Abstract

A new scheme is proposed for achieving a closed, homogeneous, and isotropic optical circuit necessary for high-accuracy optical-current sensors. It makes use of a single solid polygonal solid with reflection surfaces coated by quarter-wavelength dielectric thin-film layers for the Faraday cell. We derive the design principle and show numerically its applicability in various Faraday materials. The cross talk with the surrounding current is investigated in particular detail both theoretically and experimentally. In the example experiment with a SF57 Faraday material, a low cross talk is demonstrated for nearby currents.

© 1997 Optical Society of America

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References

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  1. G. W. Day, A. H. Rose, “Faraday effect sensors: The state of the art,” in Fiber Optic and Laser Sensors VI, E. Udd, R. P. DePaula, eds., Proc. SPIE985, 138–149 (1988).
  2. M. Kanoi, G. Takahashi, T. Sato, M. Higashi, K. Okamura, “Optical voltage and current measuring system for electric power systems,” IEEE Trans. Power Delivery, PWRD-1, 91–97 (1986).
  3. Y. N. Ning, D. A. Jackson, “A miniature optical current clamp,” in Proceedings of the 9th Optical Fiber Sensors Conference (Associazione Electtrotecnica ed Elettronica Italiano, Florence, 1993), pp. 305–308.
  4. K. B. Rochford, A. H. Rose, M. N. Deeter, G. W. Day, “Faraday effect current sensor with improved sensitivity-bandwidth product,” Opt. Lett. 19, 1903–1905 (1994).
  5. H. Koide, K. Konno, M. Yamada, T. Okamoto, “Development of GIS optical current transformer,” in Proceedings of the 8th Meeting on Lightwave Sensing Technology (Japan Society of Applied Physics, Tokyo, 1991), pp. 75–80.
  6. T. Yoshino, Y. Takahashi, T. Shimoyama, “Accurate Faraday effect current sensor,” in Advances in Optical Fiber Sensors, B. Culshaw, E. L. Moore, Z. Zhang, eds. (SPIE Press, Bellingham, Wash., 1992), pp. 208–217.
  7. T. Simoyama, Y. Takahashi, T. Yoshino, “Accurate optical current sensor using Faraday effect,” in Proceedings of the Spring Meeting of Japan Society of Applied Physics, No. 3 (Japan Society of Applied Physics, Tokyo, 1992), pp. 805–806.
  8. T. Yoshino, Y. Takahashi, M. Gojyuki, T. Shimoyama, “Polygonal Faraday effect current sensor with polarization-preserving dielectric mirrors,” in Fiber Optic and Laser Sensors XII, R. P. DePaula, ed., Proc. SPIE2292, 34–41 (1994).
  9. T. Yoshino, M. Gojyuki, Y. Takahashi, “High isolation bulk current sensor,” in Proceedings of the 11th Optical Fiber Sensors Conference (Japan Society of Applied Physics, Tokyo, 1996), pp. 292–295.
  10. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 38–40.
  11. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 66–70.

1994 (1)

1986 (1)

M. Kanoi, G. Takahashi, T. Sato, M. Higashi, K. Okamura, “Optical voltage and current measuring system for electric power systems,” IEEE Trans. Power Delivery, PWRD-1, 91–97 (1986).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 66–70.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 38–40.

Day, G. W.

K. B. Rochford, A. H. Rose, M. N. Deeter, G. W. Day, “Faraday effect current sensor with improved sensitivity-bandwidth product,” Opt. Lett. 19, 1903–1905 (1994).

G. W. Day, A. H. Rose, “Faraday effect sensors: The state of the art,” in Fiber Optic and Laser Sensors VI, E. Udd, R. P. DePaula, eds., Proc. SPIE985, 138–149 (1988).

Deeter, M. N.

Gojyuki, M.

T. Yoshino, Y. Takahashi, M. Gojyuki, T. Shimoyama, “Polygonal Faraday effect current sensor with polarization-preserving dielectric mirrors,” in Fiber Optic and Laser Sensors XII, R. P. DePaula, ed., Proc. SPIE2292, 34–41 (1994).

T. Yoshino, M. Gojyuki, Y. Takahashi, “High isolation bulk current sensor,” in Proceedings of the 11th Optical Fiber Sensors Conference (Japan Society of Applied Physics, Tokyo, 1996), pp. 292–295.

Higashi, M.

