Abstract

The technique of polarization-optical time-domain reflectometry is analyzed to see how the polarization properties of an optical fiber may be deduced from the backscattered light. It is shown that, subject to certain assumptions, the polarization is modified as it would be by a linear retarder. The results of measurements on a fiber showing both linear and circular retardation are given and compared with a theoretical model. The experiments show that the accuracy of measurement is limited by changes in the polarization, due to the scattering process, which vary randomly along the fiber.

© 1982 Optical Society of America

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References

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  1. A. J. Rogers, Electron. Lett. 16, 489 (1980).
    [Crossref]
  2. A. J. Rogers, Appl. Opt. 20, 1060 (1981).
    [Crossref] [PubMed]
  3. A. W. Hartog, P. N. Payne, A. J. Conduit, “Polarization Optical Time-Domain Reflectometry: Experimental Results and Applications to Loss and Birefringence Measurements in Single-Mode Optical Fibers,” in Technical Digest, Sixth ECOC, U. York, 1980, p. 472.
  4. B. Y. Kim, S. S. Choi, Electron. Lett. 17, 193 (1981).
    [Crossref]
  5. M. Nakazawa, T. Horiguchi, M. Tokuda, N. Uchida, Electron. Lett. 17, 513 (1981).
    [Crossref]
  6. B. Y. Kim, S. S. Choi, Opt. Lett. 6, 578 (1981).
    [Crossref] [PubMed]
  7. E. Brinkmeyer, Opt. Lett. 6, 575 (1981).
    [Crossref] [PubMed]
  8. J. N. Ross, Electron. Lett. 17, 596 (1981).
    [Crossref]
  9. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).
  10. A. Gerrard, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975).
  11. R. C. Jones, J. Opt. Soc. Am. 31, 488 (1941).
    [Crossref]
  12. M. Hurowitz, R. C. Jones, J. Opt. Soc. Am. 31, 493 (1941).
    [Crossref]
  13. A. J. Barlow, D. N. Payne, “Birefringence Testing in Single-Mode Fibers Manufactured with Controlled Polarization Characteristics,” in IEE Colloquium Digest, (Institution of Electrical Engineers, London, 1981), 1981/51.
  14. R. Ulrich, S. C. Rashleigh, W. Eickhoff, Opt. Lett. 5, 273 (1980).
    [Crossref] [PubMed]
  15. R. C. Jones, J. Opt. Soc. Am. 38, 671 (1948).
    [Crossref]

1981 (6)

B. Y. Kim, S. S. Choi, Electron. Lett. 17, 193 (1981).
[Crossref]

M. Nakazawa, T. Horiguchi, M. Tokuda, N. Uchida, Electron. Lett. 17, 513 (1981).
[Crossref]

J. N. Ross, Electron. Lett. 17, 596 (1981).
[Crossref]

B. Y. Kim, S. S. Choi, Opt. Lett. 6, 578 (1981).
[Crossref] [PubMed]

A. J. Rogers, Appl. Opt. 20, 1060 (1981).
[Crossref] [PubMed]

E. Brinkmeyer, Opt. Lett. 6, 575 (1981).
[Crossref] [PubMed]

1980 (2)

1948 (1)

1941 (2)

Barlow, A. J.

A. J. Barlow, D. N. Payne, “Birefringence Testing in Single-Mode Fibers Manufactured with Controlled Polarization Characteristics,” in IEE Colloquium Digest, (Institution of Electrical Engineers, London, 1981), 1981/51.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

Brinkmeyer, E.

Burch, J. M.

A. Gerrard, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975).

Choi, S. S.

B. Y. Kim, S. S. Choi, Opt. Lett. 6, 578 (1981).
[Crossref] [PubMed]

B. Y. Kim, S. S. Choi, Electron. Lett. 17, 193 (1981).
[Crossref]

Conduit, A. J.

A. W. Hartog, P. N. Payne, A. J. Conduit, “Polarization Optical Time-Domain Reflectometry: Experimental Results and Applications to Loss and Birefringence Measurements in Single-Mode Optical Fibers,” in Technical Digest, Sixth ECOC, U. York, 1980, p. 472.

Eickhoff, W.

Gerrard, A.

A. Gerrard, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975).

Hartog, A. W.

A. W. Hartog, P. N. Payne, A. J. Conduit, “Polarization Optical Time-Domain Reflectometry: Experimental Results and Applications to Loss and Birefringence Measurements in Single-Mode Optical Fibers,” in Technical Digest, Sixth ECOC, U. York, 1980, p. 472.

Horiguchi, T.

M. Nakazawa, T. Horiguchi, M. Tokuda, N. Uchida, Electron. Lett. 17, 513 (1981).
[Crossref]

Hurowitz, M.

Jones, R. C.

Kim, B. Y.

B. Y. Kim, S. S. Choi, Opt. Lett. 6, 578 (1981).
[Crossref] [PubMed]

B. Y. Kim, S. S. Choi, Electron. Lett. 17, 193 (1981).
[Crossref]

Nakazawa, M.

M. Nakazawa, T. Horiguchi, M. Tokuda, N. Uchida, Electron. Lett. 17, 513 (1981).
[Crossref]

Payne, D. N.

A. J. Barlow, D. N. Payne, “Birefringence Testing in Single-Mode Fibers Manufactured with Controlled Polarization Characteristics,” in IEE Colloquium Digest, (Institution of Electrical Engineers, London, 1981), 1981/51.

