Abstract

By combining twisted optical sensing fiber and heterodyne phase detection of circular birefringence we have (a) overcome the distortion problem caused by residual linear birefringence in the Faraday rotation method of measuring enclosed current and (b) used only a single output detector without requiring intensity normalization. Resolution of 400 ampere-turns has been obtained in the hostile electromagnetic environment of a working thermonuclear fusion research device. The fiber was simply wound around the existing machine. The measured values are in excellent agreement with those of the electrical Rogowski coil installed when the machine was built.

© 1986 Optical Society of America

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References

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  1. A. M. Smith, “Polarization and Magnetooptic Properties of Single-Mode Optical Fiber,” Appl. Opt. 17, 52 (1978).
    [CrossRef] [PubMed]
  2. A. Papp, H. Harms, “Magnetooptical Current Transformer. 1: Principles,” Appl. Opt. 19, 3729 (1980).
    [CrossRef] [PubMed]
  3. G. I. Chandler, F. C. Jahoda, “Current Measurements by Faraday Rotation in Single-Mode Optical Fibers,” Rev. Sci. Instrum. 56, 852 (1985).
    [CrossRef]
  4. R. C. Jones, “A New Calculus for the Treatment of Optical Systems. I,” J. Opt. Soc. Am. 31, 488 (1941).
    [CrossRef]
  5. W. J. Tabor, F. S. Chen, “Electronmagnetic Propagation Through Materials Possessing Both Faraday Rotation and Birefringence: Experiments with Ytterbium Orthoferrite,” J. Appl. Phys. 40, 2760 (1969).
    [CrossRef]
  6. R. C. Jones, “A New Calculus for the Treatment of Optical Systems. VII: Properties of the N-Matrices,” J. Opt. Soc. Am. 38, 671 (1948).
    [CrossRef]
  7. The equivalence of the derivations of Refs. 5 and 6 follows from (a) the matrix given as Eq. (4.17) in Ref. 6 with the definitions of Table I in the same reference that equate g0 and ω with the per unit length values of δ/2 and F in the Smith notation, respectively; (b) the substitution of g45 = 0 for this particular example; and (c) Jones's definitions of g and Γ in his Eqs. (4.11) and (4.17).
  8. S. C. Rashleigh, R. Ulrich, “Magneto-Optic Current Sensing with Birefringence Fibers,” Appl. Phys. Lett. 34, 768 (1979).
    [CrossRef]
  9. R. Ulrich, A. Simon, “Polarization Optics of Twisted Single-Moded Fibers,” Appl. Opt. 18, 2241 (1979).
    [CrossRef] [PubMed]
  10. EOTec,Inc., 420 Frontage Road, West Haven, CT 06516.
  11. R. Ulrich, S. C. Rashleigh, W. Eickhoff, “Bending-Induced Birefringence in Single-Mode Fibers,” Opt. Lett. 5, 273 (1980).
    [CrossRef] [PubMed]
  12. S. C. Rashleigh, “Origins and Control of Polarization Effects in Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-1, 312 (1983).
    [CrossRef]
  13. G. I. Chandler, P. R. Forman, F. C. Jahoda, “Measurement of Faraday Rotation in Twisted Optical Fiber Using Rotating Polarization and Analog Phase Detection,” Proc. Soc. Photo-Opt. Instrum. Eng. 566, 206 (1985).
  14. D. A. Baker et al., “Plasma Physics and Controlled Nuclear Fusion Research 1982” (IAEA, Vienna, 1983), Vol. 1, p. 587.
  15. C. F. Buhrer, L. R. Bloom, D. H. Baird, “Electrooptic Light Modulation with Cubic Crystals,” Appl. Opt. 2, 839 (1963).
    [CrossRef]
  16. J. P. Campbell, W. H. Steier, “Rotating-Waveplate Optical-Frequency Shifting in Lithium Niobate,” IEEE J. Quantum Electron. QE-7, 450 (1971).
    [CrossRef]
  17. T. Okoshi, N. Fukaya, K. Kikuchi, “New Polarization-State Control Device: Rotatable Fibre Cranks,” Electron. Lett. 21, 895 (1985).
    [CrossRef]
  18. M. M. Fejer, J. L. Nightingale, G. A. Magel, R. L. Byer, “Laser-Heated Miniature Pedestal Growth Apparatus for Single-Crystal Optical Fibers,” Rev. Sci. Instrum. 55, 1791 (1984).
    [CrossRef]
  19. See for example, P. Horowitz, W. Hill, The Art of Electronics (Cambridge U.P., London, 1980), p. 429.

