Abstract

To investigate the beam dependence of a fiber-optic voltage sensor by using a LiNbO3 crystal, I undertook a series of calculations of various beam conditions expressed as Gauss functions by using the plane-wave method, treating each linear electro-optic term as a perturbation of the birefringence of a uniaxial crystal caused by an off-axis beam. The approximation proved to be accurate to within 0.2%. I discovered that the performance of the sensor is closely dependent on the beam angle from the z axis and the beam angle on the xy plane but that its fabrication requires an impractical degree of control of the collimated beam. I also found the optimal uncollimated beam condition, which provides immunity to temperature changes and variations in the direction of the propagating beam, compensating for the temperature dependence of the quartz 1/4 wave plate. The experimental data support the simulated results.

© 2001 Optical Society of America

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References

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  1. W. R. Rutgers, H. J. M. Hulshof, J. J. Laurensse, A. H. van der Wey, “Optical sensors for the measurement of electric current and voltage,” Vol. 5, No. 1 of Kema Scientific and Techni. Rep. (Kema, Arnhem, The Netherlands, 1987), pp. 281–292.
  2. T. Sawa, K. Kurosawa, T. Kaminishi, and T. Yokota, “Development of optical instrument transformers,” presented at the 11th IEEE/PES Transmission and Distribution Conference, Monterey, Calif., April 2–7, 1989.
  3. D. Ishiko, K. Toda, H. Hamada, N. Itoh, S. Ishizuka, M. Wada, H. Fudo, and T. Nishiyama, “Fiber-optic monitoring sensor system for power distribution lines,” Vol. 38, No. 2 of National Technical Report (Matsushita Electric Industrial Co., Ltd., Moriguchi, Osaka, Japan, 1992; in Japanese).
  4. A. Yariv, Optical Electronics (Saunders, Philadelphia, Pa., 1991).
  5. T. Mitui, K. Hosoe, H. Usami, and S. Miyamoto, “Development of fiber-optic voltage and magnetic-field sensors,” IEEE Trans. Power Deliv. PWRD-2, 87–93 (1987).
    [CrossRef]
  6. K. S. Lee, “New compensation method for bulk optical sensors with multiple birefringences,” Appl. Opt. 28, 2001–2011 (1989).
    [CrossRef] [PubMed]
  7. M. Didomenico, Jr., and S. H. Wemple, “Oxygen-octahedra ferroelectrics. I. Theory of electro-optical and nonlinear optical effects,” J. Appl. Phys. 40, 720–735 (1969).
    [CrossRef]
  8. P. V. Lenzo, E. G. Spencer, and K. Nassau, “Electro-optic coefficients in single-domain ferroelectric lithium niobate,” J. Opt. Soc. Am. 56, 633–635 (1966).
    [CrossRef]
  9. S. C. Abrahams, J. M. Reddy, and J. L. Bernstein, “Ferroelectric lithium niobate 3 single crystal x-ray diffraction study at 24 C,” J. Phys. Chem. Solids 27, 997–1012 (1966).
    [CrossRef]
  10. G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, and A. Savage, “Electro-optic properties of LiNbO3,” Appl. Phys. Lett. 5, 234–236 (1964).
    [CrossRef]
  11. E. Bernal, G. D. Chen, and T. C. Lee, “Low frequency electro-optic and dielectric constants of lithium niobate,” Phys. Lett. 21, 259–260 (1966).
    [CrossRef]
  12. R. C. Miller and A. Savage, “Temperature dependence of the optical properties of ferroelectric LiNbO3 and LiTaO3,” Appl. Phys. Lett. 8, 169–170 (1966).
    [CrossRef]
  13. J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
    [CrossRef]
  14. N. Saito, “Measurement of current and voltage for electric power by laser,” Vol. 28, No. 5 of Report of the Institute of Industrial Science (University of Tokyo, Tokyo, 1976; in Japanese).
  15. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).
  16. K. Terasawa, Outline of Mathematics for Natural Scientists, (Iwanami, Tokyo, 1972).