M. Kanoi, G. Takahashi, T. Sato, M. Higashi, K. Okamura, “Optical voltage and current measuring system for electric power systems,” IEEE Trans. Power Delivery, PWRD-1, 91–97 (1986).

Jackson, D. A.

Y. N. Ning, D. A. Jackson, “A miniature optical current clamp,” in Proceedings of the 9th Optical Fiber Sensors Conference (Associazione Electtrotecnica ed Elettronica Italiano, Florence, 1993), pp. 305–308.

Kanoi, M.

M. Kanoi, G. Takahashi, T. Sato, M. Higashi, K. Okamura, “Optical voltage and current measuring system for electric power systems,” IEEE Trans. Power Delivery, PWRD-1, 91–97 (1986).

Koide, H.

H. Koide, K. Konno, M. Yamada, T. Okamoto, “Development of GIS optical current transformer,” in Proceedings of the 8th Meeting on Lightwave Sensing Technology (Japan Society of Applied Physics, Tokyo, 1991), pp. 75–80.

Konno, K.

H. Koide, K. Konno, M. Yamada, T. Okamoto, “Development of GIS optical current transformer,” in Proceedings of the 8th Meeting on Lightwave Sensing Technology (Japan Society of Applied Physics, Tokyo, 1991), pp. 75–80.

Ning, Y. N.

Y. N. Ning, D. A. Jackson, “A miniature optical current clamp,” in Proceedings of the 9th Optical Fiber Sensors Conference (Associazione Electtrotecnica ed Elettronica Italiano, Florence, 1993), pp. 305–308.

Okamoto, T.

H. Koide, K. Konno, M. Yamada, T. Okamoto, “Development of GIS optical current transformer,” in Proceedings of the 8th Meeting on Lightwave Sensing Technology (Japan Society of Applied Physics, Tokyo, 1991), pp. 75–80.

Okamura, K.

M. Kanoi, G. Takahashi, T. Sato, M. Higashi, K. Okamura, “Optical voltage and current measuring system for electric power systems,” IEEE Trans. Power Delivery, PWRD-1, 91–97 (1986).

Rochford, K. B.

Rose, A. H.

K. B. Rochford, A. H. Rose, M. N. Deeter, G. W. Day, “Faraday effect current sensor with improved sensitivity-bandwidth product,” Opt. Lett. 19, 1903–1905 (1994).

G. W. Day, A. H. Rose, “Faraday effect sensors: The state of the art,” in Fiber Optic and Laser Sensors VI, E. Udd, R. P. DePaula, eds., Proc. SPIE985, 138–149 (1988).

Sato, T.

M. Kanoi, G. Takahashi, T. Sato, M. Higashi, K. Okamura, “Optical voltage and current measuring system for electric power systems,” IEEE Trans. Power Delivery, PWRD-1, 91–97 (1986).

Shimoyama, T.

T. Yoshino, Y. Takahashi, M. Gojyuki, T. Shimoyama, “Polygonal Faraday effect current sensor with polarization-preserving dielectric mirrors,” in Fiber Optic and Laser Sensors XII, R. P. DePaula, ed., Proc. SPIE2292, 34–41 (1994).

T. Yoshino, Y. Takahashi, T. Shimoyama, “Accurate Faraday effect current sensor,” in Advances in Optical Fiber Sensors, B. Culshaw, E. L. Moore, Z. Zhang, eds. (SPIE Press, Bellingham, Wash., 1992), pp. 208–217.

Simoyama, T.

T. Simoyama, Y. Takahashi, T. Yoshino, “Accurate optical current sensor using Faraday effect,” in Proceedings of the Spring Meeting of Japan Society of Applied Physics, No. 3 (Japan Society of Applied Physics, Tokyo, 1992), pp. 805–806.

Takahashi, G.

M. Kanoi, G. Takahashi, T. Sato, M. Higashi, K. Okamura, “Optical voltage and current measuring system for electric power systems,” IEEE Trans. Power Delivery, PWRD-1, 91–97 (1986).

Takahashi, Y.

T. Yoshino, M. Gojyuki, Y. Takahashi, “High isolation bulk current sensor,” in Proceedings of the 11th Optical Fiber Sensors Conference (Japan Society of Applied Physics, Tokyo, 1996), pp. 292–295.