1985 (3)

G. I. Chandler, F. C. Jahoda, “Current Measurements by Faraday Rotation in Single-Mode Optical Fibers,” Rev. Sci. Instrum. 56, 852 (1985).
[CrossRef]

T. Okoshi, N. Fukaya, K. Kikuchi, “New Polarization-State Control Device: Rotatable Fibre Cranks,” Electron. Lett. 21, 895 (1985).
[CrossRef]

G. I. Chandler, P. R. Forman, F. C. Jahoda, “Measurement of Faraday Rotation in Twisted Optical Fiber Using Rotating Polarization and Analog Phase Detection,” Proc. Soc. Photo-Opt. Instrum. Eng. 566, 206 (1985).

1984 (1)

M. M. Fejer, J. L. Nightingale, G. A. Magel, R. L. Byer, “Laser-Heated Miniature Pedestal Growth Apparatus for Single-Crystal Optical Fibers,” Rev. Sci. Instrum. 55, 1791 (1984).
[CrossRef]

1983 (1)

S. C. Rashleigh, “Origins and Control of Polarization Effects in Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-1, 312 (1983).
[CrossRef]

1980 (2)

1979 (2)

R. Ulrich, A. Simon, “Polarization Optics of Twisted Single-Moded Fibers,” Appl. Opt. 18, 2241 (1979).
[CrossRef] [PubMed]

S. C. Rashleigh, R. Ulrich, “Magneto-Optic Current Sensing with Birefringence Fibers,” Appl. Phys. Lett. 34, 768 (1979).
[CrossRef]

1978 (1)

1971 (1)

J. P. Campbell, W. H. Steier, “Rotating-Waveplate Optical-Frequency Shifting in Lithium Niobate,” IEEE J. Quantum Electron. QE-7, 450 (1971).
[CrossRef]

1969 (1)

W. J. Tabor, F. S. Chen, “Electronmagnetic Propagation Through Materials Possessing Both Faraday Rotation and Birefringence: Experiments with Ytterbium Orthoferrite,” J. Appl. Phys. 40, 2760 (1969).
[CrossRef]

1963 (1)

1948 (1)

1941 (1)

Baird, D. H.

Baker, D. A.

D. A. Baker et al., “Plasma Physics and Controlled Nuclear Fusion Research 1982” (IAEA, Vienna, 1983), Vol. 1, p. 587.

Bloom, L. R.

Buhrer, C. F.

Byer, R. L.

M. M. Fejer, J. L. Nightingale, G. A. Magel, R. L. Byer, “Laser-Heated Miniature Pedestal Growth Apparatus for Single-Crystal Optical Fibers,” Rev. Sci. Instrum. 55, 1791 (1984).
[CrossRef]

Campbell, J. P.

J. P. Campbell, W. H. Steier, “Rotating-Waveplate Optical-Frequency Shifting in Lithium Niobate,” IEEE J. Quantum Electron. QE-7, 450 (1971).
[CrossRef]

Chandler, G. I.

G. I. Chandler, P. R. Forman, F. C. Jahoda, “Measurement of Faraday Rotation in Twisted Optical Fiber Using Rotating Polarization and Analog Phase Detection,” Proc. Soc. Photo-Opt. Instrum. Eng. 566, 206 (1985).

G. I. Chandler, F. C. Jahoda, “Current Measurements by Faraday Rotation in Single-Mode Optical Fibers,” Rev. Sci. Instrum. 56, 852 (1985).
[CrossRef]

Chen, F. S.

