Abstract

In this work we find the exact solution for the evolution of the polarization state of a light wave that propagates in a material medium with uniform linear birefringence and a nonuniform external magnetic field. The obtained results could be used to improve the precision of existing Faraday current sensors.

© 2008 Optical Society of America

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References

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  1. R. C. Jones, “A new calculus for the treatment of optical systems. VII. Properties of the N-matrices,” J. Opt. Soc. Am. 38, 671-685 (1948).
    [CrossRef]
  2. Y. N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, and D. A. Jackson, “Recent progress in optical current sensing techniques,” Rev. Sci. Instrum. 66, 3097-3111 (1995).
    [CrossRef]
  3. J. Rogers, J. Xu, and J. Yao, “Vibration immunity for optical-fiber current measurement,” J. Lightwave Technol. 13, 1371-1377 (1995).
    [CrossRef]
  4. P. Menke and T. Bosselmann, “Temperature compensation in magnetooptic AC current sensors using an intelligent AC-DC signal evaluation,” J. Lightwave Technol. 13, 1362-1370 (1995).
    [CrossRef]
  5. A. H. Rose, S. M. Etzel, and K. B. Rochford, “Optical fiber current sensors in high electric field environments,” J. Lightwave Technol. 17, 1042-1048 (1999).
    [CrossRef]
  6. X. Fang, A. Wang, R. G. May, and R. O. Claus, “A reciprocal-compensated fiber-optic electric current sensor,” J. Lightwave Technol. 12, 1882-1890 (1994).
    [CrossRef]
  7. H. Lin, W.-W. Lin, M.-H. Chen, and S.-C. Huang, “Vibration insensitive optical fiber current sensor with a modified reciprocal reflection interferometer,” Opt. Eng. (Bellingham) 38, 1722-1729 (1999).
    [CrossRef]
  8. F. Maystre and A. Bertholds, “Magneto-optic current sensor using a helical-fiber Fabry-Perot resonator,” Opt. Lett. 14, 587-589 (1989).
    [CrossRef] [PubMed]
  9. C. Li, X. Cui, and T. Yoshino, “Optical electric-power sensor by use of one bismuth germanate crystal,” J. Lightwave Technol. 21, 1328-1333 (2003).
    [CrossRef]
  10. X. Ma and C. Luo, “A method to eliminate birefringence of a magneto-optic AC current transducer with glass ring sensor head,” IEEE Trans. Power Deliv. 13, 1015-1019 (1998).
    [CrossRef]
  11. K. Kyuma, S. Tai, M. Nunoshita, N. Mikami, and Y. Ida, “Fiber-optic current and voltage sensors using a Bi12GeO20 single crystal,” J. Lightwave Technol. LT-1, 93-97 (1983).
    [CrossRef]
  12. E. A. Ulmer, Jr., “A high-accuracy optical current transducer for electric power systems,” IEEE Trans. Power Deliv. 5, 892-898 (1990).
    [CrossRef]
  13. Z. P. Wang, Q. B. Li, Y. Qi, Z. J. Huang, and J. H. Shi, “Effect of dispersion of linear birefringence upon the sensitivity of an optical current sensor,” Opt. Laser Technol. 36, 587-590 (2004).
    [CrossRef]

2004 (1)

Z. P. Wang, Q. B. Li, Y. Qi, Z. J. Huang, and J. H. Shi, “Effect of dispersion of linear birefringence upon the sensitivity of an optical current sensor,” Opt. Laser Technol. 36, 587-590 (2004).
[CrossRef]

2003 (1)

1999 (2)

H. Lin, W.-W. Lin, M.-H. Chen, and S.-C. Huang, “Vibration insensitive optical fiber current sensor with a modified reciprocal reflection interferometer,” Opt. Eng. (Bellingham) 38, 1722-1729 (1999).
[CrossRef]

A. H. Rose, S. M. Etzel, and K. B. Rochford, “Optical fiber current sensors in high electric field environments,” J. Lightwave Technol. 17, 1042-1048 (1999).
[CrossRef]

