Abstract

Reflection-induced phase retardance inside bulk optic-material current sensors makes the state of polarization of the light change, which reduces the immunity of the sensors against electromagnetic interference. These effects are analyzed theoretically for the first time, to our knowledge. A comparison between the theoretical analysis and the experimental results are given.

© 1998 Optical Society of America

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References

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  1. N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, D. A. Jackson, “Recent process in optical current sensing techniques,” Rev. Sci. Instrum. 66, 3097–3111 (1995).
    [CrossRef]
  2. T. Sato, G. Takahashi, Y. Inui, “Method and apparatus for optically measuring a current,” European patent0088419A1 (14September1983).
  3. Z. P. Wang, W. M. Sun, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “An optical current sensor employing a novel multi-optic-loop sensing element,” Acta Photon. Sin. 25, 831–835 (1996) (in Chinese).
  4. Y. N. Ning, B. C. B. Chu, D. A. Jackson, “Miniature Faraday current sensor based on multiple critical angle reflections in a bulk-optic ring,” Opt. Lett. 16, 1996–1998 (1991).
    [CrossRef] [PubMed]
  5. Z. P. Wang, W. M. Sun, S. L. Ruan, Z. J. Huang, C. Kang, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “Optical current sensing element with polarization-preserving coating surfaces,” in Proceedings of the Eighth Conference on Sensors and Their Applications, A. T. Augousti, N. M. White, eds. (Institute of Physics, Glasgow, Scotland, 1997), pp. 353–357.
  6. R. C. Jones, “A new calculation for the treatment of optical systems: I, II, III,” J. Opt. Soc. Am. 31, 488–503 (1941).
    [CrossRef]

1996

Z. P. Wang, W. M. Sun, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “An optical current sensor employing a novel multi-optic-loop sensing element,” Acta Photon. Sin. 25, 831–835 (1996) (in Chinese).

1995

N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, D. A. Jackson, “Recent process in optical current sensing techniques,” Rev. Sci. Instrum. 66, 3097–3111 (1995).
[CrossRef]

1991

1941

Chu, B. C. B.

Grattan, K. T. V.

Z. P. Wang, W. M. Sun, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “An optical current sensor employing a novel multi-optic-loop sensing element,” Acta Photon. Sin. 25, 831–835 (1996) (in Chinese).

N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, D. A. Jackson, “Recent process in optical current sensing techniques,” Rev. Sci. Instrum. 66, 3097–3111 (1995).
[CrossRef]

Z. P. Wang, W. M. Sun, S. L. Ruan, Z. J. Huang, C. Kang, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “Optical current sensing element with polarization-preserving coating surfaces,” in Proceedings of the Eighth Conference on Sensors and Their Applications, A. T. Augousti, N. M. White, eds. (Institute of Physics, Glasgow, Scotland, 1997), pp. 353–357.

Huang, Z. J.

Z. P. Wang, W. M. Sun, S. L. Ruan, Z. J. Huang, C. Kang, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “Optical current sensing element with polarization-preserving coating surfaces,” in Proceedings of the Eighth Conference on Sensors and Their Applications, A. T. Augousti, N. M. White, eds. (Institute of Physics, Glasgow, Scotland, 1997), pp. 353–357.

Inui, Y.

T. Sato, G. Takahashi, Y. Inui, “Method and apparatus for optically measuring a current,” European patent0088419A1 (14September1983).

Jackson, D. A.

N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, D. A. Jackson, “Recent process in optical current sensing techniques,” Rev. Sci. Instrum. 66, 3097–3111 (1995).
[CrossRef]

Y. N. Ning, B. C. B. Chu, D. A. Jackson, “Miniature Faraday current sensor based on multiple critical angle reflections in a bulk-optic ring,” Opt. Lett. 16, 1996–1998 (1991).
[CrossRef] [PubMed]

Jones, R. C.

Kang, C.

Z. P. Wang, W. M. Sun, S. L. Ruan, Z. J. Huang, C. Kang, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “Optical current sensing element with polarization-preserving coating surfaces,” in Proceedings of the Eighth Conference on Sensors and Their Applications, A. T. Augousti, N. M. White, eds. (Institute of Physics, Glasgow, Scotland, 1997), pp. 353–357.

