Abstract

A three-section fiber model has been used to derive the formula for measuring the birefringence of single-mode optical fibers. This analysis relieves the problems associated with measurements of the birefringence of optical fibers with very short beat length. The distortion of the measured curves for fibers with nonuniform birefringence is discussed. A newly developed nulling scheme makes the measurement accurate and stable.

© 1985 Optical Society of America

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References

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  1. S. R. Norman, D. N. Payne, M. J. Adams, “Fabrication of Single-Mode Fibers Exhibiting Extremely Low Polarisation Birefringence,” Electron. Lett. 15, 309 (1979).
    [CrossRef]
  2. K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation Characteristics in Long Length V.A.D. Single-Mode Fibers,” Electron. Lett. 16, 768 (1980).
    [CrossRef]
  3. A. M. Smith, “Automated Birefringence Measurement System,” J. Phys. E 12, 927 (1979).
    [CrossRef]
  4. A. M. Smith, “Polarization and Magnetooptic Properties of Single-Mode Optical Fiber,” Appl. Opt. 17, 52 (1978).
    [CrossRef] [PubMed]
  5. A. Papp, H. Harms, “Polarization Optics of Index-Gradient Optical Waveguide Fibers,” Appl. Opt. 14, 2406 (1975).
    [CrossRef] [PubMed]
  6. A. Simon, R. Ulrich, “Evolution of Polarization along a Single-Mode Fiber,” Appl. Phys. Lett. 31, 517 (1977).
    [CrossRef]
  7. A. H. Hartog, D. N. Payne, A. J. Conduit, “Polarisation Optical Time-Domain Reflectometry: Experimental Results and Application to Loss and Birefringence Measurements in Single-Mode Optical Fibers,” in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980).
  8. K. Kikuchi, T. Okoshi, “Wavelength-Sweeping Technique for Measuring the Beat Length of Linearly Birefringent Optical Fibers,” Opt. Lett. 8, 122 (1983).
    [CrossRef] [PubMed]
  9. S. C. Rashleigh, “Measurement of Fiber Birefringence by Wavelength Scanning: Effect of Dispersion,” Opt. Lett. 8, 336 (1983).
    [CrossRef] [PubMed]
  10. M. Monerie, P. Lamouler, “Birefringence Measurement in Twisted Single-Mode Fibers,” Electron. Lett. 17, 252 (1981).
    [CrossRef]
  11. T. Okoshi, S. Ryu, K. Emura, “Measurement of Polarization Parameters of a Single-Mode Optical Fiber,” J. Opt. Commun. 2, 134 (1981).
  12. M. Monerie, L. Jeunhomme, “Polarization Mode Coupling in Long Single-Mode Fibers,” Opt. Quantum Electron. 12, 449 (1980).
    [CrossRef]
  13. R. C. Jones, “A New Calculus for the Treatment of Optical Systems,” J. Opt. Soc. Am. 31, 488 (1941).
    [CrossRef]
  14. R. Ulrich, A. Simon, “Polarization Optics of Twisted Single-Moded Fibers,” Appl. Opt. 18, 2241 (1979).
    [CrossRef] [PubMed]

1983 (2)

1981 (2)

M. Monerie, P. Lamouler, “Birefringence Measurement in Twisted Single-Mode Fibers,” Electron. Lett. 17, 252 (1981).
[CrossRef]

T. Okoshi, S. Ryu, K. Emura, “Measurement of Polarization Parameters of a Single-Mode Optical Fiber,” J. Opt. Commun. 2, 134 (1981).

1980 (2)

M. Monerie, L. Jeunhomme, “Polarization Mode Coupling in Long Single-Mode Fibers,” Opt. Quantum Electron. 12, 449 (1980).
[CrossRef]

K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation Characteristics in Long Length V.A.D. Single-Mode Fibers,” Electron. Lett. 16, 768 (1980).
[CrossRef]

1979 (3)

A. M. Smith, “Automated Birefringence Measurement System,” J. Phys. E 12, 927 (1979).
[CrossRef]

S. R. Norman, D. N. Payne, M. J. Adams, “Fabrication of Single-Mode Fibers Exhibiting Extremely Low Polarisation Birefringence,” Electron. Lett. 15, 309 (1979).
[CrossRef]

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

1978 (1)

1977 (1)

A. Simon, R. Ulrich, “Evolution of Polarization along a Single-Mode Fiber,” Appl. Phys. Lett. 31, 517 (1977).
[CrossRef]

1975 (1)

1941 (1)

Adams, M. J.