1998 (1)

X. Ma and C. Luo, “A method to eliminate birefringence of a magneto-optic AC current transducer with glass ring sensor head,” IEEE Trans. Power Deliv. 13, 1015-1019 (1998).
[CrossRef]

1995 (3)

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

J. Rogers, J. Xu, and J. Yao, “Vibration immunity for optical-fiber current measurement,” J. Lightwave Technol. 13, 1371-1377 (1995).
[CrossRef]

P. Menke and T. Bosselmann, “Temperature compensation in magnetooptic AC current sensors using an intelligent AC-DC signal evaluation,” J. Lightwave Technol. 13, 1362-1370 (1995).
[CrossRef]

1994 (1)

X. Fang, A. Wang, R. G. May, and R. O. Claus, “A reciprocal-compensated fiber-optic electric current sensor,” J. Lightwave Technol. 12, 1882-1890 (1994).
[CrossRef]

1990 (1)

E. A. Ulmer, Jr., “A high-accuracy optical current transducer for electric power systems,” IEEE Trans. Power Deliv. 5, 892-898 (1990).
[CrossRef]

1989 (1)

1983 (1)

K. Kyuma, S. Tai, M. Nunoshita, N. Mikami, and Y. Ida, “Fiber-optic current and voltage sensors using a Bi12GeO20 single crystal,” J. Lightwave Technol. LT-1, 93-97 (1983).
[CrossRef]

1948 (1)

Bertholds, A.

Bosselmann, T.

P. Menke and T. Bosselmann, “Temperature compensation in magnetooptic AC current sensors using an intelligent AC-DC signal evaluation,” J. Lightwave Technol. 13, 1362-1370 (1995).
[CrossRef]

Chen, M.-H.

H. Lin, W.-W. Lin, M.-H. Chen, and S.-C. Huang, “Vibration insensitive optical fiber current sensor with a modified reciprocal reflection interferometer,” Opt. Eng. (Bellingham) 38, 1722-1729 (1999).
[CrossRef]

Claus, R. O.

X. Fang, A. Wang, R. G. May, and R. O. Claus, “A reciprocal-compensated fiber-optic electric current sensor,” J. Lightwave Technol. 12, 1882-1890 (1994).
[CrossRef]

Cui, X.

Etzel, S. M.

Fang, X.

X. Fang, A. Wang, R. G. May, and R. O. Claus, “A reciprocal-compensated fiber-optic electric current sensor,” J. Lightwave Technol. 12, 1882-1890 (1994).
[CrossRef]

Grattan, K. T. V.

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

Huang, S.-C.

H. Lin, W.-W. Lin, M.-H. Chen, and S.-C. Huang, “Vibration insensitive optical fiber current sensor with a modified reciprocal reflection interferometer,” Opt. Eng. (Bellingham) 38, 1722-1729 (1999).
[CrossRef]

Huang, Z. J.

Z. P. Wang, Q. B. Li, Y. Qi, Z. J. Huang, and J. H. Shi, “Effect of dispersion of linear birefringence upon the sensitivity of an optical current sensor,” Opt. Laser Technol. 36, 587-590 (2004).
[CrossRef]

Ida, Y.

K. Kyuma, S. Tai, M. Nunoshita, N. Mikami, and Y. Ida, “Fiber-optic current and voltage sensors using a Bi12GeO20 single crystal,” J. Lightwave Technol. LT-1, 93-97 (1983).
[CrossRef]

Jackson, D. A.

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

Jones, R. C.

Kyuma, K.

K. Kyuma, S. Tai, M. Nunoshita, N. Mikami, and Y. Ida, “Fiber-optic current and voltage sensors using a Bi12GeO20 single crystal,” J. Lightwave Technol. LT-1, 93-97 (1983).
[CrossRef]

Li, C.

Li, Q. B.

Z. P. Wang, Q. B. Li, Y. Qi, Z. J. Huang, and J. H. Shi, “Effect of dispersion of linear birefringence upon the sensitivity of an optical current sensor,” Opt. Laser Technol. 36, 587-590 (2004).
[CrossRef]

Lin, H.

