Abstract

Polarization transmission in single-mode fibers for forward and backward directions is studied on the basis of reciprocity and polarization-independent attenuation. The analysis yields a simple formula to calculate the ellipticity of the light along the fiber from time-resolved and polarization-sensitive measurements of the backscattered power.

© 1981 Optical Society of America

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References

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  1. I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15 (1981).
    [CrossRef]
  2. E. Brinkmeyer, “Magneto-optic current measurement using single-mode fibers,” (1981, unpublished, patent pending).
  3. A. H. Hartog, D. N. Payne, A. J. Conduit, “Polarization optical time-domain reflectometry: experimental results and application to loss and birefringence measurements in single-mode fibers,” presented at Sixth European Conference on Optical Communication, York, England, 1980.
  4. B. Y. Kimm, S. S. Choi, “Backscattering measurements of bending-induced birefringence in single-mode fibres,” Electron. Lett. 17, 193 (1981).
    [CrossRef]
  5. A. J. Rogers, “Polarization-optical time domain reflectometry: a technique for measurement of field distribution,” Appl. Opt. 20, 1060 (1981).
    [CrossRef] [PubMed]
  6. R. F. Collin, Foundations for Microwave Engineering (McGraw-Hill, New York, 1966).
  7. A. Simon, R. Ulrich, “Evolution of polarization along a single-mode fiber,” Appl. Phys. Lett. 31, 517 (1977).
    [CrossRef]
  8. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979).
  9. E. Brinkmeyer, “Analysis of the backscattering method for single-mode optical fibers,” J. Opt. Soc. Am. 70, 1010 (1980).
    [CrossRef]

1981 (3)

I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

B. Y. Kimm, S. S. Choi, “Backscattering measurements of bending-induced birefringence in single-mode fibres,” Electron. Lett. 17, 193 (1981).
[CrossRef]

A. J. Rogers, “Polarization-optical time domain reflectometry: a technique for measurement of field distribution,” Appl. Opt. 20, 1060 (1981).
[CrossRef] [PubMed]

1980 (1)

1977 (1)

A. Simon, R. Ulrich, “Evolution of polarization along a single-mode fiber,” Appl. Phys. Lett. 31, 517 (1977).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979).

Brinkmeyer, E.

E. Brinkmeyer, “Analysis of the backscattering method for single-mode optical fibers,” J. Opt. Soc. Am. 70, 1010 (1980).
[CrossRef]

E. Brinkmeyer, “Magneto-optic current measurement using single-mode fibers,” (1981, unpublished, patent pending).

Choi, S. S.

B. Y. Kimm, S. S. Choi, “Backscattering measurements of bending-induced birefringence in single-mode fibres,” Electron. Lett. 17, 193 (1981).
[CrossRef]

Collin, R. F.

R. F. Collin, Foundations for Microwave Engineering (McGraw-Hill, New York, 1966).

Conduit, A. J.

A. H. Hartog, D. N. Payne, A. J. Conduit, “Polarization optical time-domain reflectometry: experimental results and application to loss and birefringence measurements in single-mode fibers,” presented at Sixth European Conference on Optical Communication, York, England, 1980.

Hartog, A. H.

A. H. Hartog, D. N. Payne, A. J. Conduit, “Polarization optical time-domain reflectometry: experimental results and application to loss and birefringence measurements in single-mode fibers,” presented at Sixth European Conference on Optical Communication, York, England, 1980.

Kaminow, I. P.

I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

Kimm, B. Y.

B. Y. Kimm, S. S. Choi, “Backscattering measurements of bending-induced birefringence in single-mode fibres,” Electron. Lett. 17, 193 (1981).
[CrossRef]

Payne, D. N.

A. H. Hartog, D. N. Payne, A. J. Conduit, “Polarization optical time-domain reflectometry: experimental results and application to loss and birefringence measurements in single-mode fibers,” presented at Sixth European Conference on Optical Communication, York, England, 1980.

Rogers, A. J.

Simon, A.

A. Simon, R. Ulrich, “Evolution of polarization along a single-mode fiber,” Appl. Phys. Lett. 31, 517 (1977).
[CrossRef]

Ulrich, R.

A. Simon, R. Ulrich, “Evolution of polarization along a single-mode fiber,” Appl. Phys. Lett. 31, 517 (1977).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Simon, R. Ulrich, “Evolution of polarization along a single-mode fiber,” Appl. Phys. Lett. 31, 517 (1977).
[CrossRef]

Electron. Lett. (1)

B. Y. Kimm, S. S. Choi, “Backscattering measurements of bending-induced birefringence in single-mode fibres,” Electron. Lett. 17, 193 (1981).
[CrossRef]

IEEE J. Quantum Electron. (1)

I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (4)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1979).

E. Brinkmeyer, “Magneto-optic current measurement using single-mode fibers,” (1981, unpublished, patent pending).

A. H. Hartog, D. N. Payne, A. J. Conduit, “Polarization optical time-domain reflectometry: experimental results and application to loss and birefringence measurements in single-mode fibers,” presented at Sixth European Conference on Optical Communication, York, England, 1980.

R. F. Collin, Foundations for Microwave Engineering (McGraw-Hill, New York, 1966).

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Figures (2)

Fig. 1
Fig. 1

Definition of input and output states of a section of a single-mode fiber when using (a) the scattering matrix S and (b) the Jones matrices T and T b w.

Fig. 2
Fig. 2

Quantity K as determinable from backscattering measurements versus fiber length for a model fiber with three sections.

Equations (8)

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( b 1 b 2 b 3 b 4 ) = ( 0 0 S 13 S 14 0 0 S 23 S 24 S 31 S 32 0 0 S 41 S 42 0 0 ) ( a 1 a 2 a 3 a 4 ) .
S i k = S k i .
i = 1 4 | b i | 2 = η i = 1 4 | a i | 2 for all a 1 ' s .
S = η 1 / 2 exp ( j ψ 13 ) ( 1 + | χ e 0 | 2 ) 1 / 2 ( 0 0 1 χ e 0 0 0 χ e 0 * exp ( j Δ χ ) exp ( j Δ ψ ) 1 χ e 0 * exp ( j Δ χ ) 0 0 χ e 0 exp ( j Δ ψ ) 0 0 ) .
T = T b w t = η 1 / 2 exp ( j ψ 13 ) ( 1 + | ψ e 0 | 2 ) 1 / 2 ( 1 χ e 0 * exp ( j Δ ψ ) χ e 0 exp ( j Δ ψ ) ) .
| χ 0 | 2 = P 0 / P 0 = tan 2 ( 2 e )
K = ( P 0 P 0 ) / ( P 0 + P 0 ) = cos ( 4 e ) ,
K α = ( P 0 + P up / 2 ) ( P 0 + P up / 2 ) ( P 0 + P up / 2 ) + ( P 0 + P up / 2 ) = α p × K ,

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