Abstract

The spatial and temporal coherence properties of laser light scattered by a liquid crystal cell under the application of an external dc field are studied. It is shown that the scattered field constitutes a source with very long coherence time. The coherence time can be changed by changing the value of the applied voltage, and the spatial coherence can be adjusted by varying the dimension of the illuminated spot on the cell. The effects produced when the length of correlation of fluctuations in the liquid crystal is not negligible with respect to the dimension of the spot in the cell are also studied. The scattered field is proposed as a new quasi-thermal source, alternative of the rotating ground glass disk.

© 1974 Optical Society of America

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References

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  1. W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
    [Crossref]
  2. See, for example, R. Williams, J. Chem. Phys. 39, 384 (1963).
    [Crossref]
  3. G. Heilmeier, L. A. Zanoni, L. A. Barton, Proc. IEEE 56, 1162 (1968).
    [Crossref]
  4. N. Koelmans, A. M. van Boxtel, Phys. Lett. 32A, 32 (1970).
  5. G. Durand, M. Veyssie, F. Rondelez, L. Loger, Compt. Rend. 270B, 97 (1970).
  6. M. Bertolotti, S. Lagomarsino, F. Scudieri, D. Sette, J. Phys. C 6, L177 (1973).
    [Crossref]
  7. C. Deutsch, P. N. Keating, J. Appl. Phys. 40, 4049 (1969).
    [Crossref]
  8. M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. A 4, 197 (1971).
    [Crossref]
  9. M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. Supplem. fasc. 2-3 33, CI-63 (1972).
  10. F. Gori, D. Sette, Phys. Rev. Lett. 17, 361 (1966).
    [Crossref]
  11. M. Bertolotti, M. Carnevale, L. Muzii, D. Sette, Appl. Opt. 9, 510 (1970).
    [Crossref]
  12. M. Bertolotti, L. Muzii, D. Sette, J. Opt. Soc. Am. 60, 1603 (1970).
    [Crossref]
  13. R. Bartolino, M. Bertolotti, F. Scudieri, D. Sette, Appl. Opt. 12, 2917 (December1973).
    [Crossref] [PubMed]
  14. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965).
  15. M. Bertolotti, F. Scudieri, unpublished.

1973 (2)

M. Bertolotti, S. Lagomarsino, F. Scudieri, D. Sette, J. Phys. C 6, L177 (1973).
[Crossref]

R. Bartolino, M. Bertolotti, F. Scudieri, D. Sette, Appl. Opt. 12, 2917 (December1973).
[Crossref] [PubMed]

1972 (1)

M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. Supplem. fasc. 2-3 33, CI-63 (1972).

1971 (1)

M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. A 4, 197 (1971).
[Crossref]

1970 (4)

N. Koelmans, A. M. van Boxtel, Phys. Lett. 32A, 32 (1970).

G. Durand, M. Veyssie, F. Rondelez, L. Loger, Compt. Rend. 270B, 97 (1970).

M. Bertolotti, M. Carnevale, L. Muzii, D. Sette, Appl. Opt. 9, 510 (1970).
[Crossref]

M. Bertolotti, L. Muzii, D. Sette, J. Opt. Soc. Am. 60, 1603 (1970).
[Crossref]

1969 (1)

C. Deutsch, P. N. Keating, J. Appl. Phys. 40, 4049 (1969).
[Crossref]

1968 (1)

G. Heilmeier, L. A. Zanoni, L. A. Barton, Proc. IEEE 56, 1162 (1968).
[Crossref]

1966 (1)

F. Gori, D. Sette, Phys. Rev. Lett. 17, 361 (1966).
[Crossref]

1964 (1)

W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
[Crossref]

1963 (1)

See, for example, R. Williams, J. Chem. Phys. 39, 384 (1963).
[Crossref]

Bartolino, R.

Barton, L. A.

G. Heilmeier, L. A. Zanoni, L. A. Barton, Proc. IEEE 56, 1162 (1968).
[Crossref]

Bertolotti, M.

M. Bertolotti, S. Lagomarsino, F. Scudieri, D. Sette, J. Phys. C 6, L177 (1973).
[Crossref]

R. Bartolino, M. Bertolotti, F. Scudieri, D. Sette, Appl. Opt. 12, 2917 (December1973).
[Crossref] [PubMed]

M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. Supplem. fasc. 2-3 33, CI-63 (1972).

M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. A 4, 197 (1971).
[Crossref]

M. Bertolotti, L. Muzii, D. Sette, J. Opt. Soc. Am. 60, 1603 (1970).
[Crossref]

M. Bertolotti, M. Carnevale, L. Muzii, D. Sette, Appl. Opt. 9, 510 (1970).
[Crossref]

M. Bertolotti, F. Scudieri, unpublished.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965).

Carnevale, M.

Daino, B.

M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. Supplem. fasc. 2-3 33, CI-63 (1972).

M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. A 4, 197 (1971).
[Crossref]

Deutsch, C.

C. Deutsch, P. N. Keating, J. Appl. Phys. 40, 4049 (1969).
[Crossref]

Di Porto, P.

M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. Supplem. fasc. 2-3 33, CI-63 (1972).

M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. A 4, 197 (1971).
[Crossref]

Durand, G.

G. Durand, M. Veyssie, F. Rondelez, L. Loger, Compt. Rend. 270B, 97 (1970).

Gori, F.

F. Gori, D. Sette, Phys. Rev. Lett. 17, 361 (1966).
[Crossref]

Heilmeier, G.

G. Heilmeier, L. A. Zanoni, L. A. Barton, Proc. IEEE 56, 1162 (1968).
[Crossref]

Keating, P. N.

C. Deutsch, P. N. Keating, J. Appl. Phys. 40, 4049 (1969).
[Crossref]

Koelmans, N.