1989

1987

T. Mitui, K. Hosoe, H. Usami, and S. Miyamoto, “Development of fiber-optic voltage and magnetic-field sensors,” IEEE Trans. Power Deliv. PWRD-2, 87–93 (1987).
[CrossRef]

1969

M. Didomenico, Jr., and S. H. Wemple, “Oxygen-octahedra ferroelectrics. I. Theory of electro-optical and nonlinear optical effects,” J. Appl. Phys. 40, 720–735 (1969).
[CrossRef]

1967

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

1966

S. C. Abrahams, J. M. Reddy, and J. L. Bernstein, “Ferroelectric lithium niobate 3 single crystal x-ray diffraction study at 24 C,” J. Phys. Chem. Solids 27, 997–1012 (1966).
[CrossRef]

P. V. Lenzo, E. G. Spencer, and K. Nassau, “Electro-optic coefficients in single-domain ferroelectric lithium niobate,” J. Opt. Soc. Am. 56, 633–635 (1966).
[CrossRef]

E. Bernal, G. D. Chen, and T. C. Lee, “Low frequency electro-optic and dielectric constants of lithium niobate,” Phys. Lett. 21, 259–260 (1966).
[CrossRef]

R. C. Miller and A. Savage, “Temperature dependence of the optical properties of ferroelectric LiNbO3 and LiTaO3,” Appl. Phys. Lett. 8, 169–170 (1966).
[CrossRef]

1964

G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, and A. Savage, “Electro-optic properties of LiNbO3,” Appl. Phys. Lett. 5, 234–236 (1964).
[CrossRef]

Abrahams, S. C.

S. C. Abrahams, J. M. Reddy, and J. L. Bernstein, “Ferroelectric lithium niobate 3 single crystal x-ray diffraction study at 24 C,” J. Phys. Chem. Solids 27, 997–1012 (1966).
[CrossRef]

Bernal, E.

E. Bernal, G. D. Chen, and T. C. Lee, “Low frequency electro-optic and dielectric constants of lithium niobate,” Phys. Lett. 21, 259–260 (1966).
[CrossRef]

Bernstein, J. L.

S. C. Abrahams, J. M. Reddy, and J. L. Bernstein, “Ferroelectric lithium niobate 3 single crystal x-ray diffraction study at 24 C,” J. Phys. Chem. Solids 27, 997–1012 (1966).
[CrossRef]

Bond, W. L.

G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, and A. Savage, “Electro-optic properties of LiNbO3,” Appl. Phys. Lett. 5, 234–236 (1964).
[CrossRef]

Boyd, G. D.

G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, and A. Savage, “Electro-optic properties of LiNbO3,” Appl. Phys. Lett. 5, 234–236 (1964).
[CrossRef]

Chen, D.

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

Chen, G. D.

E. Bernal, G. D. Chen, and T. C. Lee, “Low frequency electro-optic and dielectric constants of lithium niobate,” Phys. Lett. 21, 259–260 (1966).
[CrossRef]

Didomenico Jr., M.

M. Didomenico, Jr., and S. H. Wemple, “Oxygen-octahedra ferroelectrics. I. Theory of electro-optical and nonlinear optical effects,” J. Appl. Phys. 40, 720–735 (1969).
[CrossRef]

Hosoe, K.

T. Mitui, K. Hosoe, H. Usami, and S. Miyamoto, “Development of fiber-optic voltage and magnetic-field sensors,” IEEE Trans. Power Deliv. PWRD-2, 87–93 (1987).
[CrossRef]

Lee, K. S.

Lee, T. C.

E. Bernal, G. D. Chen, and T. C. Lee, “Low frequency electro-optic and dielectric constants of lithium niobate,” Phys. Lett. 21, 259–260 (1966).
[CrossRef]

Lenzo, P. V.

Miller, R. C.

R. C. Miller and A. Savage, “Temperature dependence of the optical properties of ferroelectric LiNbO3 and LiTaO3,” Appl. Phys. Lett. 8, 169–170 (1966).
[CrossRef]

G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, and A. Savage, “Electro-optic properties of LiNbO3,” Appl. Phys. Lett. 5, 234–236 (1964).
[CrossRef]

Mitui, T.

T. Mitui, K. Hosoe, H. Usami, and S. Miyamoto, “Development of fiber-optic voltage and magnetic-field sensors,” IEEE Trans. Power Deliv. PWRD-2, 87–93 (1987).
[CrossRef]

Miyamoto, S.

T. Mitui, K. Hosoe, H. Usami, and S. Miyamoto, “Development of fiber-optic voltage and magnetic-field sensors,” IEEE Trans. Power Deliv. PWRD-2, 87–93 (1987).
[CrossRef]

Nassau, K.