Ning, N.

N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, D. A. Jackson, “Recent process in optical current sensing techniques,” Rev. Sci. Instrum. 66, 3097–3111 (1995).
[CrossRef]

Ning, Y. N.

Z. P. Wang, W. M. Sun, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “An optical current sensor employing a novel multi-optic-loop sensing element,” Acta Photon. Sin. 25, 831–835 (1996) (in Chinese).

Y. N. Ning, B. C. B. Chu, D. A. Jackson, “Miniature Faraday current sensor based on multiple critical angle reflections in a bulk-optic ring,” Opt. Lett. 16, 1996–1998 (1991).
[CrossRef] [PubMed]

Z. P. Wang, W. M. Sun, S. L. Ruan, Z. J. Huang, C. Kang, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “Optical current sensing element with polarization-preserving coating surfaces,” in Proceedings of the Eighth Conference on Sensors and Their Applications, A. T. Augousti, N. M. White, eds. (Institute of Physics, Glasgow, Scotland, 1997), pp. 353–357.

Palmer, A. W.

Z. P. Wang, W. M. Sun, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “An optical current sensor employing a novel multi-optic-loop sensing element,” Acta Photon. Sin. 25, 831–835 (1996) (in Chinese).

N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, D. A. Jackson, “Recent process in optical current sensing techniques,” Rev. Sci. Instrum. 66, 3097–3111 (1995).
[CrossRef]

Z. P. Wang, W. M. Sun, S. L. Ruan, Z. J. Huang, C. Kang, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “Optical current sensing element with polarization-preserving coating surfaces,” in Proceedings of the Eighth Conference on Sensors and Their Applications, A. T. Augousti, N. M. White, eds. (Institute of Physics, Glasgow, Scotland, 1997), pp. 353–357.

Ruan, S. L.

Z. P. Wang, W. M. Sun, S. L. Ruan, Z. J. Huang, C. Kang, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “Optical current sensing element with polarization-preserving coating surfaces,” in Proceedings of the Eighth Conference on Sensors and Their Applications, A. T. Augousti, N. M. White, eds. (Institute of Physics, Glasgow, Scotland, 1997), pp. 353–357.

Sato, T.

T. Sato, G. Takahashi, Y. Inui, “Method and apparatus for optically measuring a current,” European patent0088419A1 (14September1983).

Sun, W. M.

Z. P. Wang, W. M. Sun, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “An optical current sensor employing a novel multi-optic-loop sensing element,” Acta Photon. Sin. 25, 831–835 (1996) (in Chinese).

Z. P. Wang, W. M. Sun, S. L. Ruan, Z. J. Huang, C. Kang, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “Optical current sensing element with polarization-preserving coating surfaces,” in Proceedings of the Eighth Conference on Sensors and Their Applications, A. T. Augousti, N. M. White, eds. (Institute of Physics, Glasgow, Scotland, 1997), pp. 353–357.

Takahashi, G.

T. Sato, G. Takahashi, Y. Inui, “Method and apparatus for optically measuring a current,” European patent0088419A1 (14September1983).

Wang, Z. P.

Z. P. Wang, W. M. Sun, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “An optical current sensor employing a novel multi-optic-loop sensing element,” Acta Photon. Sin. 25, 831–835 (1996) (in Chinese).

N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, D. A. Jackson, “Recent process in optical current sensing techniques,” Rev. Sci. Instrum. 66, 3097–3111 (1995).
[CrossRef]

Z. P. Wang, W. M. Sun, S. L. Ruan, Z. J. Huang, C. Kang, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “Optical current sensing element with polarization-preserving coating surfaces,” in Proceedings of the Eighth Conference on Sensors and Their Applications, A. T. Augousti, N. M. White, eds. (Institute of Physics, Glasgow, Scotland, 1997), pp. 353–357.

Acta Photon. Sin.