T. Yoshino, Y. Takahashi, M. Gojyuki, T. Shimoyama, “Polygonal Faraday effect current sensor with polarization-preserving dielectric mirrors,” in Fiber Optic and Laser Sensors XII, R. P. DePaula, ed., Proc. SPIE2292, 34–41 (1994).

T. Simoyama, Y. Takahashi, T. Yoshino, “Accurate optical current sensor using Faraday effect,” in Proceedings of the Spring Meeting of Japan Society of Applied Physics, No. 3 (Japan Society of Applied Physics, Tokyo, 1992), pp. 805–806.

T. Yoshino, Y. Takahashi, T. Shimoyama, “Accurate Faraday effect current sensor,” in Advances in Optical Fiber Sensors, B. Culshaw, E. L. Moore, Z. Zhang, eds. (SPIE Press, Bellingham, Wash., 1992), pp. 208–217.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 38–40.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 66–70.

Yamada, M.

H. Koide, K. Konno, M. Yamada, T. Okamoto, “Development of GIS optical current transformer,” in Proceedings of the 8th Meeting on Lightwave Sensing Technology (Japan Society of Applied Physics, Tokyo, 1991), pp. 75–80.

Yoshino, T.

T. Yoshino, Y. Takahashi, M. Gojyuki, T. Shimoyama, “Polygonal Faraday effect current sensor with polarization-preserving dielectric mirrors,” in Fiber Optic and Laser Sensors XII, R. P. DePaula, ed., Proc. SPIE2292, 34–41 (1994).

T. Yoshino, M. Gojyuki, Y. Takahashi, “High isolation bulk current sensor,” in Proceedings of the 11th Optical Fiber Sensors Conference (Japan Society of Applied Physics, Tokyo, 1996), pp. 292–295.

T. Simoyama, Y. Takahashi, T. Yoshino, “Accurate optical current sensor using Faraday effect,” in Proceedings of the Spring Meeting of Japan Society of Applied Physics, No. 3 (Japan Society of Applied Physics, Tokyo, 1992), pp. 805–806.

T. Yoshino, Y. Takahashi, T. Shimoyama, “Accurate Faraday effect current sensor,” in Advances in Optical Fiber Sensors, B. Culshaw, E. L. Moore, Z. Zhang, eds. (SPIE Press, Bellingham, Wash., 1992), pp. 208–217.

IEEE Trans. Power Delivery (1)

M. Kanoi, G. Takahashi, T. Sato, M. Higashi, K. Okamura, “Optical voltage and current measuring system for electric power systems,” IEEE Trans. Power Delivery, PWRD-1, 91–97 (1986).

Opt. Lett. (1)

Other (9)

G. W. Day, A. H. Rose, “Faraday effect sensors: The state of the art,” in Fiber Optic and Laser Sensors VI, E. Udd, R. P. DePaula, eds., Proc. SPIE985, 138–149 (1988).

Y. N. Ning, D. A. Jackson, “A miniature optical current clamp,” in Proceedings of the 9th Optical Fiber Sensors Conference (Associazione Electtrotecnica ed Elettronica Italiano, Florence, 1993), pp. 305–308.

H. Koide, K. Konno, M. Yamada, T. Okamoto, “Development of GIS optical current transformer,” in Proceedings of the 8th Meeting on Lightwave Sensing Technology (Japan Society of Applied Physics, Tokyo, 1991), pp. 75–80.

T. Yoshino, Y. Takahashi, T. Shimoyama, “Accurate Faraday effect current sensor,” in Advances in Optical Fiber Sensors, B. Culshaw, E. L. Moore, Z. Zhang, eds. (SPIE Press, Bellingham, Wash., 1992), pp. 208–217.

T. Simoyama, Y. Takahashi, T. Yoshino, “Accurate optical current sensor using Faraday effect,” in Proceedings of the Spring Meeting of Japan Society of Applied Physics, No. 3 (Japan Society of Applied Physics, Tokyo, 1992), pp. 805–806.

T. Yoshino, Y. Takahashi, M. Gojyuki, T. Shimoyama, “Polygonal Faraday effect current sensor with polarization-preserving dielectric mirrors,” in Fiber Optic and Laser Sensors XII, R. P. DePaula, ed., Proc. SPIE2292, 34–41 (1994).

