Abstract

To assess the suitability of bismuth germanate as an electro-optic material for high precision applications, we have confirmed and extended previous data on its refractive index, electro-optic tensor element r 41, and thermal expansion coefficient. In addition, we have measured the thermo-optic coefficient dn/dT, the temperature dependence of the electro-optic coefficient, and the stress-optic tensor elements. From the stress-optic tensor elements and previously published data, we have computed the strain-optic tensor elements. The index of refraction is given, to a good approximation, by the single-term Sellmeier equation, n 2 − 1 = s 0λ0 2/[1 − (λ0/λ)2], with s 0 = 95.608 μm−2 and λ0 = 0.1807 μm. The thermo-optic coefficient is 3.9 × 10−5/°C at 632.8 nm and 3.5 × 10−5/°C at 1152.3 nm. The electro-optic tensor element varies between approximately 1.05 and 1.11 pm/V over the spectral range of 550–1000 nm; its normalized effective change with temperature is approximately 1.54 × 10−4/°C. The thermal expansion coefficient is 6.3 × 10−6/°C over the range 15–125 °C. Values of the stress-optic tensor elements are q 11q 12 = −2.995 × 10−13 m2/N and q 44 = −0.1365 3 10−12 m2/N. The strain-optic tensor elements are p 11p 12 = −0.0266 and p 44 = −0.0595.

© 1996 Optical Society of America

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  1. S. Weikel, G. Stranovshky, “Application of an electro-optic voltage transducer at 345 kV,” in Proceedings of the EPRI Workshop on Optical Sensors for Utility T&D Applications (Electric Power Research Institute, Palo Alto, Calif., 1996);K. Kurosawa, “Development and field tests of optical fiber sensors for electric power systems,” in Proceedings, 7th International Conference on Optical Fiber Sensors (Institution of Radio and Electronics Engineers Australia, Edgecliff, NSW, 1990), pp. 67–72;G. W. Day, P. D. Hale, M. N. Deeter, T. E. Milner, D. Conrad, S. M. Etzel, “Limits to the precision of electro-optic and magneto-optic sensors,” Natl. Bur. Stand. (U.S.) Tech. Note 1307, 3-1–4-23 (1987);M. Kanoi, G. Takahashi, T. Sato, M. Higaki, E. Mori, K. Okamura, “Optical voltage and current measuring system for electric power systems,” IEEE Trans. Power Deliv. PWRD-1, 91–97 (1986);B. N. Nelson, C. Menzel, T. G. DiGiuseppe, “Fiber-optic electric field sensor configurations for high bandwidth lightning research measurement applications,” in High Bandwidth Analog Applications of Photonics, J. S. Chang, ed., Proc. SPIE720, 85–90 (1986);K. Shibata, “A fibre optic electric field sensor using the electro-optic effect of Bi4Ge3O12,” in Proceedings, First International Conference on Optical Fibre Sensors (Institution of Electrical Engineers, London, 1983), pp. 164–168.
    [Crossref]
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    [Crossref]
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    [Crossref]
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1993 (1)

O. Kamada, K. Kakishita, “Electro-optical effect of Bi4Ge3O12 crystals for optical voltage sensors,” Jpn. J. Appl. Phys. 32, 4288–4291 (1993).
[Crossref]

1992 (1)

1989 (1)

1982 (1)

M. Young, “Refracted ray scanning,” Natl. Bur. Stand. (U.S.) Spec. Publ. 637, 130–134 (1982).

1979 (1)

A. Feldman, D. Horowitz, R. M. Waxler, M. J. Dodge, “Optical materials characterization,” Natl. Bur. Stand. (U.S.) Tech. Note 993, 7–15 (1979).