S. R. Norman, D. N. Payne, M. J. Adams, “Fabrication of Single-Mode Fibers Exhibiting Extremely Low Polarisation Birefringence,” Electron. Lett. 15, 309 (1979).
[CrossRef]

Conduit, A. J.

A. H. Hartog, D. N. Payne, A. J. Conduit, “Polarisation Optical Time-Domain Reflectometry: Experimental Results and Application to Loss and Birefringence Measurements in Single-Mode Optical Fibers,” in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980).

Edahiro, T.

K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation Characteristics in Long Length V.A.D. Single-Mode Fibers,” Electron. Lett. 16, 768 (1980).
[CrossRef]

Emura, K.

T. Okoshi, S. Ryu, K. Emura, “Measurement of Polarization Parameters of a Single-Mode Optical Fiber,” J. Opt. Commun. 2, 134 (1981).

Harms, H.

Hartog, A. H.

A. H. Hartog, D. N. Payne, A. J. Conduit, “Polarisation Optical Time-Domain Reflectometry: Experimental Results and Application to Loss and Birefringence Measurements in Single-Mode Optical Fibers,” in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980).

Jeunhomme, L.

M. Monerie, L. Jeunhomme, “Polarization Mode Coupling in Long Single-Mode Fibers,” Opt. Quantum Electron. 12, 449 (1980).
[CrossRef]

Jones, R. C.

Kawachi, M.

K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation Characteristics in Long Length V.A.D. Single-Mode Fibers,” Electron. Lett. 16, 768 (1980).
[CrossRef]

Kikuchi, K.

Lamouler, P.

M. Monerie, P. Lamouler, “Birefringence Measurement in Twisted Single-Mode Fibers,” Electron. Lett. 17, 252 (1981).
[CrossRef]

Miya, T.

K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation Characteristics in Long Length V.A.D. Single-Mode Fibers,” Electron. Lett. 16, 768 (1980).
[CrossRef]

Monerie, M.

M. Monerie, P. Lamouler, “Birefringence Measurement in Twisted Single-Mode Fibers,” Electron. Lett. 17, 252 (1981).
[CrossRef]

M. Monerie, L. Jeunhomme, “Polarization Mode Coupling in Long Single-Mode Fibers,” Opt. Quantum Electron. 12, 449 (1980).
[CrossRef]

Norman, S. R.

S. R. Norman, D. N. Payne, M. J. Adams, “Fabrication of Single-Mode Fibers Exhibiting Extremely Low Polarisation Birefringence,” Electron. Lett. 15, 309 (1979).
[CrossRef]

Okamoto, K.

K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation Characteristics in Long Length V.A.D. Single-Mode Fibers,” Electron. Lett. 16, 768 (1980).
[CrossRef]

Okoshi, T.

K. Kikuchi, T. Okoshi, “Wavelength-Sweeping Technique for Measuring the Beat Length of Linearly Birefringent Optical Fibers,” Opt. Lett. 8, 122 (1983).
[CrossRef] [PubMed]

T. Okoshi, S. Ryu, K. Emura, “Measurement of Polarization Parameters of a Single-Mode Optical Fiber,” J. Opt. Commun. 2, 134 (1981).

Papp, A.

Payne, D. N.

S. R. Norman, D. N. Payne, M. J. Adams, “Fabrication of Single-Mode Fibers Exhibiting Extremely Low Polarisation Birefringence,” Electron. Lett. 15, 309 (1979).
[CrossRef]

A. H. Hartog, D. N. Payne, A. J. Conduit, “Polarisation Optical Time-Domain Reflectometry: Experimental Results and Application to Loss and Birefringence Measurements in Single-Mode Optical Fibers,” in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980).

Rashleigh, S. C.

Ryu, S.

