Abstract

An optical interference method has been developed to measure the distribution of the molecular director in an oriented cylindrical sample of nematic liquid crystal. The ratio of the elastic constants KB/KS can be obtained. Unlike other methods this one does not require independently measured quantities or the application of an external field. One interferogram is sufficient to determine refractive indexes and the elastic constant ratio. The hypothesis of strong anchoring can be tested directly.

© 1981 Optical Society of America

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References

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  1. F. Scudieri, Appl. Opt. 9, 1455 (1979).
  2. For a general discussion, see P. G. de Gennes, Physics of Liquid Crystals (Oxford U.P., New York, 1975).
  3. F. C. Frank, Discuss. Faraday Soc. 25, 19 (1958).
  4. P. E. Cladis, M. Kleman, J. Phys. Paris 33, 591 (1972).
  5. F. T. Stone, Appl. Opt. 16, 2738 (1977).
  6. G. D. Kahl, D. C. Mylin, J. Opt. Soc. Am. 55, 364 (1965).

1979 (1)

F. Scudieri, Appl. Opt. 9, 1455 (1979).

1977 (1)

1972 (1)

P. E. Cladis, M. Kleman, J. Phys. Paris 33, 591 (1972).

1965 (1)

1958 (1)

F. C. Frank, Discuss. Faraday Soc. 25, 19 (1958).

Cladis, P. E.

P. E. Cladis, M. Kleman, J. Phys. Paris 33, 591 (1972).

de Gennes, P. G.

For a general discussion, see P. G. de Gennes, Physics of Liquid Crystals (Oxford U.P., New York, 1975).

Frank, F. C.

F. C. Frank, Discuss. Faraday Soc. 25, 19 (1958).

Kahl, G. D.

Kleman, M.

P. E. Cladis, M. Kleman, J. Phys. Paris 33, 591 (1972).

Mylin, D. C.

Scudieri, F.

F. Scudieri, Appl. Opt. 9, 1455 (1979).

Stone, F. T.

Appl. Opt. (2)

F. Scudieri, Appl. Opt. 9, 1455 (1979).

F. T. Stone, Appl. Opt. 16, 2738 (1977).

Discuss. Faraday Soc. (1)

F. C. Frank, Discuss. Faraday Soc. 25, 19 (1958).

J. Opt. Soc. Am. (1)

J. Phys. Paris (1)

P. E. Cladis, M. Kleman, J. Phys. Paris 33, 591 (1972).

Other (1)

For a general discussion, see P. G. de Gennes, Physics of Liquid Crystals (Oxford U.P., New York, 1975).

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Figures (7)

Fig. 1
Fig. 1

Molecular arrangement in a cylindrical capillary with boundary homeotropic anchoring.

Fig. 2
Fig. 2

Equilibrium radial configuration for a nematic with KB > KS for different values of the KB/KS ratio.

Fig. 3
Fig. 3

Geometry for the differential interferometric observation.

Fig. 4
Fig. 4

Fringe profiles observed for homeotropic nematic in monochromatic light.

Fig. 5
Fig. 5

Fringe profiles evaluated for different values of KB/KS for no = 1.513, ne = 1.670.

Fig. 6
Fig. 6

Maximum fringe shift Δ2M/no vs a = no/ne for no = 1.513.

Fig. 7
Fig. 7

The Δ2M − Δ2(o) vs KB/KS ratio for no = 1.513, ne = 1.670.

Equations (7)

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H c i = π d ( K i χ a ) 1 / 2 ,
r ( φ ) = R 1 | cos k cos φ 1 sin 2 k cos 2 φ cos k cos φ + 1 sin 2 k cos 2 φ | 1 / 2 exp ( ψ tan k ) ,
tan 2 k = K B K S 1 , sin ψ = sin k cos φ ,
Δ ( x ) = 2 0 ( R 1 2 x 2 ) 1 / 2 [ n ( r , φ ) n r ] dy ,
n ( r , φ ) = n o [ 1 + tan 2 φ 1 + tan 2 φ + ( a 2 1 ) ( 1 + sin 2 α tan 2 φ ) ] 1 / 2 ,
Δ T ( x ) = 2 ( R 2 2 x 2 ) 1 / 2 R 2 ( n r n r ) dy = 2 ( n r n r ) R 2 η ,
Δ T ( x M ) = Δ T ( R 1 ) R 2 R 2 2 x M 2 R 2 R 2 2 R 1 2 = | Δ T ( R 1 ) Δ T ( R 2 ) | R 2 R 2 2 x M 2 R 2 2 R 1 2 .

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