N. Koelmans, A. M. van Boxtel, Phys. Lett. 32A, 32 (1970).

Lagomarsino, S.

M. Bertolotti, S. Lagomarsino, F. Scudieri, D. Sette, J. Phys. C 6, L177 (1973).
[Crossref]

Loger, L.

G. Durand, M. Veyssie, F. Rondelez, L. Loger, Compt. Rend. 270B, 97 (1970).

Martienssen, W.

W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
[Crossref]

Muzii, L.

Rondelez, F.

G. Durand, M. Veyssie, F. Rondelez, L. Loger, Compt. Rend. 270B, 97 (1970).

Scudieri, F.

M. Bertolotti, S. Lagomarsino, F. Scudieri, D. Sette, J. Phys. C 6, L177 (1973).
[Crossref]

R. Bartolino, M. Bertolotti, F. Scudieri, D. Sette, Appl. Opt. 12, 2917 (December1973).
[Crossref] [PubMed]

M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. Supplem. fasc. 2-3 33, CI-63 (1972).

M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. A 4, 197 (1971).
[Crossref]

M. Bertolotti, F. Scudieri, unpublished.

Sette, D.

R. Bartolino, M. Bertolotti, F. Scudieri, D. Sette, Appl. Opt. 12, 2917 (December1973).
[Crossref] [PubMed]

M. Bertolotti, S. Lagomarsino, F. Scudieri, D. Sette, J. Phys. C 6, L177 (1973).
[Crossref]

M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. Supplem. fasc. 2-3 33, CI-63 (1972).

M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. A 4, 197 (1971).
[Crossref]

M. Bertolotti, L. Muzii, D. Sette, J. Opt. Soc. Am. 60, 1603 (1970).
[Crossref]

M. Bertolotti, M. Carnevale, L. Muzii, D. Sette, Appl. Opt. 9, 510 (1970).
[Crossref]

F. Gori, D. Sette, Phys. Rev. Lett. 17, 361 (1966).
[Crossref]

Spiller, E.

W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
[Crossref]

van Boxtel, A. M.

N. Koelmans, A. M. van Boxtel, Phys. Lett. 32A, 32 (1970).

Veyssie, M.

G. Durand, M. Veyssie, F. Rondelez, L. Loger, Compt. Rend. 270B, 97 (1970).

Williams, R.

See, for example, R. Williams, J. Chem. Phys. 39, 384 (1963).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965).

Zanoni, L. A.

G. Heilmeier, L. A. Zanoni, L. A. Barton, Proc. IEEE 56, 1162 (1968).
[Crossref]

Am. J. Phys. (1)

W. Martienssen, E. Spiller, Am. J. Phys. 32, 919 (1964).
[Crossref]

Appl. Opt. (2)

Compt. Rend. (1)

G. Durand, M. Veyssie, F. Rondelez, L. Loger, Compt. Rend. 270B, 97 (1970).

J. Appl. Phys. (1)

C. Deutsch, P. N. Keating, J. Appl. Phys. 40, 4049 (1969).
[Crossref]

J. Chem. Phys. (1)

See, for example, R. Williams, J. Chem. Phys. 39, 384 (1963).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. A (1)

M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. A 4, 197 (1971).
[Crossref]

J. Phys. C (1)

M. Bertolotti, S. Lagomarsino, F. Scudieri, D. Sette, J. Phys. C 6, L177 (1973).
[Crossref]

J. Phys. Supplem. fasc. 2-3 (1)

M. Bertolotti, B. Daino, P. Di Porto, F. Scudieri, D. Sette, J. Phys. Supplem. fasc. 2-3 33, CI-63 (1972).

Phys. Lett. (1)

N. Koelmans, A. M. van Boxtel, Phys. Lett. 32A, 32 (1970).

Phys. Rev. Lett. (1)

F. Gori, D. Sette, Phys. Rev. Lett. 17, 361 (1966).
[Crossref]

Proc. IEEE (1)

G. Heilmeier, L. A. Zanoni, L. A. Barton, Proc. IEEE 56, 1162 (1968).
[Crossref]

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965).

M. Bertolotti, F. Scudieri, unpublished.

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Figures (6)

Fig. 1
Fig. 1

Experimental setup used for studying spatial coherence of the scattered light.

Fig. 2
Fig. 2

The fringes obtained from the scattered beam with the reversing front interferometer.

Fig. 3
Fig. 3

Coherence length lc vs D. The applied voltage was V = 50 V, the observation angle θ ≃ 9°. Temperature T = 25°C. Black dots refer to MBBA, squares to the rotating disk. The continuous curve is from Eq. (2).

Fig. 4
Fig. 4

Coherence length lc vs V at θ ≃ 17°, T = 25°C.

Fig. 5
Fig. 5

Line width Δω/2π of scattered light as a function of the square of the applied electric field E. The MBBA (black circles) cell was 6 μm thick, temperature was 25°C, angle of scattering θ ≃ 10°. The APAPA (open circles) cell was 6 μm thick, temperature 93.5°C, angle of scattering θ ≃ 9°.

Fig. 6
Fig. 6

Line width Δω/2π of scattered light as a function of the transferred momentum k. Black dots refer to a 6-μm cell of MBBA. The applied electric field was E = 3.3 × 104. Curve (α) refers to an APAPA cell 6 μm thick at T = 93.5°C, E = 2.6 × 104 V/cm and curve (β) refers to an APAPA cell 25 μm thick at the same temperature (E = 3 × 104 V/cm).

Equations (3)

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I ( k , ω ) = C ( k , E ) exp ( - { ( ω - ω 0 ) 2 / [ 2 k 2 u 1 2 ( E ) ¯ ] } )
u 1 2 ( E ) ¯
l c = ( 0.61 λ ¯ ) / α .

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