Payne, P. N.

A. W. Hartog, P. N. Payne, A. J. Conduit, “Polarization Optical Time-Domain Reflectometry: Experimental Results and Applications to Loss and Birefringence Measurements in Single-Mode Optical Fibers,” in Technical Digest, Sixth ECOC, U. York, 1980, p. 472.

Rashleigh, S. C.

Rogers, A. J.

A. J. Rogers, Appl. Opt. 20, 1060 (1981).
[Crossref] [PubMed]

A. J. Rogers, Electron. Lett. 16, 489 (1980).
[Crossref]

Ross, J. N.

J. N. Ross, Electron. Lett. 17, 596 (1981).
[Crossref]

Tokuda, M.

M. Nakazawa, T. Horiguchi, M. Tokuda, N. Uchida, Electron. Lett. 17, 513 (1981).
[Crossref]

Uchida, N.

M. Nakazawa, T. Horiguchi, M. Tokuda, N. Uchida, Electron. Lett. 17, 513 (1981).
[Crossref]

Ulrich, R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

Appl. Opt. (1)

Electron. Lett. (4)

J. N. Ross, Electron. Lett. 17, 596 (1981).
[Crossref]

B. Y. Kim, S. S. Choi, Electron. Lett. 17, 193 (1981).
[Crossref]

M. Nakazawa, T. Horiguchi, M. Tokuda, N. Uchida, Electron. Lett. 17, 513 (1981).
[Crossref]

A. J. Rogers, Electron. Lett. 16, 489 (1980).
[Crossref]

J. Opt. Soc. Am. (3)

Opt. Lett. (3)

Other (4)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959).

A. Gerrard, J. M. Burch, Introduction to Matrix Methods in Optics (Wiley, London, 1975).

A. W. Hartog, P. N. Payne, A. J. Conduit, “Polarization Optical Time-Domain Reflectometry: Experimental Results and Applications to Loss and Birefringence Measurements in Single-Mode Optical Fibers,” in Technical Digest, Sixth ECOC, U. York, 1980, p. 472.

A. J. Barlow, D. N. Payne, “Birefringence Testing in Single-Mode Fibers Manufactured with Controlled Polarization Characteristics,” in IEE Colloquium Digest, (Institution of Electrical Engineers, London, 1981), 1981/51.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of POTDR: (a) complete system, (b) simplified outward path, (c) simplified return path, and (d) path to detector.

Fig. 2
Fig. 2

Arrangement for measuring Stokes parameters of backscattered light.

Fig. 3
Fig. 3

Logarithmic plot of total intensity against time delay.

Fig. 4
Fig. 4

Equivalent retardation of the fiber.

Fig. 5
Fig. 5

Cosine of half the equivalent retardation plotted against time. Circles and triangles are experimental points, the solid curve is a fit of the theoretical expression.

Fig. 6
Fig. 6

Orientation of the retardation axes of the equivalent wave plate. Circles and triangles are experimental points, the solid curve is the theoretical expression.

Fig. 7
Fig. 7

Plot of the matrix element M24 (solid line) and the sum of elements M24 and M42 (circles).

Equations (15)

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

S 0 = I ( 0 , 0 ) + I ( π / 2 , 0 )             S 2 = I ( π / 4 , 0 ) - I ( 3 π / 4 , 0 ) S 1 = I ( 0 , 0 ) - I ( π / 2 , 0 )             S 3 = I ( π / 4 , π / 2 ) - I ( 3 π / 4 , π / 2 ) .
[ S 0 S 1 S 2 S 3 ] = P S 0 [ 1 Q U V ] = ( 1 - P ) S 0 [ 1 0 0 0 ] ,
x = M 0 .
0 = M T x ,
0 = M T M 0 = M x 0 ,
M x = M T M = ( SG ) T SG = G T S T SG = GG ,
M y = ( RFSG ) T RFSG = GS T FFSG ,
S T FFS = G - 1 M y G - 1 .
S = [ 1 Q U V ] = [ 1 0 0 0 0 m 22 m 23 m 24 0 m 23 m 33 m 34 0 - m 24 - m 34 m 44 ] [ 1 Q i U i V i ] ,
m 22 = cos 2 2 θ + sin 2 2 θ cos δ , m 23 = cos 2 θ sin 2 θ ( 1 - cos δ ) , m 24 = - sin 2 θ sin δ , m 33 = sin 2 2 θ + cos 2 2 θ cos δ , m 34 = cos 2 θ sin δ , m 44 = cos δ ,
M ( z ) = exp ( i η z ) [ cos Γ z + i ( g sin Γ z ) / Γ - ω ( sin Γ z ) / Γ ω ( sin Γ z ) / Γ cos Γ z - i g ( sin Γ z ) / Γ ] ,
H = ( m 11 m 12 m 12 m 11 * ) ,
m 11 = cos 2 ( Γ z ) + ( ω 2 - g 2 ) sin 2 ( Γ z ) / Γ 2 + i ( g / Γ ) sin ( 2 Γ z ) , m 12 = - i ( 2 g ω / Γ 2 ) sin 2 Γ z .
cos γ ( z ) = cos 2 ( Γ z ) + [ ( ω 2 - g 2 ) / Γ 2 ] sin 2 ( Γ z ) ,
tan 2 θ ( z ) = - ( ω / Γ ) tan ( Γ z ) .

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