W. J. Tabor, F. S. Chen, “Electronmagnetic Propagation Through Materials Possessing Both Faraday Rotation and Birefringence: Experiments with Ytterbium Orthoferrite,” J. Appl. Phys. 40, 2760 (1969).
[CrossRef]

Eickhoff, W.

Fejer, M. M.

M. M. Fejer, J. L. Nightingale, G. A. Magel, R. L. Byer, “Laser-Heated Miniature Pedestal Growth Apparatus for Single-Crystal Optical Fibers,” Rev. Sci. Instrum. 55, 1791 (1984).
[CrossRef]

Forman, P. R.

G. I. Chandler, P. R. Forman, F. C. Jahoda, “Measurement of Faraday Rotation in Twisted Optical Fiber Using Rotating Polarization and Analog Phase Detection,” Proc. Soc. Photo-Opt. Instrum. Eng. 566, 206 (1985).

Fukaya, N.

T. Okoshi, N. Fukaya, K. Kikuchi, “New Polarization-State Control Device: Rotatable Fibre Cranks,” Electron. Lett. 21, 895 (1985).
[CrossRef]

Harms, H.

Hill, W.

See for example, P. Horowitz, W. Hill, The Art of Electronics (Cambridge U.P., London, 1980), p. 429.

Horowitz, P.

See for example, P. Horowitz, W. Hill, The Art of Electronics (Cambridge U.P., London, 1980), p. 429.

Jahoda, F. C.

G. I. Chandler, F. C. Jahoda, “Current Measurements by Faraday Rotation in Single-Mode Optical Fibers,” Rev. Sci. Instrum. 56, 852 (1985).
[CrossRef]

G. I. Chandler, P. R. Forman, F. C. Jahoda, “Measurement of Faraday Rotation in Twisted Optical Fiber Using Rotating Polarization and Analog Phase Detection,” Proc. Soc. Photo-Opt. Instrum. Eng. 566, 206 (1985).

Jones, R. C.

Kikuchi, K.

T. Okoshi, N. Fukaya, K. Kikuchi, “New Polarization-State Control Device: Rotatable Fibre Cranks,” Electron. Lett. 21, 895 (1985).
[CrossRef]

Magel, G. A.

M. M. Fejer, J. L. Nightingale, G. A. Magel, R. L. Byer, “Laser-Heated Miniature Pedestal Growth Apparatus for Single-Crystal Optical Fibers,” Rev. Sci. Instrum. 55, 1791 (1984).
[CrossRef]

Nightingale, J. L.

M. M. Fejer, J. L. Nightingale, G. A. Magel, R. L. Byer, “Laser-Heated Miniature Pedestal Growth Apparatus for Single-Crystal Optical Fibers,” Rev. Sci. Instrum. 55, 1791 (1984).
[CrossRef]

Okoshi, T.

T. Okoshi, N. Fukaya, K. Kikuchi, “New Polarization-State Control Device: Rotatable Fibre Cranks,” Electron. Lett. 21, 895 (1985).
[CrossRef]

Papp, A.

Rashleigh, S. C.

S. C. Rashleigh, “Origins and Control of Polarization Effects in Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-1, 312 (1983).
[CrossRef]

R. Ulrich, S. C. Rashleigh, W. Eickhoff, “Bending-Induced Birefringence in Single-Mode Fibers,” Opt. Lett. 5, 273 (1980).
[CrossRef] [PubMed]

S. C. Rashleigh, R. Ulrich, “Magneto-Optic Current Sensing with Birefringence Fibers,” Appl. Phys. Lett. 34, 768 (1979).
[CrossRef]

Simon, A.

Smith, A. M.

Steier, W. H.

J. P. Campbell, W. H. Steier, “Rotating-Waveplate Optical-Frequency Shifting in Lithium Niobate,” IEEE J. Quantum Electron. QE-7, 450 (1971).
[CrossRef]

Tabor, W. J.