H. Lin, W.-W. Lin, M.-H. Chen, and S.-C. Huang, “Vibration insensitive optical fiber current sensor with a modified reciprocal reflection interferometer,” Opt. Eng. (Bellingham) 38, 1722-1729 (1999).
[CrossRef]

Lin, W.-W.

H. Lin, W.-W. Lin, M.-H. Chen, and S.-C. Huang, “Vibration insensitive optical fiber current sensor with a modified reciprocal reflection interferometer,” Opt. Eng. (Bellingham) 38, 1722-1729 (1999).
[CrossRef]

Luo, C.

X. Ma and C. Luo, “A method to eliminate birefringence of a magneto-optic AC current transducer with glass ring sensor head,” IEEE Trans. Power Deliv. 13, 1015-1019 (1998).
[CrossRef]

Ma, X.

X. Ma and C. Luo, “A method to eliminate birefringence of a magneto-optic AC current transducer with glass ring sensor head,” IEEE Trans. Power Deliv. 13, 1015-1019 (1998).
[CrossRef]

May, R. G.

X. Fang, A. Wang, R. G. May, and R. O. Claus, “A reciprocal-compensated fiber-optic electric current sensor,” J. Lightwave Technol. 12, 1882-1890 (1994).
[CrossRef]

Maystre, F.

Menke, P.

P. Menke and T. Bosselmann, “Temperature compensation in magnetooptic AC current sensors using an intelligent AC-DC signal evaluation,” J. Lightwave Technol. 13, 1362-1370 (1995).
[CrossRef]

Mikami, N.

K. Kyuma, S. Tai, M. Nunoshita, N. Mikami, and Y. Ida, “Fiber-optic current and voltage sensors using a Bi12GeO20 single crystal,” J. Lightwave Technol. LT-1, 93-97 (1983).
[CrossRef]

Ning, Y. N.

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

Nunoshita, M.

K. Kyuma, S. Tai, M. Nunoshita, N. Mikami, and Y. Ida, “Fiber-optic current and voltage sensors using a Bi12GeO20 single crystal,” J. Lightwave Technol. LT-1, 93-97 (1983).
[CrossRef]

Palmer, A. W.

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

Qi, Y.

Z. P. Wang, Q. B. Li, Y. Qi, Z. J. Huang, and J. H. Shi, “Effect of dispersion of linear birefringence upon the sensitivity of an optical current sensor,” Opt. Laser Technol. 36, 587-590 (2004).
[CrossRef]

Rochford, K. B.

Rogers, J.

J. Rogers, J. Xu, and J. Yao, “Vibration immunity for optical-fiber current measurement,” J. Lightwave Technol. 13, 1371-1377 (1995).
[CrossRef]

Rose, A. H.

Shi, J. H.

Z. P. Wang, Q. B. Li, Y. Qi, Z. J. Huang, and J. H. Shi, “Effect of dispersion of linear birefringence upon the sensitivity of an optical current sensor,” Opt. Laser Technol. 36, 587-590 (2004).
[CrossRef]

Tai, S.

K. Kyuma, S. Tai, M. Nunoshita, N. Mikami, and Y. Ida, “Fiber-optic current and voltage sensors using a Bi12GeO20 single crystal,” J. Lightwave Technol. LT-1, 93-97 (1983).
[CrossRef]

Ulmer, E. A.

E. A. Ulmer, Jr., “A high-accuracy optical current transducer for electric power systems,” IEEE Trans. Power Deliv. 5, 892-898 (1990).
[CrossRef]

Wang, A.

X. Fang, A. Wang, R. G. May, and R. O. Claus, “A reciprocal-compensated fiber-optic electric current sensor,” J. Lightwave Technol. 12, 1882-1890 (1994).
[CrossRef]

Wang, Z. P.

