Abstract

Effective electro-optic coefficients are measured from the interference signal between a transmitted beam and a reflected beam passing through a crystal three times. The advantages are simplicity of configuration and ease of measurement. The experimental error caused by multiple reflections in the crystal is also discussed.

© 1982 Optical Society of America

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References

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  1. R. O’B. Carpenter, “The electro-optic effect in uniaxial crystal of the dihydrogen phosphate type,” J. Opt. Soc. Am. 40, 225–229 (1950).
    [CrossRef]
  2. S. Namba, “Electro-optical effect of zincblende,” J. Opt. Soc. Am. 51, 76–79 (1961).
    [CrossRef]
  3. I. P. Kaminow, “Barium titanate light phase modulator,” Appl. Phys. Lett. 7, 123–125 (1965).
    [CrossRef]
  4. E. H. Turner, “High-frequency electro-optic coefficients of lithium niobate,” Appl. Phys. Lett. 8, 303–304 (1966).
    [CrossRef]
  5. K. Onuki, N. Uchida, and T. Saku, “Interferometric method for measuring electro-optic coefficients in crystals,” J. Opt. Soc. Am. 62, 1030–1032 (1972).
    [CrossRef]
  6. The refractive indices of these crystals are quoted from Landolt–Börnstein and K.-H. Hellweg, ed. (Springer-Verlag, Berlin, 1979), Vol. 11.
  7. J. D. Zook, D. Chen, and G. H. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–167 (1967).
    [CrossRef]
  8. K. F. Hulme, P. H. Davies, and V. M. Cound, “The signs of the electro-optic coefficients for lithium niobate,” J. Phys. C2, 855–857 (1969).

1972 (1)

1969 (1)

K. F. Hulme, P. H. Davies, and V. M. Cound, “The signs of the electro-optic coefficients for lithium niobate,” J. Phys. C2, 855–857 (1969).

1967 (1)

J. D. Zook, D. Chen, and G. H. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–167 (1967).
[CrossRef]

1966 (1)

E. H. Turner, “High-frequency electro-optic coefficients of lithium niobate,” Appl. Phys. Lett. 8, 303–304 (1966).
[CrossRef]

1965 (1)

I. P. Kaminow, “Barium titanate light phase modulator,” Appl. Phys. Lett. 7, 123–125 (1965).
[CrossRef]

1961 (1)

1950 (1)

Carpenter, R. O’B.

Chen, D.

J. D. Zook, D. Chen, and G. H. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–167 (1967).
[CrossRef]

Cound, V. M.

K. F. Hulme, P. H. Davies, and V. M. Cound, “The signs of the electro-optic coefficients for lithium niobate,” J. Phys. C2, 855–857 (1969).

Davies, P. H.

K. F. Hulme, P. H. Davies, and V. M. Cound, “The signs of the electro-optic coefficients for lithium niobate,” J. Phys. C2, 855–857 (1969).

Hulme, K. F.

K. F. Hulme, P. H. Davies, and V. M. Cound, “The signs of the electro-optic coefficients for lithium niobate,” J. Phys. C2, 855–857 (1969).

Kaminow, I. P.

I. P. Kaminow, “Barium titanate light phase modulator,” Appl. Phys. Lett. 7, 123–125 (1965).
[CrossRef]

Namba, S.

Onuki, K.

Otto, G. H.

J. D. Zook, D. Chen, and G. H. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–167 (1967).
[CrossRef]

Saku, T.

Turner, E. H.

E. H. Turner, “High-frequency electro-optic coefficients of lithium niobate,” Appl. Phys. Lett. 8, 303–304 (1966).
[CrossRef]

Uchida, N.

Zook, J. D.

J. D. Zook, D. Chen, and G. H. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–167 (1967).
[CrossRef]

Appl. Phys. Lett. (3)

I. P. Kaminow, “Barium titanate light phase modulator,” Appl. Phys. Lett. 7, 123–125 (1965).
[CrossRef]

E. H. Turner, “High-frequency electro-optic coefficients of lithium niobate,” Appl. Phys. Lett. 8, 303–304 (1966).
[CrossRef]

J. D. Zook, D. Chen, and G. H. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–167 (1967).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Phys. (1)

K. F. Hulme, P. H. Davies, and V. M. Cound, “The signs of the electro-optic coefficients for lithium niobate,” J. Phys. C2, 855–857 (1969).

Other (1)

The refractive indices of these crystals are quoted from Landolt–Börnstein and K.-H. Hellweg, ed. (Springer-Verlag, Berlin, 1979), Vol. 11.

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Figures (3)

Fig. 1
Fig. 1

Schematic arrangement for measuring the effective EO coefficients of a crystal. The bandpass filter selects only the fundamental component sin pt.

Fig. 2
Fig. 2

Multiple reflections of light in crystal at normal incidence. The figure is drawn schematically in order to show each optical beam.

Fig. 3
Fig. 3

Dependence of the experimental error of effective EO coefficients on the reflectivity R of crystal. Straight lines show the reflectivities obtained from ordinary reflective indices of several crystals at normal incidence and λ = 600 nm.

Tables (1)

Tables Icon

Table 1 Effective EO Coefficients of LiTaO3 and LiNbO3 Crystals, Measured at λ = 633 nm by Our Methoda

Equations (9)

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α = π n 3 L V λ w ( - γ + 2 d n 2 ) ,
I = A 2 { k = 0 m R k sin [ ω t + ( 2 k + 1 ) ( α sin p t + ϕ ) ] } 2 = A 2 k = 0 m R 2 k sin 2 [ ω t + ( 2 k + 1 ) ( α sin p t + ϕ ) ] + 2 A 2 l = 0 m - 1 k = 1 m - l R k + 2 l sin [ ω t + ( 2 l + 1 ) ( α sin p t + ϕ ) ] × sin [ ω t + ( 2 k + 2 l + 1 ) ( α sin p t + ϕ ) ] .
I d = A 2 2 k = 0 m R 2 k + A 2 l = 0 m - 1 k = 1 m - l R k + 2 l cos [ 2 k ( α sin p t + ϕ ) ] = A 2 2 k = 0 m R 2 k + A 2 l = 0 m - 1 k = 1 m - l R k + 2 l × { cos ( 2 k ϕ ) [ J 0 ( 2 k α ) + 2 r = 1 J 2 r ( 2 k α ) cos ( 2 r p t ) ] - 2 sin ( 2 k ϕ ) r = 0 J 2 r + 1 ( 2 k α ) sin [ ( 2 r + 1 ) p t ] } ,
I m = - 2 A 2 l = 0 m - 1 k = 1 m - l R k + 2 l sin ( 2 k ϕ ) J 1 ( 2 k α ) sin p t .
I 1 = - 2 A 2 R sin ( 2 ϕ ) J 1 ( 2 α ) sin p t .
I 2 = - 2 A 2 R sin p t × [ ( 1 + R 2 ) sin ( 2 ϕ ) J 1 ( 2 α ) + R sin ( 4 ϕ ) J 1 ( 4 α ) ] .
ϕ ( V 1 ) = - ϕ 0 ,             ϕ ( V 2 ) = π / 2 - ϕ 0 ,
I 3 = - 2 A 2 R sin p t [ ( 1 + R 2 + R 4 ) sin ( 2 ϕ ) J 1 ( 2 α ) + ( R + R 3 ) sin ( 4 ϕ ) J 1 ( 4 α ) + R 2 sin ( 6 ϕ ) J 1 ( 6 α ) ] .
I 3 = - 2 A 2 R sin p t [ ( 1 + R 2 + R 4 ) J 1 ( 2 α ) - R 2 J 1 ( 6 α ) ] .