Z. P. Wang, W. M. Sun, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “An optical current sensor employing a novel multi-optic-loop sensing element,” Acta Photon. Sin. 25, 831–835 (1996) (in Chinese).

J. Opt. Soc. Am.

Opt. Lett.

Rev. Sci. Instrum.

N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, D. A. Jackson, “Recent process in optical current sensing techniques,” Rev. Sci. Instrum. 66, 3097–3111 (1995).
[CrossRef]

Other

T. Sato, G. Takahashi, Y. Inui, “Method and apparatus for optically measuring a current,” European patent0088419A1 (14September1983).

Z. P. Wang, W. M. Sun, S. L. Ruan, Z. J. Huang, C. Kang, Y. N. Ning, A. W. Palmer, K. T. V. Grattan, “Optical current sensing element with polarization-preserving coating surfaces,” in Proceedings of the Eighth Conference on Sensors and Their Applications, A. T. Augousti, N. M. White, eds. (Institute of Physics, Glasgow, Scotland, 1997), pp. 353–357.

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Figures (7)

Fig. 1
Fig. 1

Model of the sensing heads: 1–4, the first through fourth propagation parts of the optical path; a–c, reflection surface; D1, D2, detectors.

Fig. 2
Fig. 2

Relationship between the optical path and the current parallel to the Z axis to produce a stray field: R1–R3, reflection matrix; F1–F4, transmission matrix.

Fig. 3
Fig. 3

Relationship between the optical path and the current parallel to the Y axis to produce a stray field.

Fig. 4
Fig. 4

Relationship between the optical path and the current parallel to the X axis to produce a stray field.

Fig. 5
Fig. 5

Comparison between the theoretical and the experimental results: The outside current is in the Z-axis direction (Δ1 = Δ2 = Δ3 = 1.1 rad, b = 23.5 cm).

Fig. 6
Fig. 6

Comparison between the theoretical and the experimental results: The outside current is in the Y-axis direction (Δ1 = Δ2 = Δ3 = 1.1 rad, b = 18.0 cm, Z 0 = 17.0 cm).

Fig. 7
Fig. 7

Comparison between the theoretical and the experimental results: The outside current is in the X-axis direction (Δ1 = Δ2 = Δ3 = 1.1 rad, Y 0 = 21.0 cm, Z 0 = 20.0 cm).

Equations (23)

