Abstract

Crystals of Bi4Ge3O12 from two different sources exhibited linear birefringences of 1.7 × 10−5–5.4 × 10−5 (or phase retardations of 1.3–4.1°/cm) at a wavelength of 830 nm. These birefringences, however, are sensitive to temperature. The temperature variation of the birefringence dB/(B0dT) normalized by the room temperature birefringence B0 was −1 to −7 × 10−3/°C. The effects of the temperature dependent birefringence and the birefringence induced by pressure on an electrooptic voltage sensor were measured and quantitatively compared to the predictions. To remove the temperature dependent birefringences, the crystals were annealed over two days. The birefringences were reduced to about half of their original values after a first annealing process, but the values remained unchanged after a second annealing process. To eliminate the effects of the birefringences, a compensation method was used. After applying this compensation method to an electrooptic voltage sensor, the temperature stability of the sensor was improved to ±0.75% from ±7.0% in the temperature range between −2 and 65°C, and the pressure stability was improved to ±0.2% from ±2% under pressure as high as 1 × 105 N/m2.

© 1990 Optical Society of America

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References

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  1. K. Shibata, “A Fiber Optic Electric Field Sensor Using the Electrooptic Effect of Bi4Ge3O12,” in Proceedings, First International Conference on Optical Fibre Sensors, London (1983), pp. 164–168.
  2. G. W. Day, K. S. Lee, A. H. Rose, L. R. Veeser, B. J. Papatheofanis, H. K. Whitesel, “Optical Fiber Sensors for Electromagnetic Quantities,” in Proceedings, Department of Defenses, Fiber Optics Conference ’88 (1988).
  3. K. S. Lee, “New Compensation for Bulk Optical Sensors with Multiple Birefringences,” Appl. Opt. 28, 2001–2011 (1989).
    [CrossRef] [PubMed]
  4. A. Horowitz, G. Kramer, “The Nature of Imperfections in Bismuth Germanate (BGO) Crystals,” J. Cryst. Growth 78, 121–128 (1986).
    [CrossRef]
  5. D. P. Bortfeld, M. Meier, “Refractive Indices and Electrooptic Coefficients of the Eulitities Bi4Ge3O12 and Bi4Si3O12,” J. Appl. Phys. 43, 5110–5112 (1972).
    [CrossRef]
  6. A. Horowitz, G. Kramer, in Proceedings, Eighth International Conference on Crystal Growth, ICCG-8, York (1986), pp. 121–128.
  7. W. P. Unruh, International Workshop on Bismuth Germanate, Department of Physics, Princeton U. (Nov.1982), p. 168.
  8. G. W. Morey, The Properties of Glass (Reinhold, New York, 1954).
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    [CrossRef]
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    [CrossRef]
  11. E. G. Tsitsishvili, O. V. Gogolin, J. L. Deiss, V. N. Bagdavadze, “Natural Birefringence of Cubic CuCl Crystals,” Solid State Commun. 56, 717–720 (1985).
    [CrossRef]
  12. C. S. Namba, “Electrooptical Effect of Zincblende,” J. Opt. Soc. Am. 51, 76–79 (1961).
    [CrossRef]
  13. K. S. Lee, D. Conrad, G. W. Day, P. D. Hale, “Measurement of Optical, Electro-optical, and Photoelastic Properties of Crystalline Bi4Ge3O12,” Appl. Opt. to be submitted for publication.

1989

1986

A. Horowitz, G. Kramer, “The Nature of Imperfections in Bismuth Germanate (BGO) Crystals,” J. Cryst. Growth 78, 121–128 (1986).
[CrossRef]

C. Zaldo, C. Lopez, F. Meseguer, “Natural Birefringence in Alkali Halide Single Crystals,” Phys. Rev. B 33, 4283–4288 (1986).
[CrossRef]

1985

E. G. Tsitsishvili, O. V. Gogolin, J. L. Deiss, V. N. Bagdavadze, “Natural Birefringence of Cubic CuCl Crystals,” Solid State Commun. 56, 717–720 (1985).
[CrossRef]

1972

D. P. Bortfeld, M. Meier, “Refractive Indices and Electrooptic Coefficients of the Eulitities Bi4Ge3O12 and Bi4Si3O12,” J. Appl. Phys. 43, 5110–5112 (1972).
[CrossRef]

1967

R. T. Denton, F. S. Chen, A. A. Ballman, “Lithium Tantalate Light Modulators,” J. Appl. Phys. 38, 1611–1617 (1967).
[CrossRef]

1961

Bagdavadze, V. N.

E. G. Tsitsishvili, O. V. Gogolin, J. L. Deiss, V. N. Bagdavadze, “Natural Birefringence of Cubic CuCl Crystals,” Solid State Commun. 56, 717–720 (1985).
[CrossRef]

Ballman, A. A.