1975 (1)

A. Feldman, W. J. McKean, “Improved stressing apparatus for photoelasticity measurements,” Rev. Sci. Instrum. 46, 1588–1589 (1975).
[Crossref]

1972 (1)

D. P. Bortfeld, H. Meier, “Refractive indices and electro-optic coefficients of the eulytites Bi4Ge3O12,” J. Appl. Phys. 43, 5110–5111 (1972).
[Crossref]

1969 (1)

H. Schweppe, “Electro-mechanical properties of bismuth germanate, Bi4(GeO4)3,” IEEE Trans. Sonics Ultrason. SU-16, 219 (1969).

1965 (1)

R. Nitsche, “Crystal growth and electro-optic effect of bismuth germanate, Bi4(GeO4)3,” J. Appl. Phys. 36, 2358–2360 (1965).
[Crossref]

1961 (1)

1941 (1)

1940 (1)

H. Barrel, J. E. Sears, “The refraction and dispersion of air for the visible spectrum,” Philos. Trans. R. Soc. London 238, 1–64 (1940).
[Crossref]

Barrel, H.

H. Barrel, J. E. Sears, “The refraction and dispersion of air for the visible spectrum,” Philos. Trans. R. Soc. London 238, 1–64 (1940).
[Crossref]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 7, p. 330.

Bortfeld, D. P.

D. P. Bortfeld, H. Meier, “Refractive indices and electro-optic coefficients of the eulytites Bi4Ge3O12,” J. Appl. Phys. 43, 5110–5111 (1972).
[Crossref]

Dodge, M. J.

A. Feldman, D. Horowitz, R. M. Waxler, M. J. Dodge, “Optical materials characterization,” Natl. Bur. Stand. (U.S.) Tech. Note 993, 7–15 (1979).

Feldman, A.

A. Feldman, D. Horowitz, R. M. Waxler, M. J. Dodge, “Optical materials characterization,” Natl. Bur. Stand. (U.S.) Tech. Note 993, 7–15 (1979).

A. Feldman, W. J. McKean, “Improved stressing apparatus for photoelasticity measurements,” Rev. Sci. Instrum. 46, 1588–1589 (1975).
[Crossref]

Günter, P.

Horowitz, D.

A. Feldman, D. Horowitz, R. M. Waxler, M. J. Dodge, “Optical materials characterization,” Natl. Bur. Stand. (U.S.) Tech. Note 993, 7–15 (1979).

Jones, R. C.

Kakishita, K.

O. Kamada, K. Kakishita, “Electro-optical effect of Bi4Ge3O12 crystals for optical voltage sensors,” Jpn. J. Appl. Phys. 32, 4288–4291 (1993).
[Crossref]

Kamada, O.

O. Kamada, K. Kakishita, “Electro-optical effect of Bi4Ge3O12 crystals for optical voltage sensors,” Jpn. J. Appl. Phys. 32, 4288–4291 (1993).
[Crossref]

Lee, K. S.

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics (Longmans, London, 1973), Chap. 5, pp. 82–89.

McKean, W. J.

A. Feldman, W. J. McKean, “Improved stressing apparatus for photoelasticity measurements,” Rev. Sci. Instrum. 46, 1588–1589 (1975).
[Crossref]

Meier, H.

D. P. Bortfeld, H. Meier, “Refractive indices and electro-optic coefficients of the eulytites Bi4Ge3O12,” J. Appl. Phys. 43, 5110–5111 (1972).
[Crossref]

Montemezzani, G.

Namba, S.

Narasimhamurty, T. S.

T. S. Narasimhamurty, Photoelastic and Electro-Optic Properties of Crystals (Plenum, New York, 1981), Chap. 2, pp. 23–45; Chap. 5, pp. 197–274.

Nitsche, R.

R. Nitsche, “Crystal growth and electro-optic effect of bismuth germanate, Bi4(GeO4)3,” J. Appl. Phys. 36, 2358–2360 (1965).
[Crossref]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Oxford, U. Press, New York, 1964), Chap. 1, pp. 3–32.

Pfändler, S.

Schweppe, H.

H. Schweppe, “Electro-mechanical properties of bismuth germanate, Bi4(GeO4)3,” IEEE Trans. Sonics Ultrason. SU-16, 219 (1969).

