, 53 (1972).
[CrossRef]

Journeaux, R.

M. Laurent, R. Journeaux, Mol. Cryst. Liq. Cryst. 36, 171 (1976).
[CrossRef]

Jungk, G.

Kobayashi, S.

H. Mada, S. Kobayashi, Appl. Phys. Lett. 35, 4 (1979).
[CrossRef]

Kuczynski, W.

W. Kuczynski, B. Stryla, Mol. Cryst. Liq. Cryst. 31, 267 (1975).
[CrossRef]

Laurent, M.

M. Laurent, R. Journeaux, Mol. Cryst. Liq. Cryst. 36, 171 (1976).
[CrossRef]

Mada, H.

H. Mada, S. Kobayashi, Appl. Phys. Lett. 35, 4 (1979).
[CrossRef]

Masubuchi, S.

T. Akahane, T. Tako, S. Masubuchi, Opt. Acta 26, 943 (1979).
[CrossRef]

Miraldi, E.

E. Miraldi, C. Oldano, L. Trossi, P. T. Valabrega: Nuovo Cimento B 60, 165 (1980).
[CrossRef]

Oldano, C.

E. Miraldi, C. Oldano, L. Trossi, P. T. Valabrega: Nuovo Cimento B 60, 165 (1980).
[CrossRef]

Sarna, R. K.

R. K. Sarna, B. Bahadur, V. Bhide, Mol. Cryst. Liq. Cryst. 51, 117 (1979).
[CrossRef]

Scudieri, F.

Shen, Y. R.

E. G. Hanson, Y. R. Shen, Mol. Cryst. Liq. Cryst. 36, 193 (1976).
[CrossRef]

Sheu, Y. R.

K. C. Chu, C. K. Chen, Y. R. Sheu, Mol. Cryst. Liq. Cryst. 59, 97 (1980).
[CrossRef]

Stryla, B.

W. Kuczynski, B. Stryla, Mol. Cryst. Liq. Cryst. 31, 267 (1975).
[CrossRef]

Tako, T.

T. Akahane, T. Tako, S. Masubuchi, Opt. Acta 26, 943 (1979).
[CrossRef]

Trossi, L.

E. Miraldi, C. Oldano, L. Trossi, P. T. Valabrega: Nuovo Cimento B 60, 165 (1980).
[CrossRef]

Valabrega, P. T.

E. Miraldi, C. Oldano, L. Trossi, P. T. Valabrega: Nuovo Cimento B 60, 165 (1980).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

H. Mada, S. Kobayashi, Appl. Phys. Lett. 35, 4 (1979).
[CrossRef]

Bull. Soc. Fr. Mineral Cristallogr. (1)

P. Chatelain, Bull. Soc. Fr. Mineral Cristallogr. 78, 262 (1955).

Bull. Soc. Fr. Mineral. Cristallogr. (1)

P. Chatelain, Bull. Soc. Fr. Mineral. Cristallogr. 50, 280 (1937).

C. R. Acad. Sci. Ser. B (1)

M. B. Germain, C. R. Acad. Sci. Ser. B 271, 1075 (1970).

Mol. Cryst. Liq. Cryst. (7)

I. Haller, H. A. Huggings, M. J. Freiser, Mol. Cryst. Liq. Cryst. 16, 53 (1972).
[CrossRef]

W. Kuczynski, B. Stryla, Mol. Cryst. Liq. Cryst. 31, 267 (1975).
[CrossRef]

R. Chang, Mol. Cryst. Liq. Cryst. 30, 155 (1975).
[CrossRef]

M. Laurent, R. Journeaux, Mol. Cryst. Liq. Cryst. 36, 171 (1976).
[CrossRef]

E. G. Hanson, Y. R. Shen, Mol. Cryst. Liq. Cryst. 36, 193 (1976).
[CrossRef]

R. K. Sarna, B. Bahadur, V. Bhide, Mol. Cryst. Liq. Cryst. 51, 117 (1979).
[CrossRef]

K. C. Chu, C. K. Chen, Y. R. Sheu, Mol. Cryst. Liq. Cryst. 59, 97 (1980).
[CrossRef]

Nuovo Cimento B (1)

E. Miraldi, C. Oldano, L. Trossi, P. T. Valabrega: Nuovo Cimento B 60, 165 (1980).
[CrossRef]

Opt. Acta (1)

T. Akahane, T. Tako, S. Masubuchi, Opt. Acta 26, 943 (1979).
[CrossRef]

Phys. Rev. Lett. (1)

D. A. Balzarini, Phys. Rev. Lett. 25, 914 (1970).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Total scattering cross section σ1 and σ2 vs θr for the extraordinary and ordinary beams, respectively.

Fig. 2
Fig. 2

Experimental setup for the measurement of the principal refractive indexes of nematic liquid crystals: L is the incident laser beam; Sp the specimen; CC′ two Helmholtz coils to create the oscillating field H′; P is a polarizer; Ph the photodetector; A an ac coupled amplifier; and SA a spectrum analyzer. The polarization plane coincides with the incidence plane of the laser beam, which also is parallel to the magnetic field H.

Fig. 3
Fig. 3

Typical display of the spectrum analyzer when the conditions of the refracted beam being parallel or perpendicular to the magnetic field H are not exactly met. The line disappears when these conditions are satisfied. fo is the frequency of the oscillating field H′.

Fig. 4
Fig. 4

Change of the line amplitude a vs the incident beam angle with respect to the conditions when the refracted beam inside the specimen is perpendicular to H.

Fig. 5
Fig. 5

Two incidence angles at which the measurements are performed and the corresponding ordinary and extraordinary refracted beams and magnetic field directions are reported.

Fig. 6
Fig. 6

Director profile of a nematic liquid crystal slab under a magnetic field H. The thickness of the distortion layer has been purposely exaggerated.

Tables (2)

Tables Icon

Table I Deviation Angle as a Function of the Magnetic Field for θH Nearly Parallel to θr

Tables Icon

Table II Deviation Angle as a Function of the Magnetic Field for θH Nearly Perpendicular to θr

Equations (6)

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

( d σ d Ω ) α , β = k B T ɛ a 2 ( ω 2 4 π c 2 ) 2 n β ( θ f ) n α ( θ i ) cos ( θ i r - θ i ) cos 2 ( θ F r - θ f ) · γ = 1 2 G α β γ ( K γ γ sin 2 θ q + K 33 cos 2 θ q ) q 2 + χ a H 2 .
G α β γ = [ ( n o · ι α ) ( n γ · f β ) + ( n o · f β ) ( n γ · ι α ) ] 2 ,
σ α ( θ r ) = β 4 π ( d σ d Ω ) α β d Ω .
Δ n n = Δ θ r tan θ r < 0.15 % ,
A ( θ H ) = ( Π T i ) exp { - 0 d σ x [ θ ( x , θ H ) - θ r ( x ) ] d x cos θ r } ,
ξ = k χ a · 1 H .

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