R. T. Denton, F. S. Chen, A. A. Ballman, “Lithium Tantalate Light Modulators,” J. Appl. Phys. 38, 1611–1617 (1967).
[CrossRef]

Bortfeld, D. P.

D. P. Bortfeld, M. Meier, “Refractive Indices and Electrooptic Coefficients of the Eulitities Bi4Ge3O12 and Bi4Si3O12,” J. Appl. Phys. 43, 5110–5112 (1972).
[CrossRef]

Chen, F. S.

R. T. Denton, F. S. Chen, A. A. Ballman, “Lithium Tantalate Light Modulators,” J. Appl. Phys. 38, 1611–1617 (1967).
[CrossRef]

Conrad, D.

K. S. Lee, D. Conrad, G. W. Day, P. D. Hale, “Measurement of Optical, Electro-optical, and Photoelastic Properties of Crystalline Bi4Ge3O12,” Appl. Opt. to be submitted for publication.

Day, G. W.

K. S. Lee, D. Conrad, G. W. Day, P. D. Hale, “Measurement of Optical, Electro-optical, and Photoelastic Properties of Crystalline Bi4Ge3O12,” Appl. Opt. to be submitted for publication.

G. W. Day, K. S. Lee, A. H. Rose, L. R. Veeser, B. J. Papatheofanis, H. K. Whitesel, “Optical Fiber Sensors for Electromagnetic Quantities,” in Proceedings, Department of Defenses, Fiber Optics Conference ’88 (1988).

Deiss, J. L.

E. G. Tsitsishvili, O. V. Gogolin, J. L. Deiss, V. N. Bagdavadze, “Natural Birefringence of Cubic CuCl Crystals,” Solid State Commun. 56, 717–720 (1985).
[CrossRef]

Denton, R. T.

R. T. Denton, F. S. Chen, A. A. Ballman, “Lithium Tantalate Light Modulators,” J. Appl. Phys. 38, 1611–1617 (1967).
[CrossRef]

Gogolin, O. V.

E. G. Tsitsishvili, O. V. Gogolin, J. L. Deiss, V. N. Bagdavadze, “Natural Birefringence of Cubic CuCl Crystals,” Solid State Commun. 56, 717–720 (1985).
[CrossRef]

Hale, P. D.

K. S. Lee, D. Conrad, G. W. Day, P. D. Hale, “Measurement of Optical, Electro-optical, and Photoelastic Properties of Crystalline Bi4Ge3O12,” Appl. Opt. to be submitted for publication.

Horowitz, A.

A. Horowitz, G. Kramer, “The Nature of Imperfections in Bismuth Germanate (BGO) Crystals,” J. Cryst. Growth 78, 121–128 (1986).
[CrossRef]

A. Horowitz, G. Kramer, in Proceedings, Eighth International Conference on Crystal Growth, ICCG-8, York (1986), pp. 121–128.

Kramer, G.

A. Horowitz, G. Kramer, “The Nature of Imperfections in Bismuth Germanate (BGO) Crystals,” J. Cryst. Growth 78, 121–128 (1986).
[CrossRef]

A. Horowitz, G. Kramer, in Proceedings, Eighth International Conference on Crystal Growth, ICCG-8, York (1986), pp. 121–128.

Lee, K. S.

K. S. Lee, “New Compensation for Bulk Optical Sensors with Multiple Birefringences,” Appl. Opt. 28, 2001–2011 (1989).
[CrossRef] [PubMed]

K. S. Lee, D. Conrad, G. W. Day, P. D. Hale, “Measurement of Optical, Electro-optical, and Photoelastic Properties of Crystalline Bi4Ge3O12,” Appl. Opt. to be submitted for publication.

G. W. Day, K. S. Lee, A. H. Rose, L. R. Veeser, B. J. Papatheofanis, H. K. Whitesel, “Optical Fiber Sensors for Electromagnetic Quantities,” in Proceedings, Department of Defenses, Fiber Optics Conference ’88 (1988).

Lopez, C.

C. Zaldo, C. Lopez, F. Meseguer, “Natural Birefringence in Alkali Halide Single Crystals,” Phys. Rev. B 33, 4283–4288 (1986).
[CrossRef]

Meier, M.

D. P. Bortfeld, M. Meier, “Refractive Indices and Electrooptic Coefficients of the Eulitities Bi4Ge3O12 and Bi4Si3O12,” J. Appl. Phys. 43, 5110–5112 (1972).
[CrossRef]

Meseguer, F.

C. Zaldo, C. Lopez, F. Meseguer, “Natural Birefringence in Alkali Halide Single Crystals,” Phys. Rev. B 33, 4283–4288 (1986).
[CrossRef]

Morey, G. W.