Sears, J. E.

H. Barrel, J. E. Sears, “The refraction and dispersion of air for the visible spectrum,” Philos. Trans. R. Soc. London 238, 1–64 (1940).
[Crossref]

Stranovshky, G.

S. Weikel, G. Stranovshky, “Application of an electro-optic voltage transducer at 345 kV,” in Proceedings of the EPRI Workshop on Optical Sensors for Utility T&D Applications (Electric Power Research Institute, Palo Alto, Calif., 1996);K. Kurosawa, “Development and field tests of optical fiber sensors for electric power systems,” in Proceedings, 7th International Conference on Optical Fiber Sensors (Institution of Radio and Electronics Engineers Australia, Edgecliff, NSW, 1990), pp. 67–72;G. W. Day, P. D. Hale, M. N. Deeter, T. E. Milner, D. Conrad, S. M. Etzel, “Limits to the precision of electro-optic and magneto-optic sensors,” Natl. Bur. Stand. (U.S.) Tech. Note 1307, 3-1–4-23 (1987);M. Kanoi, G. Takahashi, T. Sato, M. Higaki, E. Mori, K. Okamura, “Optical voltage and current measuring system for electric power systems,” IEEE Trans. Power Deliv. PWRD-1, 91–97 (1986);B. N. Nelson, C. Menzel, T. G. DiGiuseppe, “Fiber-optic electric field sensor configurations for high bandwidth lightning research measurement applications,” in High Bandwidth Analog Applications of Photonics, J. S. Chang, ed., Proc. SPIE720, 85–90 (1986);K. Shibata, “A fibre optic electric field sensor using the electro-optic effect of Bi4Ge3O12,” in Proceedings, First International Conference on Optical Fibre Sensors (Institution of Electrical Engineers, London, 1983), pp. 164–168.
[Crossref]

Waxler, R. M.

A. Feldman, D. Horowitz, R. M. Waxler, M. J. Dodge, “Optical materials characterization,” Natl. Bur. Stand. (U.S.) Tech. Note 993, 7–15 (1979).

Weikel, S.

S. Weikel, G. Stranovshky, “Application of an electro-optic voltage transducer at 345 kV,” in Proceedings of the EPRI Workshop on Optical Sensors for Utility T&D Applications (Electric Power Research Institute, Palo Alto, Calif., 1996);K. Kurosawa, “Development and field tests of optical fiber sensors for electric power systems,” in Proceedings, 7th International Conference on Optical Fiber Sensors (Institution of Radio and Electronics Engineers Australia, Edgecliff, NSW, 1990), pp. 67–72;G. W. Day, P. D. Hale, M. N. Deeter, T. E. Milner, D. Conrad, S. M. Etzel, “Limits to the precision of electro-optic and magneto-optic sensors,” Natl. Bur. Stand. (U.S.) Tech. Note 1307, 3-1–4-23 (1987);M. Kanoi, G. Takahashi, T. Sato, M. Higaki, E. Mori, K. Okamura, “Optical voltage and current measuring system for electric power systems,” IEEE Trans. Power Deliv. PWRD-1, 91–97 (1986);B. N. Nelson, C. Menzel, T. G. DiGiuseppe, “Fiber-optic electric field sensor configurations for high bandwidth lightning research measurement applications,” in High Bandwidth Analog Applications of Photonics, J. S. Chang, ed., Proc. SPIE720, 85–90 (1986);K. Shibata, “A fibre optic electric field sensor using the electro-optic effect of Bi4Ge3O12,” in Proceedings, First International Conference on Optical Fibre Sensors (Institution of Electrical Engineers, London, 1983), pp. 164–168.
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 7, p. 330.

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 7, pp. 220–275.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 7, pp. 220–275.

Young, M.