W. J. Tabor, F. S. Chen, “Electronmagnetic Propagation Through Materials Possessing Both Faraday Rotation and Birefringence: Experiments with Ytterbium Orthoferrite,” J. Appl. Phys. 40, 2760 (1969).
[CrossRef]

Ulrich, R.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

S. C. Rashleigh, R. Ulrich, “Magneto-Optic Current Sensing with Birefringence Fibers,” Appl. Phys. Lett. 34, 768 (1979).
[CrossRef]

Electron. Lett. (1)

T. Okoshi, N. Fukaya, K. Kikuchi, “New Polarization-State Control Device: Rotatable Fibre Cranks,” Electron. Lett. 21, 895 (1985).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. P. Campbell, W. H. Steier, “Rotating-Waveplate Optical-Frequency Shifting in Lithium Niobate,” IEEE J. Quantum Electron. QE-7, 450 (1971).
[CrossRef]

IEEE/OSA J. Lightwave Technol. (1)

S. C. Rashleigh, “Origins and Control of Polarization Effects in Single-Mode Fibers,” IEEE/OSA J. Lightwave Technol. LT-1, 312 (1983).
[CrossRef]

J. Appl. Phys. (1)

W. J. Tabor, F. S. Chen, “Electronmagnetic Propagation Through Materials Possessing Both Faraday Rotation and Birefringence: Experiments with Ytterbium Orthoferrite,” J. Appl. Phys. 40, 2760 (1969).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

G. I. Chandler, P. R. Forman, F. C. Jahoda, “Measurement of Faraday Rotation in Twisted Optical Fiber Using Rotating Polarization and Analog Phase Detection,” Proc. Soc. Photo-Opt. Instrum. Eng. 566, 206 (1985).

Rev. Sci. Instrum. (2)

G. I. Chandler, F. C. Jahoda, “Current Measurements by Faraday Rotation in Single-Mode Optical Fibers,” Rev. Sci. Instrum. 56, 852 (1985).
[CrossRef]

M. M. Fejer, J. L. Nightingale, G. A. Magel, R. L. Byer, “Laser-Heated Miniature Pedestal Growth Apparatus for Single-Crystal Optical Fibers,” Rev. Sci. Instrum. 55, 1791 (1984).
[CrossRef]

Other (4)

See for example, P. Horowitz, W. Hill, The Art of Electronics (Cambridge U.P., London, 1980), p. 429.

EOTec,Inc., 420 Frontage Road, West Haven, CT 06516.

The equivalence of the derivations of Refs. 5 and 6 follows from (a) the matrix given as Eq. (4.17) in Ref. 6 with the definitions of Table I in the same reference that equate g0 and ω with the per unit length values of δ/2 and F in the Smith notation, respectively; (b) the substitution of g45 = 0 for this particular example; and (c) Jones's definitions of g and Γ in his Eqs. (4.11) and (4.17).

D. A. Baker et al., “Plasma Physics and Controlled Nuclear Fusion Research 1982” (IAEA, Vienna, 1983), Vol. 1, p. 587.

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Figures (2)

Fig. 1
Fig. 1

Schematic for producing rotating linear polarization light at the fiber sensor input and for generating a local oscillator signal for heterodyne detection of the fiber sensor output.

Fig. 2
Fig. 2

(a) ZT-40M plasma current as a function of time derived from the fiber-optic sensor. (b) Difference between fiber-optic sensor current and electrical Rogowski coil current on the same plasma discharge as (a) with a ten-times expanded vertical scale.

Equations (9)

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

( E x E y ) out = ( A B B A * ) ( E x E y ) in ,
Á = cos ( ϕ / 2 ) + i sin ( ϕ / 2 ) cos χ ,
B = sin ( ϕ / 2 ) sin χ ,
ϕ / 2 = 1 / 2 [ ( δ ) 2 + ( 2 F ) 2 ] 1 / 2 ,
tan χ = 2 F / δ .
Δ δ = 1.34 × 10 6 r 2 / R 2 rad / m .
( E x 0 ) = ( 1 0 0 0 ) ( A B B A * ) ( cos ω t / 2 sin ω t / 2 ) .
I = 1 + cos ( ω t Φ ) ,
Φ = tan 1 [ sin ϕ sin χ cos 2 ( ϕ / 2 ) sin 2 ( ϕ / 2 ) ( sin 2 χ cos 2 χ ) ] + m π .

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