Abstract

Bismuth germanate (Bi4Ge3O12, BGO) has been widely utilized for the application of Pockels effect-based voltage and electric field sensors, because it possesses no unwanted effects ideally. However, there are multiple birefringences in BGO crystal induced by natural imperfections, temperature-dependent strain, and external pressure (or stress), which influences the demodulation of the Pockels effect induced by the voltage to be measured. For a Pockels effect-based quasi-reciprocal reflective optical voltage sensor, the influences of the multiple birefringences in BGO crystal are investigated and an elimination scheme is also proposed in this paper. The feasibility of the proposed elimination scheme is simulated and experimentally verified.

© 2013 Optical Society of America

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References

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  1. C. Zhang, X. Feng, S. Liang, C. Zhang, and C. Li, “Quasi-reciprocal reflective optical voltage sensor based on Pockels effect with digital closed-loop detection technique,” Opt. Commun. 283, 3878–3883 (2010).
    [CrossRef]
  2. K. Bohnert, S. Wildermuth, A. Frank, and H. Brändle, “Fiber-optic voltage sensor using fiber gyro technology,” Procedia Eng. 5, 1091–1094 (2010).
    [CrossRef]
  3. S. Wildermuth, K. Bohnert, and H. Brändle, “Interrogation of a birefringent fiber sensor by nonreciprocal phase modulation,” IEEE Photon. Technol. Lett. 22, 1388–1390 (2010).
    [CrossRef]
  4. K. S. Lee, “New compensation method for bulk optical sensors with multiple birefringences,” Appl. Opt. 28, 2001–2011 (1989).
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  5. K. S. Lee, “Electrooptic voltage sensor: birefringence effects and compensation methods,” Appl. Opt. 29, 4453–4461(1990).
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    [CrossRef]
  8. A. Horowitz and G. Kramer, “The growth of high quality large Bi4Ge3O12 (BGO) crystals,” J. Cryst. Growth 79, 296–302 (1986).
    [CrossRef]
  9. P. A. Williams, A. H. Rose, K. S. Lee, D. C. Conrad, G. W. Day, and P. D. Hale, “Optical, thermo-optic, electro-optic, and photoelastic properties of bismuth germanate (Bi4Ge3O12),” Appl. Opt. 35, 3562–3569 (1996).
    [CrossRef]
  10. F. Cecelja, W. Balachandran, and M. Bordowski, “Validation of electro-optic sensors for measurement of DC fields in the presence of space charge,” Measurement 40, 450–458(2007).
    [CrossRef]
  11. K. Kurosawa, S. Yoshida, E. Mori, G. Takahashi, and S. Saito, “Development of an optical instrument transformer for DC voltage measurement,” IEEE Trans. Power Delivery 8, 1721–1726 (1993).
    [CrossRef]

2010 (3)

C. Zhang, X. Feng, S. Liang, C. Zhang, and C. Li, “Quasi-reciprocal reflective optical voltage sensor based on Pockels effect with digital closed-loop detection technique,” Opt. Commun. 283, 3878–3883 (2010).
[CrossRef]

K. Bohnert, S. Wildermuth, A. Frank, and H. Brändle, “Fiber-optic voltage sensor using fiber gyro technology,” Procedia Eng. 5, 1091–1094 (2010).
[CrossRef]

S. Wildermuth, K. Bohnert, and H. Brändle, “Interrogation of a birefringent fiber sensor by nonreciprocal phase modulation,” IEEE Photon. Technol. Lett. 22, 1388–1390 (2010).
[CrossRef]

2007 (1)

F. Cecelja, W. Balachandran, and M. Bordowski, “Validation of electro-optic sensors for measurement of DC fields in the presence of space charge,” Measurement 40, 450–458(2007).
[CrossRef]

1996 (1)

1993 (1)

K. Kurosawa, S. Yoshida, E. Mori, G. Takahashi, and S. Saito, “Development of an optical instrument transformer for DC voltage measurement,” IEEE Trans. Power Delivery 8, 1721–1726 (1993).
[CrossRef]

1990 (1)

1989 (1)

1986 (2)

A. Horowitz and G. Kramer, “The nature of imperfections in bismuth germanate (BGO) crystals,” J. Cryst. Growth 78, 121–128 (1986).
[CrossRef]

A. Horowitz and G. Kramer, “The growth of high quality large Bi4Ge3O12 (BGO) crystals,” J. Cryst. Growth 79, 296–302 (1986).
[CrossRef]

Balachandran, W.

F. Cecelja, W. Balachandran, and M. Bordowski, “Validation of electro-optic sensors for measurement of DC fields in the presence of space charge,” Measurement 40, 450–458(2007).
[CrossRef]

Bohnert, K.

K. Bohnert, S. Wildermuth, A. Frank, and H. Brändle, “Fiber-optic voltage sensor using fiber gyro technology,” Procedia Eng. 5, 1091–1094 (2010).
[CrossRef]

S. Wildermuth, K. Bohnert, and H. Brändle, “Interrogation of a birefringent fiber sensor by nonreciprocal phase modulation,” IEEE Photon. Technol. Lett. 22, 1388–1390 (2010).
[CrossRef]

Bordowski, M.