M. Young, “Refracted ray scanning,” Natl. Bur. Stand. (U.S.) Spec. Publ. 637, 130–134 (1982).

Appl. Opt. (1)

IEEE Trans. Sonics Ultrason. (1)

H. Schweppe, “Electro-mechanical properties of bismuth germanate, Bi4(GeO4)3,” IEEE Trans. Sonics Ultrason. SU-16, 219 (1969).

J. Appl. Phys. (2)

R. Nitsche, “Crystal growth and electro-optic effect of bismuth germanate, Bi4(GeO4)3,” J. Appl. Phys. 36, 2358–2360 (1965).
[Crossref]

D. P. Bortfeld, H. Meier, “Refractive indices and electro-optic coefficients of the eulytites Bi4Ge3O12,” J. Appl. Phys. 43, 5110–5111 (1972).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (1)

O. Kamada, K. Kakishita, “Electro-optical effect of Bi4Ge3O12 crystals for optical voltage sensors,” Jpn. J. Appl. Phys. 32, 4288–4291 (1993).
[Crossref]

Natl. Bur. Stand. (U.S.) Spec. Publ. (1)

M. Young, “Refracted ray scanning,” Natl. Bur. Stand. (U.S.) Spec. Publ. 637, 130–134 (1982).

Natl. Bur. Stand. (U.S.) Tech. Note (1)

A. Feldman, D. Horowitz, R. M. Waxler, M. J. Dodge, “Optical materials characterization,” Natl. Bur. Stand. (U.S.) Tech. Note 993, 7–15 (1979).

Philos. Trans. R. Soc. London (1)

H. Barrel, J. E. Sears, “The refraction and dispersion of air for the visible spectrum,” Philos. Trans. R. Soc. London 238, 1–64 (1940).
[Crossref]

Rev. Sci. Instrum. (1)

A. Feldman, W. J. McKean, “Improved stressing apparatus for photoelasticity measurements,” Rev. Sci. Instrum. 46, 1588–1589 (1975).
[Crossref]

Other (6)

T. S. Narasimhamurty, Photoelastic and Electro-Optic Properties of Crystals (Plenum, New York, 1981), Chap. 2, pp. 23–45; Chap. 5, pp. 197–274.

J. F. Nye, Physical Properties of Crystals (Oxford, U. Press, New York, 1964), Chap. 1, pp. 3–32.

S. Weikel, G. Stranovshky, “Application of an electro-optic voltage transducer at 345 kV,” in Proceedings of the EPRI Workshop on Optical Sensors for Utility T&D Applications (Electric Power Research Institute, Palo Alto, Calif., 1996);K. Kurosawa, “Development and field tests of optical fiber sensors for electric power systems,” in Proceedings, 7th International Conference on Optical Fiber Sensors (Institution of Radio and Electronics Engineers Australia, Edgecliff, NSW, 1990), pp. 67–72;G. W. Day, P. D. Hale, M. N. Deeter, T. E. Milner, D. Conrad, S. M. Etzel, “Limits to the precision of electro-optic and magneto-optic sensors,” Natl. Bur. Stand. (U.S.) Tech. Note 1307, 3-1–4-23 (1987);M. Kanoi, G. Takahashi, T. Sato, M. Higaki, E. Mori, K. Okamura, “Optical voltage and current measuring system for electric power systems,” IEEE Trans. Power Deliv. PWRD-1, 91–97 (1986);B. N. Nelson, C. Menzel, T. G. DiGiuseppe, “Fiber-optic electric field sensor configurations for high bandwidth lightning research measurement applications,” in High Bandwidth Analog Applications of Photonics, J. S. Chang, ed., Proc. SPIE720, 85–90 (1986);K. Shibata, “A fibre optic electric field sensor using the electro-optic effect of Bi4Ge3O12,” in Proceedings, First International Conference on Optical Fibre Sensors (Institution of Electrical Engineers, London, 1983), pp. 164–168.
[Crossref]

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), Chap. 7, pp. 220–275.

R. S. Longhurst, Geometrical and Physical Optics (Longmans, London, 1973), Chap. 5, pp. 82–89.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 7, p. 330.