Z. P. Wang, Q. B. Li, Y. Qi, Z. J. Huang, and J. H. Shi, “Effect of dispersion of linear birefringence upon the sensitivity of an optical current sensor,” Opt. Laser Technol. 36, 587-590 (2004).
[CrossRef]

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

Xu, J.

J. Rogers, J. Xu, and J. Yao, “Vibration immunity for optical-fiber current measurement,” J. Lightwave Technol. 13, 1371-1377 (1995).
[CrossRef]

Yao, J.

J. Rogers, J. Xu, and J. Yao, “Vibration immunity for optical-fiber current measurement,” J. Lightwave Technol. 13, 1371-1377 (1995).
[CrossRef]

Yoshino, T.

IEEE Trans. Power Deliv. (2)

X. Ma and C. Luo, “A method to eliminate birefringence of a magneto-optic AC current transducer with glass ring sensor head,” IEEE Trans. Power Deliv. 13, 1015-1019 (1998).
[CrossRef]

E. A. Ulmer, Jr., “A high-accuracy optical current transducer for electric power systems,” IEEE Trans. Power Deliv. 5, 892-898 (1990).
[CrossRef]

J. Lightwave Technol. (6)

C. Li, X. Cui, and T. Yoshino, “Optical electric-power sensor by use of one bismuth germanate crystal,” J. Lightwave Technol. 21, 1328-1333 (2003).
[CrossRef]

K. Kyuma, S. Tai, M. Nunoshita, N. Mikami, and Y. Ida, “Fiber-optic current and voltage sensors using a Bi12GeO20 single crystal,” J. Lightwave Technol. LT-1, 93-97 (1983).
[CrossRef]

J. Rogers, J. Xu, and J. Yao, “Vibration immunity for optical-fiber current measurement,” J. Lightwave Technol. 13, 1371-1377 (1995).
[CrossRef]

P. Menke and T. Bosselmann, “Temperature compensation in magnetooptic AC current sensors using an intelligent AC-DC signal evaluation,” J. Lightwave Technol. 13, 1362-1370 (1995).
[CrossRef]

A. H. Rose, S. M. Etzel, and K. B. Rochford, “Optical fiber current sensors in high electric field environments,” J. Lightwave Technol. 17, 1042-1048 (1999).
[CrossRef]

X. Fang, A. Wang, R. G. May, and R. O. Claus, “A reciprocal-compensated fiber-optic electric current sensor,” J. Lightwave Technol. 12, 1882-1890 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (Bellingham) (1)

H. Lin, W.-W. Lin, M.-H. Chen, and S.-C. Huang, “Vibration insensitive optical fiber current sensor with a modified reciprocal reflection interferometer,” Opt. Eng. (Bellingham) 38, 1722-1729 (1999).
[CrossRef]

Opt. Laser Technol. (1)

Z. P. Wang, Q. B. Li, Y. Qi, Z. J. Huang, and J. H. Shi, “Effect of dispersion of linear birefringence upon the sensitivity of an optical current sensor,” Opt. Laser Technol. 36, 587-590 (2004).
[CrossRef]

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

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

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Figures (3)

Fig. 1
Fig. 1

Simple current sensor architecture composed of an input polarizer, a bulk Faraday material as the sensing element, and an output analyzer.

Fig. 2
Fig. 2

Relative errors of A C (a) and B C (b) as a function of the applied electric current and the linear birefringence.

Fig. 3
Fig. 3

Relative errors of A T (a) and B T (b) as a function of the applied electric current and the linear birefringence.

Equations (35)