P. V. Lenzo, E. G. Spencer, and K. Nassau, “Electro-optic coefficients in single-domain ferroelectric lithium niobate,” J. Opt. Soc. Am. 56, 633–635 (1966).
[CrossRef]

G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, and A. Savage, “Electro-optic properties of LiNbO3,” Appl. Phys. Lett. 5, 234–236 (1964).
[CrossRef]

Otto, G. N.

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

Reddy, J. M.

S. C. Abrahams, J. M. Reddy, and J. L. Bernstein, “Ferroelectric lithium niobate 3 single crystal x-ray diffraction study at 24 C,” J. Phys. Chem. Solids 27, 997–1012 (1966).
[CrossRef]

Savage, A.

R. C. Miller and A. Savage, “Temperature dependence of the optical properties of ferroelectric LiNbO3 and LiTaO3,” Appl. Phys. Lett. 8, 169–170 (1966).
[CrossRef]

G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, and A. Savage, “Electro-optic properties of LiNbO3,” Appl. Phys. Lett. 5, 234–236 (1964).
[CrossRef]

Spencer, E. G.

Usami, H.

T. Mitui, K. Hosoe, H. Usami, and S. Miyamoto, “Development of fiber-optic voltage and magnetic-field sensors,” IEEE Trans. Power Deliv. PWRD-2, 87–93 (1987).
[CrossRef]

Wemple, S. H.

M. Didomenico, Jr., and S. H. Wemple, “Oxygen-octahedra ferroelectrics. I. Theory of electro-optical and nonlinear optical effects,” J. Appl. Phys. 40, 720–735 (1969).
[CrossRef]

Zook, J. D.

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

G. D. Boyd, R. C. Miller, K. Nassau, W. L. Bond, and A. Savage, “Electro-optic properties of LiNbO3,” Appl. Phys. Lett. 5, 234–236 (1964).
[CrossRef]

R. C. Miller and A. Savage, “Temperature dependence of the optical properties of ferroelectric LiNbO3 and LiTaO3,” Appl. Phys. Lett. 8, 169–170 (1966).
[CrossRef]

J. D. Zook, D. Chen, and G. N. Otto, “Temperature dependence and model of the electro-optic effect in LiNbO3,” Appl. Phys. Lett. 11, 159–161 (1967).
[CrossRef]

IEEE Trans. Power Deliv.

T. Mitui, K. Hosoe, H. Usami, and S. Miyamoto, “Development of fiber-optic voltage and magnetic-field sensors,” IEEE Trans. Power Deliv. PWRD-2, 87–93 (1987).
[CrossRef]

J. Appl. Phys.

M. Didomenico, Jr., and S. H. Wemple, “Oxygen-octahedra ferroelectrics. I. Theory of electro-optical and nonlinear optical effects,” J. Appl. Phys. 40, 720–735 (1969).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. Chem. Solids

S. C. Abrahams, J. M. Reddy, and J. L. Bernstein, “Ferroelectric lithium niobate 3 single crystal x-ray diffraction study at 24 C,” J. Phys. Chem. Solids 27, 997–1012 (1966).
[CrossRef]

Phys. Lett.

E. Bernal, G. D. Chen, and T. C. Lee, “Low frequency electro-optic and dielectric constants of lithium niobate,” Phys. Lett. 21, 259–260 (1966).
[CrossRef]

Other

N. Saito, “Measurement of current and voltage for electric power by laser,” Vol. 28, No. 5 of Report of the Institute of Industrial Science (University of Tokyo, Tokyo, 1976; in Japanese).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals (Princeton U. Press, Princeton, N.J., 1995).

K. Terasawa, Outline of Mathematics for Natural Scientists, (Iwanami, Tokyo, 1972).

W. R. Rutgers, H. J. M. Hulshof, J. J. Laurensse, A. H. van der Wey, “Optical sensors for the measurement of electric current and voltage,” Vol. 5, No. 1 of Kema Scientific and Techni. Rep. (Kema, Arnhem, The Netherlands, 1987), pp. 281–292.

T. Sawa, K. Kurosawa, T. Kaminishi, and T. Yokota, “Development of optical instrument transformers,” presented at the 11th IEEE/PES Transmission and Distribution Conference, Monterey, Calif., April 2–7, 1989.

D. Ishiko, K. Toda, H. Hamada, N. Itoh, S. Ishizuka, M. Wada, H. Fudo, and T. Nishiyama, “Fiber-optic monitoring sensor system for power distribution lines,” Vol. 38, No. 2 of National Technical Report (Matsushita Electric Industrial Co., Ltd., Moriguchi, Osaka, Japan, 1992; in Japanese).