T. Okoshi, S. Ryu, K. Emura, “Measurement of Polarization Parameters of a Single-Mode Optical Fiber,” J. Opt. Commun. 2, 134 (1981).

Sasaki, Y.

K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation Characteristics in Long Length V.A.D. Single-Mode Fibers,” Electron. Lett. 16, 768 (1980).
[CrossRef]

Simon, A.

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

A. Simon, R. Ulrich, “Evolution of Polarization along a Single-Mode Fiber,” Appl. Phys. Lett. 31, 517 (1977).
[CrossRef]

Smith, A. M.

Ulrich, R.

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

A. Simon, R. Ulrich, “Evolution of Polarization along a Single-Mode Fiber,” Appl. Phys. Lett. 31, 517 (1977).
[CrossRef]

Appl. Opt. (3)

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. (3)

S. R. Norman, D. N. Payne, M. J. Adams, “Fabrication of Single-Mode Fibers Exhibiting Extremely Low Polarisation Birefringence,” Electron. Lett. 15, 309 (1979).
[CrossRef]

K. Okamoto, Y. Sasaki, T. Miya, M. Kawachi, T. Edahiro, “Polarisation Characteristics in Long Length V.A.D. Single-Mode Fibers,” Electron. Lett. 16, 768 (1980).
[CrossRef]

M. Monerie, P. Lamouler, “Birefringence Measurement in Twisted Single-Mode Fibers,” Electron. Lett. 17, 252 (1981).
[CrossRef]

J. Opt. Commun. (1)

T. Okoshi, S. Ryu, K. Emura, “Measurement of Polarization Parameters of a Single-Mode Optical Fiber,” J. Opt. Commun. 2, 134 (1981).

J. Opt. Soc. Am. (1)

J. Phys. E (1)

A. M. Smith, “Automated Birefringence Measurement System,” J. Phys. E 12, 927 (1979).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

M. Monerie, L. Jeunhomme, “Polarization Mode Coupling in Long Single-Mode Fibers,” Opt. Quantum Electron. 12, 449 (1980).
[CrossRef]

Other (1)

A. H. Hartog, D. N. Payne, A. J. Conduit, “Polarisation Optical Time-Domain Reflectometry: Experimental Results and Application to Loss and Birefringence Measurements in Single-Mode Optical Fibers,” in Technical Digest, Sixth European Conference on Optical Communication, U. York (1980).

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Figures (6)

Fig. 1
Fig. 1

Experimental arrangement for measuring birefringence.

Fig. 2
Fig. 2

Two linear polarization azimuths obtained behind C2.

Fig. 3
Fig. 3

Test curves of two fiber samples: (a) with medium beat length, (b) with very short beat length.

Fig. 4
Fig. 4

Two-section model of the nonuniform fiber.

Fig. 5
Fig. 5

Calculated curves for two-section models (dotted line) and for corresponding uniform models (solid line). The calculated parameters for different cases are (a) 100, 100, 0, 1, 0.5, 20; (b) 200, 200, 0, 0.5, 0.5, 25; (c) 200, 200, 0, 0.5, 1, 20; (d) 300, 300, 0, 0.5, 0.5, 20; (e) 100, 100, 45, 0.5, 1, 0; (f) 100, 100, 90, 0.5, 0.5, 0; (g) 200, 200, 45, 0.5, 1, 0; (h) 300, 300, 45, 0.5, 1, 0; (i) 100, 150, 0, 0.5, 1, 0; and (j) 100, 250, 0, 0.7, 0.7, 0.

Fig. 6
Fig. 6

Experimental points and theoretical curve for a sample of fiber B84-17.