F. Cecelja, W. Balachandran, and M. Bordowski, “Validation of electro-optic sensors for measurement of DC fields in the presence of space charge,” Measurement 40, 450–458(2007).
[CrossRef]

Brändle, H.

S. Wildermuth, K. Bohnert, and H. Brändle, “Interrogation of a birefringent fiber sensor by nonreciprocal phase modulation,” IEEE Photon. Technol. Lett. 22, 1388–1390 (2010).
[CrossRef]

K. Bohnert, S. Wildermuth, A. Frank, and H. Brändle, “Fiber-optic voltage sensor using fiber gyro technology,” Procedia Eng. 5, 1091–1094 (2010).
[CrossRef]

Cecelja, F.

F. Cecelja, W. Balachandran, and M. Bordowski, “Validation of electro-optic sensors for measurement of DC fields in the presence of space charge,” Measurement 40, 450–458(2007).
[CrossRef]

Conrad, D. C.

Day, G. W.

Feng, X.

C. Zhang, X. Feng, S. Liang, C. Zhang, and C. Li, “Quasi-reciprocal reflective optical voltage sensor based on Pockels effect with digital closed-loop detection technique,” Opt. Commun. 283, 3878–3883 (2010).
[CrossRef]

Frank, A.

K. Bohnert, S. Wildermuth, A. Frank, and H. Brändle, “Fiber-optic voltage sensor using fiber gyro technology,” Procedia Eng. 5, 1091–1094 (2010).
[CrossRef]

Hale, P. D.

Horowitz, A.

A. Horowitz and G. Kramer, “The nature of imperfections in bismuth germanate (BGO) crystals,” J. Cryst. Growth 78, 121–128 (1986).
[CrossRef]

A. Horowitz and G. Kramer, “The growth of high quality large Bi4Ge3O12 (BGO) crystals,” J. Cryst. Growth 79, 296–302 (1986).
[CrossRef]

Kramer, G.

A. Horowitz and G. Kramer, “The growth of high quality large Bi4Ge3O12 (BGO) crystals,” J. Cryst. Growth 79, 296–302 (1986).
[CrossRef]

A. Horowitz and G. Kramer, “The nature of imperfections in bismuth germanate (BGO) crystals,” J. Cryst. Growth 78, 121–128 (1986).
[CrossRef]

Kurosawa, K.

K. Kurosawa, S. Yoshida, E. Mori, G. Takahashi, and S. Saito, “Development of an optical instrument transformer for DC voltage measurement,” IEEE Trans. Power Delivery 8, 1721–1726 (1993).
[CrossRef]

Lee, K. S.

Li, C.

C. Zhang, X. Feng, S. Liang, C. Zhang, and C. Li, “Quasi-reciprocal reflective optical voltage sensor based on Pockels effect with digital closed-loop detection technique,” Opt. Commun. 283, 3878–3883 (2010).
[CrossRef]

Liang, S.

C. Zhang, X. Feng, S. Liang, C. Zhang, and C. Li, “Quasi-reciprocal reflective optical voltage sensor based on Pockels effect with digital closed-loop detection technique,” Opt. Commun. 283, 3878–3883 (2010).
[CrossRef]

Mori, E.

K. Kurosawa, S. Yoshida, E. Mori, G. Takahashi, and S. Saito, “Development of an optical instrument transformer for DC voltage measurement,” IEEE Trans. Power Delivery 8, 1721–1726 (1993).
[CrossRef]

Nye, J. F.

J. F. Nye, Physical Properties of Crystals (Clarendon, 1985), pp. 232–274.

Rose, A. H.

Saito, S.

K. Kurosawa, S. Yoshida, E. Mori, G. Takahashi, and S. Saito, “Development of an optical instrument transformer for DC voltage measurement,” IEEE Trans. Power Delivery 8, 1721–1726 (1993).
[CrossRef]

Takahashi, G.

K. Kurosawa, S. Yoshida, E. Mori, G. Takahashi, and S. Saito, “Development of an optical instrument transformer for DC voltage measurement,” IEEE Trans. Power Delivery 8, 1721–1726 (1993).
[CrossRef]

Wildermuth, S.

S. Wildermuth, K. Bohnert, and H. Brändle, “Interrogation of a birefringent fiber sensor by nonreciprocal phase modulation,” IEEE Photon. Technol. Lett. 22, 1388–1390 (2010).
[CrossRef]

K. Bohnert, S. Wildermuth, A. Frank, and H. Brändle, “Fiber-optic voltage sensor using fiber gyro technology,” Procedia Eng. 5, 1091–1094 (2010).
[CrossRef]

Williams, P. A.

Yoshida, S.

K. Kurosawa, S. Yoshida, E. Mori, G. Takahashi, and S. Saito, “Development of an optical instrument transformer for DC voltage measurement,” IEEE Trans. Power Delivery 8, 1721–1726 (1993).
[CrossRef]

Zhang, C.

