Abstract

The electro-optic coefficients of two crystals have been measured by both static and dynamic methods. For NH4H2PO4, r63=2.54, r41=6.25; for KH2PO4, r63=3.15, r41=2.58 (units 10−7 c.g.s., 20°C λ5560). The variation of the electro-optic response with the frequency of the applied field is given and related to the piezoelectric vibrations of the crystal. A theoretical relation for the difference in the electro-optic constants measured at constant stress and at constant strain is derived, which provides a check on the consistency of the presently available electro-optic, photo-elastic, piezoelectric, and elastic coefficients for these crystals. The use of a.c. methods to obtain high precision in polarization measurements is discussed.

© 1950 Optical Society of America

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References

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  1. B. H. Billings, J. Opt. Soc. Am. 39, 797 (1949); J. Opt. Soc. Am. 39, 802 (1949).
    [CrossRef]
  2. W. P. Mason, Phys. Rev. 69, 173 (1946).
    [CrossRef]
  3. B. Zwicker and P. Scherrer, Helv. Phys. Acta 17, 346 (1944).
  4. H. G. Jerrard, J. Opt. Soc. Am. 38, 35 (1948).
    [CrossRef]
  5. E. P. Tawil, Comptes Rendus 183, 1099 (1926); Rev. gén. de l’élec. 25, 58 (1929); W. G. Cady, Piezoelectricity (McGraw-Hill Book Company, Inc., New York, 1946), p. 465.
  6. C. D. West and A. S. Makas, reported at April, 1949meeting of Crystallographic Society of America.

1949 (1)

1948 (1)

1946 (1)

W. P. Mason, Phys. Rev. 69, 173 (1946).
[CrossRef]

1944 (1)

B. Zwicker and P. Scherrer, Helv. Phys. Acta 17, 346 (1944).

1926 (1)

E. P. Tawil, Comptes Rendus 183, 1099 (1926); Rev. gén. de l’élec. 25, 58 (1929); W. G. Cady, Piezoelectricity (McGraw-Hill Book Company, Inc., New York, 1946), p. 465.

Billings, B. H.

Jerrard, H. G.

Makas, A. S.

C. D. West and A. S. Makas, reported at April, 1949meeting of Crystallographic Society of America.

Mason, W. P.

W. P. Mason, Phys. Rev. 69, 173 (1946).
[CrossRef]

Scherrer, P.

B. Zwicker and P. Scherrer, Helv. Phys. Acta 17, 346 (1944).

Tawil, E. P.

E. P. Tawil, Comptes Rendus 183, 1099 (1926); Rev. gén. de l’élec. 25, 58 (1929); W. G. Cady, Piezoelectricity (McGraw-Hill Book Company, Inc., New York, 1946), p. 465.

West, C. D.

C. D. West and A. S. Makas, reported at April, 1949meeting of Crystallographic Society of America.

Zwicker, B.

B. Zwicker and P. Scherrer, Helv. Phys. Acta 17, 346 (1944).

Comptes Rendus (1)

E. P. Tawil, Comptes Rendus 183, 1099 (1926); Rev. gén. de l’élec. 25, 58 (1929); W. G. Cady, Piezoelectricity (McGraw-Hill Book Company, Inc., New York, 1946), p. 465.

Helv. Phys. Acta (1)

B. Zwicker and P. Scherrer, Helv. Phys. Acta 17, 346 (1944).

J. Opt. Soc. Am. (2)

Phys. Rev. (1)

W. P. Mason, Phys. Rev. 69, 173 (1946).
[CrossRef]

Other (1)

C. D. West and A. S. Makas, reported at April, 1949meeting of Crystallographic Society of America.

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Figures (5)

Fig. 1
Fig. 1

Senarmont compensator method for static measurement of r63; F—filter, P—polarizer, Cz cut crystal of retardation, Γ=ω3r63V/λ, A—2° split field analyzer. When analyzer is rotated to match intensities, ϕ=πΓ.

Fig. 2
Fig. 2

Voltage required to produce 1 2-wave retardation in basal section of NH4H2PO4 as function of wave-length.

Fig. 3
Fig. 3

Arrangement for measuring relative frequency response of electro-optic effect.

Fig. 4
Fig. 4

High frequency response of electro-optic effect in NH4H2PO4 crystal.

Fig. 5
Fig. 5

Arrangement for measuring r41 by a.c. method; vibration direction of x cut crystal depends on the field: (α=r41Ex/(e2o2)).

Tables (1)

Tables Icon

Table I Electro-optic coefficients of NH4H2PO4 and KH2PO4 at 22°C, λ5560, in c.g.s. units (statvolts/cm)−1.

Equations (28)

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[equation omitted on the printed page]
2 α tan 2 α = - 2 r 41 E x e 2 - o 2 .
n x = ω n y = ω + 1 2 ω 5 2 ω 2 - 2 ( r 41 E x ) 2 n z = - 1 2 5 ω 2 ω 2 - 2 ( r 41 E x ) 2 .
y - z = 0.
B y z = 1 2 ( ω - ) - ( ω 3 / 2 ) r 41 E x .
Γ = B z d λ = ω 2 r 63 V λ ,
Ω = 2 ω ( 2 r 63 E z e 2 - o 2 ) 1 2 .
I I 0 = cos 2 ( π Γ - ϕ ) ,
I / I 0 = sin 2 π Γ = 1 2 ( 1 - cos 2 π Γ ) .
Γ = 1 4 + ω 3 r 63 V s sin ω t λ .
I I 0 = 1 2 - π ω 3 r 63 V s λ sin ω t .
a 1 x 2 + a 2 y 2 + a 3 z 2 + 2 a 4 y z + 2 a 5 z x + 2 a 6 x y = 1.
Δ a i = j = 1 3 r i j E j + j = 1 6 π i j X j
Δ a i = j = 1 3 r i j E j + k = 1 6 p i k x k ,
x k = - j = 1 6 s k j X j + j = 1 3 d j k E j ,
Δ a i = j = 1 3 { r i j + k = 1 6 p i k d j k } E j + j = 1 6 { k = 1 6 p i k s r j } X j .
π i j = k = 1 6 p i k s k j
r i j = r i j + k = 1 6 p i k d j k .
r 63 = r 63 + p 66 d 36 .
I / I 0 = 1 2 + 1 2 sin 2 π Γ sin 4 α ,
I I 0 = 1 2 + α = 1 2 - r 41 E x e 2 - o 2 .
r 41 = d ( e 2 - o 2 ) I 0 I s V s .
( I N ) r.m..s = ( G I e τ ) 1 2 ,
I ( 1 + β sin ω t )
I s I N = β ( I τ 2 G e ) 1 2
β min = ( 2 G e I τ ) 1 2 .