Equations (33)

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[ U ] = [ exp ( i ϕ ) cos ϑ exp ( i ψ ) sin ϑ exp ( i ψ ) sin ϑ exp ( i ϕ ) cos ϑ ] ,
[ U T U ] = [ exp ( i 2 ϕ ) cos 2 ϑ + exp ( i 2 ψ ) sin 2 ϑ 2 sin ϑ cos ϑ · i sin ( ψ ϕ ) 2 sin ϑ cos ϑ · i sin ( ψ ϕ ) exp ( i 2 ϕ ) cos 2 ϑ + exp ( i 2 ψ ) sin ϑ ] .
[ U T U ] [ 1 0 ] = A [ 1 0 ] , [ U T U ] [ 0 1 ] = B [ 0 1 ] ,
ψ = ϕ .
[ U ] = [ exp ( i ϕ ) cos ϑ exp ( i ϕ ) sin ϑ exp ( i ϕ ) sin ϑ exp ( i ϕ ) cos ϑ ] .
[ U ] [ 1 0 ] = exp ( i ϕ ) [ cos ϑ sin ϑ ] , [ U ] [ 0 1 ] = exp ( i ϕ ) [ sin ϑ cos ϑ ] = exp ( i ϕ ) [ cos ( ϑ + 90 ° ) sin ( ϑ + 90 ° ) ] .
[ U ] 1 2 [ 1 1 ] = 1 2 [ exp ( i ϕ ) cos ϑ exp ( i ϕ ) sin ϑ exp ( i ϕ ) sin ϑ + exp ( i ϕ ) cos ϑ ] .
[ cos ( ϑ + 45 ° ) sin ( ϑ + 45 ° ) ] 1 2 × [ exp ( i ϕ ) cos ϑ exp ( i ϕ ) cos ϑ exp ( i ϕ ) sin ϑ + exp ( i ϕ ) sin ϑ ] = cos ϕ ,
[ cos ( ϑ 45 ° ) sin ( ϑ 45 ° ) ] 1 2 × [ exp ( i ϕ ) cos ϑ exp ( i ϕ ) sin ϑ exp ( i ϕ ) sin ϑ + exp ( i ϕ ) cos ϑ ] = i sin ϕ .
ϑ = γ A γ p ,
| ϕ | = | γ A + 45 ° γ A | .
[ J l ] = [ J l 1 ] [ J l 2 ] [ J l 3 ] ,
[ J l 1 ] = [ cos Δ β l 1 2 + i sin Δ β l 1 2 0 0 cos Δ β l 1 2 i sin Δ β l 1 2 ] ,
[ J l 2 ] = [ cos Δ β + ( 2 ) l 2 2 + i η 2 c 2 sin Δ β + ( 2 ) l 2 2 ( 1 κ ) α 2 + Ω 0 | ( 1 κ ) α 2 + Ω 0 | · 1 c 2 sin Δ β + ( 2 ) l 2 2 | ( 1 κ ) α 2 + Ω 0 | ( 1 κ ) α 2 + Ω 0 · 1 c 2 sin Δ β + ( 2 ) l 2 2 cos Δ β + ( 2 ) l 2 2 i η 2 c 2 sin Δ β + ( 2 ) l 2 2 ] ,
[ J l 3 ] = [ cos Δ β l 3 2 + i sin Δ β l 3 2 0 0 cos Δ β l 3 2 i sin Δ β l 3 2 ] ,
η 2 = Δ β 2 | ( 1 κ ) α 2 + Ω 0 | , c 2 = 1 + η 2 2 , Δ β + ( 2 ) l = Δ β 2 + 4 [ ( 1 κ ) α 2 + Ω 0 ] 2 .
[ J f ] = [ cos α 2 l 2 sin α 2 l 2 sin α 2 l 2 cos α 2 l 2 ] · [ J l ] .
[ J f ] = [ cos χ sin χ sin χ cos χ ] · [ U ] [ cos χ sin χ sin χ cos χ ] = [ cos ϕ cos ϑ + i sin ϕ cos ( 2 χ + ϑ ) , cos ϕ sin ϑ + i sin ϕ sin ( 2 χ + ϑ ) , cos ϕ sin ϑ + i sin ϕ sin ( 2 χ + ϑ ) cos ϕ cos ϑ i sin ϕ cos ( 2 χ + ϑ ) ] ,