C. Zhang, X. Feng, S. Liang, C. Zhang, and C. Li, “Quasi-reciprocal reflective optical voltage sensor based on Pockels effect with digital closed-loop detection technique,” Opt. Commun. 283, 3878–3883 (2010).
[CrossRef]

C. Zhang, X. Feng, S. Liang, C. Zhang, and C. Li, “Quasi-reciprocal reflective optical voltage sensor based on Pockels effect with digital closed-loop detection technique,” Opt. Commun. 283, 3878–3883 (2010).
[CrossRef]

Appl. Opt. (3)

IEEE Photon. Technol. Lett. (1)

S. Wildermuth, K. Bohnert, and H. Brändle, “Interrogation of a birefringent fiber sensor by nonreciprocal phase modulation,” IEEE Photon. Technol. Lett. 22, 1388–1390 (2010).
[CrossRef]

IEEE Trans. Power Delivery (1)

K. Kurosawa, S. Yoshida, E. Mori, G. Takahashi, and S. Saito, “Development of an optical instrument transformer for DC voltage measurement,” IEEE Trans. Power Delivery 8, 1721–1726 (1993).
[CrossRef]

J. Cryst. Growth (2)

A. Horowitz and G. Kramer, “The nature of imperfections in bismuth germanate (BGO) crystals,” J. Cryst. Growth 78, 121–128 (1986).
[CrossRef]

A. Horowitz and G. Kramer, “The growth of high quality large Bi4Ge3O12 (BGO) crystals,” J. Cryst. Growth 79, 296–302 (1986).
[CrossRef]

Measurement (1)

F. Cecelja, W. Balachandran, and M. Bordowski, “Validation of electro-optic sensors for measurement of DC fields in the presence of space charge,” Measurement 40, 450–458(2007).
[CrossRef]

Opt. Commun. (1)

C. Zhang, X. Feng, S. Liang, C. Zhang, and C. Li, “Quasi-reciprocal reflective optical voltage sensor based on Pockels effect with digital closed-loop detection technique,” Opt. Commun. 283, 3878–3883 (2010).
[CrossRef]

Procedia Eng. (1)

K. Bohnert, S. Wildermuth, A. Frank, and H. Brändle, “Fiber-optic voltage sensor using fiber gyro technology,” Procedia Eng. 5, 1091–1094 (2010).
[CrossRef]

Other (1)

J. F. Nye, Physical Properties of Crystals (Clarendon, 1985), pp. 232–274.

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Figures (6)

Fig. 1.
Fig. 1.

Schematic illustration of the quasi-reciprocal reflective OVS.

Fig. 2.
Fig. 2.

Digital output of the OVS (a) and its frequency spectrum (b) with no applied voltage in the room temperature.

Fig. 3.
Fig. 3.

Digital output of the OVS (a) and its frequency spectrum (b) with no applied voltage and changing temperature.

Fig. 4.
Fig. 4.

Digital output of the OVS (a) and its frequency spectrum (b) with applied voltage of RMS amplitude 3375 V in the room temperature.

Fig. 5.
Fig. 5.

Digital output of the OVS with the proposed birefringence elimination scheme and no applied voltage in the room temperature.

Fig. 6.
Fig. 6.

Measurement precision of AC voltage with and without the proposed birefringence elimination scheme.

Equations (15)

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Iout=12αIin{1cos[φ(t)φ(tτ)+2δ]},
M⃗BGO=[ABCD]M⃖BGO=[ACBD],
{A=cosϕi[(εyyεxx)/(εyyεxx)2+4εxyεyx]sinϕ=D*B=(2iεxy/(εyyεxx)2+4εxyεyx)sinϕC=(2iεyx/(εyyεxx)2+4εxyεyx)sinϕ,
k±2=ω2μ2[(εxx+εyy)±(εxxεyy)2+4εxyεyx],
{εxx=ε0+12n=1NΔεnlcos2θnεyy=ε012n=1NΔεnlcos2θnεxy=12n=1NΔεnlsin2θn+m=1MΔεmc=εyx*εyx=12n=1NΔεnlsin2θnm=1MΔεmc=εxy*,
Δεnl=2δnlε0k0ln0,
Δεmc=2iε0ϕmk0ln0,
Iout=Ex22{(|Cxx|2+|Cxy|2)acos[φ(t)φ(tτ)]bsin[φ(t)φ(tτ)]},
Cxx2=(A2+C2)2,
Cxy2=(AB+A*C)2,
φ(t)φ(tτ)=±π2+ϕf,
ϕf=arctanba=angle(Cxx2).
ϕfarctan[2(n=1Nδnlcos2θn)2n=1Nδnlsin2θnm=1MΦm],
ϕf2δ1l+2(n=2Nδnlcos2θn)2n=2Nδnlsin2θnm=1MΦm.
Bs=1SF·[1ni=1n(BiB¯)2]12,

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