G. W. Morey, The Properties of Glass (Reinhold, New York, 1954).

Namba, C. S.

Papatheofanis, B. J.

G. W. Day, K. S. Lee, A. H. Rose, L. R. Veeser, B. J. Papatheofanis, H. K. Whitesel, “Optical Fiber Sensors for Electromagnetic Quantities,” in Proceedings, Department of Defenses, Fiber Optics Conference ’88 (1988).

Rose, A. H.

G. W. Day, K. S. Lee, A. H. Rose, L. R. Veeser, B. J. Papatheofanis, H. K. Whitesel, “Optical Fiber Sensors for Electromagnetic Quantities,” in Proceedings, Department of Defenses, Fiber Optics Conference ’88 (1988).

Shibata, K.

K. Shibata, “A Fiber Optic Electric Field Sensor Using the Electrooptic Effect of Bi4Ge3O12,” in Proceedings, First International Conference on Optical Fibre Sensors, London (1983), pp. 164–168.

Tsitsishvili, E. G.

E. G. Tsitsishvili, O. V. Gogolin, J. L. Deiss, V. N. Bagdavadze, “Natural Birefringence of Cubic CuCl Crystals,” Solid State Commun. 56, 717–720 (1985).
[CrossRef]

Unruh, W. P.

W. P. Unruh, International Workshop on Bismuth Germanate, Department of Physics, Princeton U. (Nov.1982), p. 168.

Veeser, L. R.

G. W. Day, K. S. Lee, A. H. Rose, L. R. Veeser, B. J. Papatheofanis, H. K. Whitesel, “Optical Fiber Sensors for Electromagnetic Quantities,” in Proceedings, Department of Defenses, Fiber Optics Conference ’88 (1988).

Whitesel, H. K.

G. W. Day, K. S. Lee, A. H. Rose, L. R. Veeser, B. J. Papatheofanis, H. K. Whitesel, “Optical Fiber Sensors for Electromagnetic Quantities,” in Proceedings, Department of Defenses, Fiber Optics Conference ’88 (1988).

Zaldo, C.

C. Zaldo, C. Lopez, F. Meseguer, “Natural Birefringence in Alkali Halide Single Crystals,” Phys. Rev. B 33, 4283–4288 (1986).
[CrossRef]

Appl. Opt.

J. Appl. Phys.

D. P. Bortfeld, M. Meier, “Refractive Indices and Electrooptic Coefficients of the Eulitities Bi4Ge3O12 and Bi4Si3O12,” J. Appl. Phys. 43, 5110–5112 (1972).
[CrossRef]

R. T. Denton, F. S. Chen, A. A. Ballman, “Lithium Tantalate Light Modulators,” J. Appl. Phys. 38, 1611–1617 (1967).
[CrossRef]

J. Cryst. Growth

A. Horowitz, G. Kramer, “The Nature of Imperfections in Bismuth Germanate (BGO) Crystals,” J. Cryst. Growth 78, 121–128 (1986).
[CrossRef]

J. Opt. Soc. Am.

Phys. Rev. B

C. Zaldo, C. Lopez, F. Meseguer, “Natural Birefringence in Alkali Halide Single Crystals,” Phys. Rev. B 33, 4283–4288 (1986).
[CrossRef]

Solid State Commun.

E. G. Tsitsishvili, O. V. Gogolin, J. L. Deiss, V. N. Bagdavadze, “Natural Birefringence of Cubic CuCl Crystals,” Solid State Commun. 56, 717–720 (1985).
[CrossRef]

Other

K. Shibata, “A Fiber Optic Electric Field Sensor Using the Electrooptic Effect of Bi4Ge3O12,” in Proceedings, First International Conference on Optical Fibre Sensors, London (1983), pp. 164–168.

G. W. Day, K. S. Lee, A. H. Rose, L. R. Veeser, B. J. Papatheofanis, H. K. Whitesel, “Optical Fiber Sensors for Electromagnetic Quantities,” in Proceedings, Department of Defenses, Fiber Optics Conference ’88 (1988).

K. S. Lee, D. Conrad, G. W. Day, P. D. Hale, “Measurement of Optical, Electro-optical, and Photoelastic Properties of Crystalline Bi4Ge3O12,” Appl. Opt. to be submitted for publication.

A. Horowitz, G. Kramer, in Proceedings, Eighth International Conference on Crystal Growth, ICCG-8, York (1986), pp. 121–128.

W. P. Unruh, International Workshop on Bismuth Germanate, Department of Physics, Princeton U. (Nov.1982), p. 168.

G. W. Morey, The Properties of Glass (Reinhold, New York, 1954).

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Figures (9)

Fig. 1
Fig. 1

Temperature dependence of birefringence (at λ = 830 nm).