A. Yariv, Optical Electronics (Saunders, Philadelphia, Pa., 1991).

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Figures (17)

Fig. 1
Fig. 1

Schematic of the fiber-optic voltage sensor. The direction of collimated beam k is decided by the angle to the z axis, α, and the angle to the z axis on the xy plane, β.

Fig. 2
Fig. 2

Curves of convergent field radii of the infinite perturbation series r0=min(r00, r01) versus beam angle α to the z axis. Each curve refers to each angle on xy plane β, showing maximum and minimum.

Fig. 3
Fig. 3

Curves of maximum normalization error of retardation Err Δ/Δ versus beam angle α to the z axis. Each curve is a response to a different electric field E1.

Fig. 4
Fig. 4

Analytical model of the optical system and power distribution. k0 is the central direction of the beam, kc is the direction of the beam edge, and ϕ is the maximum incident angle that depends on the N.A. of the step index multimode optical fiber. This figure shows the beam propagating along the z axis: α=0.

Fig. 5
Fig. 5

Schematic diagram of a signal processor for the fiber-optic voltage sensor: P.D., photodiode.

Fig. 6
Fig. 6

Curves of normalized output and its ratio of fiber-optic voltage sensor to applied voltage at 60 Hz for fiber (1). The normalized ratio is defined by the ratio of the normalized output to the normalized applied voltage at 100 V.

Fig. 7
Fig. 7

Curves of the normalized output ratio of the fiber-optic voltage sensor to temperature with a constant applied voltage of 100 V at 60 Hz. The normalized output ratio is defined by the ratio of the output to the output at 20 °C.

Fig. 8
Fig. 8

Contours of dc output Out0 (k) versus k identified by α and β. A brighter color indicates a higher value.

Fig. 9
Fig. 9

Contours of ac output [Out1(k)2+Out1(k)2] versus k identified by α and β. A brighter color indicates a higher value.

Fig. 10
Fig. 10

Contours of MOD (k) versus k identified by α and β. A brighter color indicates a higher value. Out-of-range areas are indicated by fine mesh.

Fig. 11
Fig. 11

Curves of the normalized MOD of a fiber-optic voltage sensor by the collimated beam. Each curve refers to a different beam edge angle θc at LN.

Fig. 12
Fig. 12

Relational curves of trends of a normalized MOD of the fiber-optic voltage sensor between the other beam edge angles θc and θc(=0.371°). These curves are all normalized by the MOD at θc=0.371° and α=0° and are simplified by trend approximation. Each curve refers to a different θc. The filled circles that represent 52 different samples show the relationship between fiber (2) and fiber (1) for the same samples.

Fig. 13
Fig. 13

Curves of temperature dependence of the normalized MOD of a fiber-optic voltage sensor by a collimated beam in the four principal directions β=45°, 135°, 225°, 315°. Each curve refers to a different beam edge angle θc at the LN.

Fig. 14
Fig. 14

Curves of temperature dependence of the normalized MOD of the fiber-optic voltage sensor with a collimated beam in the four directions β=45°, 135°, 225°, 315° relative to temperature dependence of a 1/4-wave-length plate. Each curve refers to a different beam angle α at LN. Each sample is identical to its counterpart in Fig. 7.

Fig. 15
Fig. 15

Curves of the normalized MOD of a fiber-optic voltage sensor by a collimated beam and schematic representation of the beam and temperature dependence of the output shown in Fig. 7. Each curve refers to two optical fibers used for the experiment and to three temperatures, -20, 20, and 80 °C. Parts of the curves for -20° and 80 °C are omitted to enhance readability. The plots and connecting lines show the change in output in response to the temperature change from -20 to 80 °C.

Fig. 16
Fig. 16

Curves of the normalized loss by input power along the two directions β=45°, 135°. Each curve refers to a different causative element and to a different fiber or a different beam edge angle θc at LN.

Fig. 17
Fig. 17

Relational curves of loss trends of the fiber-optic voltage sensor between the optical fibers (1) and (2). Each curve refers to each kind of loss. The practical loss can be shifted by other elements independently of beam conditions such as scatter or absorption by the resin and optical components. Filled circles, 52 different data samples, which show the relationship between fiber (1) and fiber (2) for the same samples.