T. Yoshino, M. Gojyuki, Y. Takahashi, “High isolation bulk current sensor,” in Proceedings of the 11th Optical Fiber Sensors Conference (Japan Society of Applied Physics, Tokyo, 1996), pp. 292–295.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 38–40.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1964), pp. 66–70.

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Figures (13)

Fig. 1
Fig. 1

General configuration of Faraday effect current sensor.

Fig. 2
Fig. 2

Reflection surface medium structure of Faraday material (refractive index n0) coated with dielectric thin films (n1/n2)M/n1.

Fig. 3
Fig. 3

Illustration of angles [see Eq. (8)] associated with Brewster and critical angles.

Fig. 4
Fig. 4

Conditions between relative refractive indices of coating thin films N1 and N2 for achieving no-retardation reflection.

Fig. 5
Fig. 5

Graphical conditions among light beam incident angles α, β, and γ and refractive indices n0, n1, n2 for achieving no-retardation reflection.

Fig. 6
Fig. 6

Fresnel reflection coefficients (a) rs for s polarization and (b) rp for p polarization, calculated as a function of sines of incident angles α and β. Points A and B correspond to the designed case: SF57/SiO2/TiO2 with α = 50° and λ = 633 nm.

Fig. 7
Fig. 7

Incident-angle dependence of amplitude ratio P and retardation Δ at reflection from SF57/(SiO2/TiO2)7/SiO2 with α = 50° and λ = 633 nm.

Fig. 8
Fig. 8

Model for imperfect optical circuit in current sensing.

Fig. 9
Fig. 9

Geometry for cross-talk measurement.

Fig. 10
Fig. 10

Measured analyzer–angle dependence of output light intensity from Faraday cell for closed path (●) and open path yielding minimum extinction ratio (⋄).

Fig. 11
Fig. 11

Dependence of cross-talk value e on angular position of current ξ at radial distance r = 60 mm. The open diamonds represent measurements for closed loop with compensating plate; the solid curve represents the calculation for open loop without compensating plate.

Fig. 12
Fig. 12

Dependence of cross talk e on current distance r at ξ = 0°. The open diamonds represent measurements for closed loop with compensating plate; the filled circles represent measurements and the solid curve represents calculations for open loop without compensating plate.

Fig. 13
Fig. 13

Constructed fiber-guide current sensor.

Tables (4)

Tables Icon

Table 1 Conditions Necessary for Achieving No-Retardation Reflectiona

Tables Icon

Table 2 Medium Parameters and Judgment about No-Retardation Reflection

Tables Icon

Table 3 Angle Parametersa for Designed Faraday Cellb

Tables Icon

Table 4 Dependence of Amplitude Reflection Coefficients Rs and Rp on Pair Number of Alternative Quarter-Wavelength-Thick Thin Filmsa

Equations (21)

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α B < α < α c   for   N 1 < 1 , 90 °   for   N 1 > 1 ,
β B < β < β c   for   N 2 / N 1 < 1 , 90 °   for   N 2 / N 1 > 1 ,
tan   α B = N 1 ; tan β B = N 2 / N 1 ;
sin   α c = N 1 for   N 1 < 1 ; sin   β c = N 2 / N 1 for   N 2 / N 1 < 1 .
N 1 / ( N 1 2 + 1 ) 1 / 2 < sin   α < min ( N 1 ,   1 ) ,
N 2 / ( N 1 2 + N 2 2 ) 1 / 2 < sin   β < min ( N 2 / N 1 ,   1 ) ,
N 1 / ( N 1 2 + 1 ) 1 / 2 < sin   α < min ( N 1 ,   1 ) ,
N 1 N 2 / ( N 1 2 + N 2 2 ) 1 / 2 < sin   α < N 1 · min ( N 2 / N 1 ,   1 ) .
α B = sin 1 ( N 1   sin   β B ) ; α c = sin 1 N 2 , for   N 2 < 1 ,
sin 2   α + sin 2   β > 1 ,
sin 2   γ + sin 2   β > 1 .
41.5 ° < α < 52.0 ° .
e = | ( V V ) / V | ( θ / 2 π ) ,
e = x y ,
x = ( θ / 2 π ) ,
y = | ( V V ) / V | .
e open = θ / 2 π .
θ 1 = 2   tan 1 ( L / 2 d ) .
V = V   cos δ ,
ρ = tan 2 ( δ / 2 ) .
e ellip = [ ρ / ( 1 + ρ ) ] ( θ / π ) .

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