Fig. 2
Fig. 2

Orientation of crystal (BGO) used for an EO voltage sensor.

Fig. 3
Fig. 3

Measurement setup for observing the effect of the temperature dependent birefringence on an EO voltage sensor: FIL, optical bandpass filter [peak wavelength = 850 nm, spectral width (FWHM) = 10 nm]; CH, chopper; POL, polarizer; OSC, voltage oscillator; WP, quarterwave plate (wavelength = 850 nm).

Fig. 4
Fig. 4

Effect of the temperature dependent birefringence on an EO voltage sensor. Top data are the modulation depths after the parallel polarizers, bottom data are the modulation depths after the crossed polarizers, and middle data are the modulation depths averaged over both top and bottom data. Solid dots are theoretical data, and open dots are measured data.

Fig. 5
Fig. 5

Change in dc levels of the sensor output due to phase retardation caused by pressure-induced birefringence. Top data are the normalized dc levels after the crossed polarizers, and bottom data are the normalized dc levels after the parallel polarizers.

Fig. 6
Fig. 6

Effect of the pressure-induced birefringence on an EO voltage sensor. Top data are the modulation depths after the parallel polarizers, bottom data are the modulation depths after the crossed polarizers, and middle data are the modulation depths averaged over both top and bottom data. Black dots are theoretical data, and open dots are measured data.

Fig. 7
Fig. 7

Birefringences (or phase retardations caused by the birefringences) before and after annealing. Top data are for the crystal from Crystal Technology, and bottom data are for the crystal from Crismatec. Top and bottom arrows indicate the minimum measurable phase retardations limited by the depolarization in the crystals of Crystal Technology and Crismatec, respectively.

Fig. 8
Fig. 8

Temperature stability of an EO voltage sensor with and without compensation. The sensor outputs (Γ m ||, Γ m , and Γmavg) at various temperatures are normalized by their own average values. Open and solid dots are the voltage sensor outputs (Γ m || m ) without compensation, and * marks represent the voltage sensor outputs (Γmavg) with the compensation.

Fig. 9
Fig. 9

FIressure stability of an EO voltage sensor with and without the compensation. Open and solid dots are the voltage sensor outputs (Γ m || m ) without the compensation, and * marks are the voltage sensor outputs (Γmavg) with the compensation at various pressures.

Tables (3)

Tables Icon

Table I Optical Properties in Bi4Ge3O12 at 830 nm

Tables Icon

Table II Effect of Temperature Dependent Birefringence on the Voltage Sensor

Tables Icon

Table III Effect of Birefringence Induced by Pressure on the Voltage Sensor Output

Equations (15)

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η ( dB ) = - 10 log ( P y / P x ) ,
s = P y P x + P y .
B = ( n x - n y ) = λ δ / ( 2 π L )
P P i = 1 2 [ 1 - ( δ 00 + n = 1 N δ n sin 2 θ n ) ] ,
P P i = 1 2 [ 1 + ( δ 00 + n = 1 N δ n sin 2 θ n ) ] ,
δ 00 = 2 π n 0 3 r 41 E L / λ 0 ( for cubic crystal class 4 ¯ 3 m ) , δ n = π n 0 L Δ n / 0 λ 0 .
Γ m ( T , P ) = Γ m ( T ) 1 - n = 1 N δ n ( T , P ) sin 2 θ n ,
Γ m ( T , P ) = Γ m ( T ) 1 + n = 1 N δ n ( T , P ) sin 2 θ n ,
Γ m ( T ) = 2 π λ 0 n 0 ( T ) 3 r 41 ( T ) V m L d .
Γ m = Γ m 0 · ( 1 + 2.12 × 10 - 4 · Δ T ) 1 - δ ( T ) · sin 2 θ ,
Γ m = Γ m 0 · ( 1 + 2.12 × 10 - 4 · Δ T ) 1 + δ ( T ) · sin 2 θ ,
Γ mavg = ( Γ m + Γ m ) / 2 Γ m 0 ( 1 + 2.12 × 10 - 4 · Δ T ) { 1 + [ δ ( T ) · sin 2 θ ] 2 } ,
Γ m ( p 2 ) Γ m ( p 1 ) = 1 - δ ( p 1 ) · sin 2 θ 1 - δ ( p 2 ) · sin 2 θ ,
Γ m ( p 2 ) Γ m ( p 1 ) = 1 + δ ( p 1 ) · sin 2 θ 1 + δ ( p 2 ) · sin 2 θ ,
Γ mavg ( p 2 ) Γ mavg ( p 1 ) 1 + [ δ ( p 2 ) · sin 2 θ ] 2 1 + [ δ ( p 1 ) · sin 2 θ ] 2 .

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