sin 2 ϕ = [ P cos Δ β + ( 2 ) l 2 2 + Q η 2 c 2 sin Δ β + ( 2 ) l 2 2 ] 2 + [ R 1 c 2 sin Δ β + ( 2 ) l 2 2 ] 2 ,
P = sin Δ β ( l 1 + l 3 ) 2 , Q = cos Δ β ( l 1 + l 3 ) 2 , R = sin Δ β ( l 1 l 3 ) 2 .
α 2 l 2 = Ω 0 1 κ l 2 .
α 2 l 2 ¯ = α 2 l 2 + Ω 0 1 κ l 2 ,
η 2 c 2 1 , 1 c 2 0 ,
sin 2 ϕ = 1 2 { 1 cos [ Δ β ( l 1 + l 3 ) + Δ β + ( 2 ) l 2 ] } .
Δ β ( l 1 + l 3 ) + ( Δ β l 2 ) 2 + 4 ( 1 κ ) 2 ( α 2 l 2 ¯ ) 2 = ( 2 m 1 ) · 180 ° ( or = 2 m · 180 ° ) , Δ β ( l 1 + l 3 ) + ( Δ β l 2 ) 2 + 4 ( 1 κ ) 2 ( α 2 l 2 ¯ ) 2 = 2 m · 180 ° ( or = ( 2 m + 1 ) · 180 ° ) .
Δ β l 2 = { ( 1 κ ) 2 [ ( α 2 l 2 ¯ ) 2 ( α 2 l 2 ¯ ) 2 ] 90 2 90 } 2 4 ( 1 κ ) 2 ( α 2 l 2 ¯ ) 2 ,
sin 2 ϕ = ( η 2 c 2 ) 2 · 1 2 ( 1 cos Δ β + ( 2 ) l 2 ) .
[ J l ] = [ J l 1 ] · [ cos δ sin δ sin δ cos δ ] · [ J l 2 ] ,
[ J l 1 ] = [ cos Δ β + ( 1 ) l 1 2 + i η 1 c 1 sin Δ β + ( 1 ) l 1 2 α 1 | α 1 | 1 c 1 sin Δ β + ( 1 ) l 1 2 | α 1 | α 1 1 c 1 sin Δ β + ( 1 ) l 1 2 cos Δ β + ( 1 ) l 1 2 i η 1 c 1 sin Δ β + ( 1 ) l 1 2 ] , [ J l 2 ] = [ cos Δ β + ( 2 ) l 2 2 + i η 2 c 2 sin Δ β + ( 2 ) l 2 2 α 2 | α 2 | 1 c 2 sin Δ β + ( 2 ) l 2 2 | α 2 | α 2 1 c 2 sin Δ β + ( 2 ) l 2 2 cos Δ β + ( 2 ) l 2 2 i η 2 c 2 sin Δ β + ( 2 ) l 2 2 ] .
[ J f ] = [ cos ( α 1 l 1 + α 2 l 2 + δ ) sin ( α 1 l 1 + α 2 l 2 + δ ) sin ( α 1 l 1 + α 2 l 2 + δ ) cos ( α 1 l 1 + α 2 l 2 + δ ) ] · [ J l ] .
sin 2 ϕ = { cos δ [ η 1 c 1 sin Δ β + ( 1 ) l 1 2 cos Δ β + ( 2 ) l 2 2 + η 2 c 2 sin Δ β + ( 2 ) l 2 2 cos Δ β + ( 1 ) l 1 2 ] sin δ [ ( α 1 | α 1 | 1 c 1 η 2 c 2 + | α 2 | α 2 1 c 2 η 1 c 1 ) sin Δ β + ( 1 ) l 1 2 sin Δ β + ( 2 ) l 2 2 ] } 2 + { cos δ [ ( | α 2 | α 2 1 c 2 η 1 c 1 | α 1 | α 1 1 c 1 η 2 c 2 ) sin Δ β + ( 1 ) l 1 2 sin Δ β + ( 2 ) l 2 2 ] + sin δ [ η 1 c 1 sin Δ β + ( 1 ) l 1 2 cos Δ β + ( 2 ) l 2 2 η 2 c 2 cos Δ β + ( 1 ) l 1 2 sin Δ β + ( 2 ) l 2 2 ] } 2 .
sin 2 ϕ = 1 2 { 1 [ Δ β ¯ ( l 1 + l 2 ) ] } ,
Δ β ¯ = Δ β 1 l 1 + Δ β 2 l 2 l 1 + l 2 .

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