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d E d s = N ( s ) E ,
N ( s ) = [ j β ( s ) 2 τ ( s ) τ ( s ) j β ( s ) 2 ] ,
d E x d s = j β 2 E x + ε f ( s ) E y ,
d E y d s = ε f ( s ) E x j β 2 E y ,
E x ( s ) = n 0 E x , n ( s ) ε n ,
E y ( s ) = n 0 E y , n ( s ) ε n .
d E x , 0 d s = j β 2 E x , 0 ,
d E y , 0 d s = j β 2 E y , 0 .
d E x , n d s = j β 2 E x , n + f ( s ) E y , n 1 ,
d E y , n d s = j β 2 E y , n f ( s ) E x , n 1 .
E x , n ( s ) = e j ( β 2 ) s s 0 s E y , n 1 ( u ) f ( u ) e j ( β 2 ) u d u ,
E y , n ( s ) = e j ( β 2 ) s s 0 s E x , n 1 ( u ) f ( u ) e j ( β 2 ) u d u .
E x , n ( s ) = [ cos ( n π 2 ) E x , 0 ( s 0 ) + sin ( n π 2 ) E y , 0 ( s 0 ) ] e j ( β 2 ) ( s ( 1 ) n s 0 ) F n ( s , s 0 ) ,
E y , n ( s ) = [ sin ( n π 2 ) E x , 0 ( s 0 ) + cos ( n π 2 ) E y , 0 ( s 0 ) ] e j ( β 2 ) ( s ( 1 ) n s 0 ) F n ( s , s 0 ) * ,
F n ( s , s 0 ) { 1 if n = 0 s 0 s d u 1 f ( u 1 ) e j β u 1 s 0 u 1 d u 2 f ( u 2 ) e j β u 2 s 0 u 2 s 0 u n 1 d u n f ( u n ) e ( 1 ) n j β u n if n > 0 .
d F n ( s , s 0 ) d s = f ( s ) e j β s F n 1 ( s , s 0 ) * .
E x ( s ) = n 0 { [ cos ( n π 2 ) E x , 0 ( s 0 ) + sin ( n π 2 ) E y , 0 ( s 0 ) ] e j ( β 2 ) ( s ( 1 ) n s 0 ) F n ( s , s 0 ) } ε n ,
E y ( s ) = n 0 { [ sin ( n π 2 ) E x , 0 ( s 0 ) + cos ( n π 2 ) E y , 0 ( s 0 ) ] e j ( β 2 ) ( s ( 1 ) n s 0 ) F n ( s , s 0 ) * } ε n ,
M ( s 1 , s 0 ) = [ A ( s 1 , s 0 ) B ( s 1 , s 0 ) B ( s 1 , s 0 ) * A ( s 1 , s 0 ) * ] ,
A ( s 1 , s 0 ) = e j ( β 2 ) ( s 1 s 0 ) [ m 0 ( 1 ) m F 2 m ( s 1 , s 0 ) ε 2 m ] ,
B ( s 1 , s 0 ) = e j ( β 2 ) ( s + s 0 ) [ m 0 ( 1 ) m F 2 m + 1 ( s 1 , s 0 ) ε 2 m + 1 ] .
M C = [ A C B C B C A C * ] ,
A C = cos ( ψ 2 ) + j sin ( ψ 2 ) cos ( χ ) ,
B C = sin ( ψ 2 ) sin ( χ ) ,
M = P o u t F P i n ,
τ ( s ) = ( I μ 0 V d 4 π ) 1 d 2 + s 2 ,
A = e j β d [ n 0 ( 1 ) n F 2 n ( d ) ε 2 n ] ,
B = n 0 ( 1 ) n F 2 n + 1 ( d ) ε 2 n + 1 ,
F n ( d ) { 1 if n = 0 d d d u 1 e j β u 1 d 2 + u 1 2 d u 1 d u 2 e j β u 2 d 2 + u 2 2 d u 2 d u n 1 d u n e ( 1 ) n j β u n d 2 + u n 2 if n > 0 .
M = [ A B B A * ] .
M T [ A T B T B T A T * ] ,
A T = e j β d [ n = 0 1 ( 1 ) n F 2 n ( d ) ε 2 n ] = e j β d ( 1 ε 2 F 2 ( d ) ) ,
B T = n = 0 1 ( 1 ) n F 2 n + 1 ( d ) ε 2 n + 1 = ε F 1 ( d ) ε 3 F 3 ( d ) .
δ A C = A C A A × 100 , δ B C = B C B B × 100
δ A T = A T A A × 100 , δ B T = B T B B × 100

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