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E out = F 4 R 3 F 3 R 2 F 2 R 1 F 1 E in ,
E in = E 0 2 1 1 ,
F i = cos   ϕ i - sin   ϕ i sin   ϕ i cos   ϕ i     i = 1 ,   2 ,   3 ,   4 ,
R i = exp j δ pi 0 0 exp j δ si = exp j δ si exp j Δ i 0 0 1     i = 1 ,   2 ,   3 ,
E out = E p E s = E 0 G p G s ,
E 0 = E 0 2 exp j   i = 1 3   δ si ,
J p = E p · E p * ,
J s = E s · E s * ,
U out = J s - J p / J s + J p .
ϕ 1 = VI 2 π tan - 1 b + a a -   tan - 1 b - a a , ϕ 2 = - VI π tan - 1 a b - a , ϕ 3 = VI 2 π tan - 1 b + a a -   tan - 1 b - a a = ϕ 1 , ϕ 4 = VI π tan - 1 a b + a ,
i = 1 4   ϕ i = 0 .
E out = E 0 G p G s ,
G p = exp j Δ 1 + Δ 2 + Δ 3 cos   ϕ 4   cos   ϕ 3   cos   ϕ 2 × cos   ϕ 1   -   sin   ϕ 1 - exp j Δ 2 + Δ 3 × cos   ϕ 4   cos   ϕ 3   sin   ϕ 2 sin   ϕ 1   +   cos   ϕ 1 - exp j Δ 1 + Δ 3 cos   ϕ 4   sin   ϕ 3   sin   ϕ 2 × cos   ϕ 1   -   sin   ϕ 1   -   exp j Δ 3 cos   ϕ 4 × sin   ϕ 3   cos   ϕ 2 sin   ϕ 1   +   cos   ϕ 1 - exp j Δ 1 + Δ 2 sin   ϕ 4   sin   ϕ 3 cos   ϕ 2 × cos   ϕ 1   -   sin   ϕ 1   +   exp j Δ 2 sin   ϕ 4 × sin   ϕ 3   sin   ϕ 2 sin   ϕ 1   +   cos   ϕ 1 - exp j Δ 1 sin   ϕ 4   cos   ϕ 3   sin   ϕ 2 × cos   ϕ 1   -   sin   ϕ 1   -   sin   ϕ 4   cos   ϕ 3 × cos   ϕ 2 sin   ϕ 1   +   cos   ϕ 1 , G s = exp j Δ 1 + Δ 2 + Δ 3 sin   ϕ 4   cos   ϕ 3   cos   ϕ 2 × cos   ϕ 1   -   sin   ϕ 1   -   exp j Δ 2 + Δ 3 × sin   ϕ 4   cos   ϕ 3   sin   ϕ 2 sin   ϕ 1   +   cos   ϕ 1 - exp j Δ 1 + Δ 3 sin   ϕ 4   sin   ϕ 3 sin   ϕ 2 × ( cos   ϕ 1 -   sin   ϕ 1 ) - exp ( j Δ 3 )   sin   ϕ 4   sin   ϕ 3   cos   ϕ 2 × ( sin   ϕ 1 + cos   ϕ 1 ) + exp j Δ 1 + Δ 2 × cos   ϕ 4   sin   ϕ 3   cos   ϕ 2 cos   ϕ 1   -   sin   ϕ 1 - exp j Δ 2 cos   ϕ 4   sin   ϕ 3   sin   ϕ 2 sin   ϕ 1   +   cos   ϕ 1 + exp j Δ 1 × cos   ϕ 4   cos   ϕ 3   sin   ϕ 2 cos   ϕ 1   -   sin   ϕ 1 + cos   ϕ 4 cos   ϕ 3 cos   ϕ 2 sin   ϕ 1   +   cos   ϕ 1 .
U out = J s - J p / J s + J p   =   sin 2   i = 1 4   ϕ i = 0 ,
G p = exp j Δ k cos i = 1 k   ϕ i cos i = 1 k   ϕ i - sin i = 1 k   ϕ i + sin i = 1 k   ϕ i cos i = 1 k   ϕ i + sin i = 1 k   ϕ i G s = - exp j Δ k sin i = 1 k   ϕ i cos i = 1 k   ϕ i - sin i = 1 k   ϕ i + cos i = 1 k   ϕ i cos i = 1 k   ϕ i + sin i = 1 k   ϕ i .     i = 1 ,   2 , ,   k ;     k = 1 ,   2 ,   3 ,
U out = 1 2 sin 4   i = 1 k   ϕ i 1 - cos   Δ k   i = 1 ,   2 , ,   k ; k = 1 ,   2 ,   3 .
i = 1 k   ϕ i 0 ,
ϕ 1 = - ϕ 3 = VI 2 π tan - 1 b - a z 0 - tan - 1 b + a z 0 , ϕ 2 = ϕ 4 = 0 , ϕ 1 + ϕ 3 = 0 .
U out = 1 2 sin 4 ϕ 1 1 - cos Δ 1 + Δ 2 .
ϕ 2 = - ϕ 4 = VI 2 π tan - 1 y 0 - a z 0 - tan - 1 y 0 + a z 0 , ϕ 1 = ϕ 3 = 0 , ϕ 2 + ϕ 4 = 0 ,
U out = 1 2 sin 4 ϕ 2 cos   Δ 1 - sin 2 ϕ 2 cos 2   ϕ 2   cos Δ 1 + Δ 2 + Δ 3 - sin 2   ϕ 2   cos Δ 3 + Δ 2 - Δ 1 .
U out = 1 2 sin 4 ϕ 2 1 - cos   Δ i   i = 2   or   i = 3 ;
U out = sin 2 ϕ 2 cos 2   ϕ 2 cos   Δ - cos 3 Δ .

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