Tables (3)

Tables Icon

Table 1 Physical Behavior of LiNbO3 Crystala

Tables Icon

Table 2 Optical Behavior of a Quartz 1/4-Wave Plate

Tables Icon

Table 3 Beam Edge Angle at LN for Several Optical Fibersa

Equations (46)

Equations on this page are rendered with MathJax. Learn more.

(γij)=0-γ22γ130γ22γ1300γ330γ510γ5100-γ2200.
QHk(r, t)=-μ0 2t2Hk(r, t),
Q=×1(k)×.
Hk(r, t)=l=12 Hl(k)Pl exp[i(k·r-ωnt)],
k2 m=121(k)lmHm(k)=μ0ωn2Hl(k)(l=1, 2).
0=1s+j=13 γjEj,
1s=1o0001o0001e,
γ1=0-γ22γ51-γ2200γ5100,
γ2=-γ220000γ22γ510γ510,γ3=γ13000γ13000γ33,
0(k)=U1s+j=13 γjEjU-1=U 1sU-1+j=13 UγjU-1Ej.
m=12U 1sU-1+Uγ1U-1E1lmHm(k)=nl-2Hl(k)
(l=1, 2),
QPl=nl-2Pl,
Q=U 1sU-1+Uγ1U-1E1mn,
Q0=U 1sU-1mn,Q1=[(Uγ1U-1)mn].
Q0pn=nn0-2pn.
nn-2=nn0-2+pn, Q1pnE1,
Pn=pn+pl, Q1pnE1nn0-2-nl0-2pl(nl).
Θβ+p1, Q1, p0E1n00-2-n10-2 p1, Q1p0E1n00-2-n10-21.
Δ=2πλ(n00-n10)L-nλ[n003p0, Q1p0-n103p1, Q1p1]E1L,
Out(k)=¼(1+sin Δ sin 2Θ),
Out(k)=14+14 J0(Δac)sin Δdc+2 n=1{J2n(Δac)×sin Δdc cos(2nωt)+J2n-1(Δac)cos Δdc×sin[(2n-1)ωt]}J0(2Θac)sin 2Θdc+2 n=1{J2n(2Θac)sin 2Θdc cos(2nωt)+J2n-1(2Θac)cos 2Θdc sin[(2n-1)ωt]},
Out(k)=Out0(k)+Out1(k)sin ωt+Out2(k)cos 2ωt,
Out0(k)=¼+¼[-J0(Δac)sin ΔdcJ0(2Θac)sin 2Θdc-2J1(Δac)cos ΔdcJ1(2Θac)cos 2Θdc],
Out1(k)=¼[-2J1(Δac)cos ΔdcJ0(2Θac)sin 2Θdc-2J0(Δac)sin ΔdcJ1(2Θqc)cos 2Θdc],
Out2(k)=¼[-2J0(Δac)sin ΔdcJ2(2Θdc)sin 2Θdc+2J1(Δac)cos ΔdcJ1(2Θac)cos 2Θdc].
Mod(k)=[Out1(k)2+Out2(k)2]1/2Out0(k).
Out(k0, kc)=all, kG(k-k0, kc)Out(k)dk,
G(k-k0, kc)
=12πkc22 exp[-|k-k0|2/2(kc/2)2].
Pn-pn=E1Tn,
Tn=m=1 E1m-1Pn(m)=Pn(1)+E1Pn(2)+ ,
Tn=-SQ1pn-E1S(Q1-pn, Q1pn)Tn+E12pn, Q1TnSTn,
1nl0-2-nn0-2.
tn=SQ1-E1S(Q1-pn, Q1pn)×tn+E12Q1pnStn2,
tn=m=1E1m-1tn(m)=tn(1)+E1tn(2)+E12tn(3)+,
Pn(m)tn(m)(m=1,2, ),
E1r0n=1S(Q1-pn, Q1pn)+2(Q1pnSSQ1)1/2,
SQ1=2 Max(Q1p0, Q1p1)|n00-2-n10-2|,
S(Q1-pn, Q1pn)
=2 Max(Q1p0, Q1p1)+pn, Q1pn|n00-2-n10-2|,
Err nn-2=nn-2-m=0u Λn(m)E1m|E1|2Q1pntn-m=2u tn(m-1)E1m-2,
Err Pn=Pn-m=0u Pn(m)E1mE1tn-m=1u E1m-1tn(m).
Err Δ=(2π/λ)L(Err n0-Err n1).
Q=1o-γ22E1-γ22E11o,
Δ=2πλo3/2γ22E1L,Θ=π4.

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