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Figures (8)

Fig. 1
Fig. 1

Index of refraction data for BGO. The open circles are from Ref. 3 and the squares are from Ref. 4. The solid circles are from this study. The curve is Eq. (4), with the parameters taken from the combined set of data in Table 2.

Fig. 2
Fig. 2

Apparatus for measuring dn/dT and α; BS, beam splitter.

Fig. 3
Fig. 3

Orientation of the crystal used in the electro-optic measurements.

Fig. 4
Fig. 4

System for measuring n 0 3 r 41; AC VM, ac voltmeter.

Fig. 5
Fig. 5

System for measuring d(n 0 3 r 41)/dT; AC VM, ac voltmeter.

Fig. 6
Fig. 6

R Δ/Σ versus temperature in BGO at 670 nm.

Fig. 7
Fig. 7

Geometry of specimens used for the stress-optic measurements.

Fig. 8
Fig. 8

Typical data for the determination of q 44.

Tables (5)

Tables Icon

Table 1 Measured Index of Refraction for Bismuth Germanate

Tables Icon

Table 2 Parameters of the Sellmeier Equation for BGO

Tables Icon

Table 3 Thermo-Optic Coefficients of BGO

Tables Icon

Table 4 Electro-Optic Properties of Bismuth Germinate at Low Frequencies

Tables Icon

Table 5 Photoelastic Constants of Bismuth Germanate at a Wavelength of 632.8 nm

Equations (24)

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n = sin ( θ m / 2 + β / 2 ) sin ( β / 2 ) .
Δ n β = n 2 [ cot ( β 2 ) cot ( β + θ m 2 ) ] Δ β ,
Δ n θ m = n 2 cot ( β + θ m 2 ) Δ θ m .
n 2 1 = s 0 λ 0 2 1 ( λ 0 / λ ) 2 .
| n 2 n 1 | = M λ 2 h 1 n 1 Δ h h 1 ,
Δ n Δ T = M λ 2 h 1 Δ T n 1 α .
Δ h h 2 h 1 = M λ 2 n a 2 h 1 Δ n a 2 n a 2 ,
α Δ h h 1 Δ T = M λ 2 h 1 n a 2 Δ T Δ n a n a 2 Δ T ,
Δ n a n a 2 Δ T ( 0.6 ± 0.06 ) × 10 6 / ° C .
δ E = 2 π λ n 0 3 r 41 V h d ,
R ( δ E , δ S ) ± = Γ ± ( 1 ± δ E sin 2 ϕ 2 ϕ ) ,
R ( δ E , δ S ) Δ / Σ = δ E sin 2 ϕ 2 ϕ .
1 R Δ / Σ d R Δ / Σ d T = ( 1 n 0 3 r 41 d n 0 3 r 41 d T + α ) ( 1 + K δ E 2 ) + ( K δ S 2 ) 1 δ S d δ S d T ,
K = cot 2 ϕ 2 ϕ 1 4 ϕ 2 .
1 n 0 3 r 41 d n 0 3 r 41 d T 1 R Δ / Σ d R Δ / Σ d T ( 5.8 ± 0.5 ) × 10 6 .
B n n = n 0 3 2 ( q 11 q 12 ) σ ,
B n n = n 0 3 2 q 44 σ .
δ σ = 2 π λ ( n n ) h ,
p 44 = q 44 c 44 ,
p 11 p 12 = ( q 11 q 12 ) ( c 11 c 12 ) .
[ E x E y ] = [ 1 0 0 0 ] [ A B C D ] 1 2 [ 1 i i 1 ] [ E x 0 ] ,
A = cos ϕ i δ S sin ϕ 2 ϕ = D * , B = 1 2 i δ E sin ϕ ϕ = C ,
ϕ 1 2 ( δ S 2 + δ E 2 ) 1 / 2 ,
R ( δ E , δ S ) ± = Γ ± ( 1 ± δ E sin 2 ϕ 2 ϕ ) ,

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