Abstract

Real single-mode fibers generally exhibit elliptical birefringence caused by deviations of the core shape from circularity, by transverse internal stress, and by residual twist. These three contributions can be individually determined by analyzing on a Poincaré sphere the wavelength dependence of the output state of polarization of a short section of fiber with fixed input polarization. Various types of polarization eigenstates of a twisted birefringent fiber are discussed, and the resulting group delay difference is derived.

© 1981 Optical Society of America

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References

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  1. J. D. Love, R. A. Sammut, A. W. Snyder, Electron. Lett 15, 615 (1979); R. A. Sammut, Electron. Lett. 16, 728 (1980).
    [CrossRef]
  2. Y. Namihira, M. Kudo, Y. Mushiako, Trans. Inst. Chem. Eng. 60C, 391 (1977); M. Johnson, Appl. Opt. 18, 1288 (1979). In Fig. 1(b) of the latter reference, the fast axis should be parallel to the direction of the force.
    [CrossRef] [PubMed]
  3. R. Ulrich, A. Simon, Appl. Opt. 18, 2241 (1979).
    [CrossRef] [PubMed]
  4. R. Ulrich, Opt. Lett. 1, 109 (1977).
    [CrossRef] [PubMed]
  5. G. B. Hocker, Appl. Opt. 18, 1445 (1979); S. C. Rashleigh, R. Ulrich, Appl Phys. Lett. 34, 768 (1979); R. Ulrich, M. Johnson, Opt. Lett. 4, 152 (1979).
    [CrossRef] [PubMed]
  6. S. C. Rashleigh, R. Ulrich, Opt. Lett. 3, 60 (1978).
    [CrossRef] [PubMed]
  7. W. Eickhoff, O. Krumpholz, Electron. Lett. 12, 405 (1976); A. Papp, H. Harms. Appl. Opt. 14, 2406 (1975).
    [CrossRef] [PubMed]
  8. V. Ramaswamy, R. H. Stolen, M. D. Divino, W. Pleibel, Appl. Opt. 18, 4080 (1979).
    [CrossRef] [PubMed]
  9. G. N. Ramachandran, S. Ramaseshan, Handbook of Physics, S. Flügge, Ed. (Springer, Berlin, 1961), Vol. 25/1, p.1.
  10. M. Johnson, Appl. Opt. 20, 2075 (1981).
    [CrossRef] [PubMed]
  11. R. Ulrich, S. C. Rashleigh, W. Eickhoff, Opt. Lett. 5, 273 (1980); S. C. Rashleigh, R. Ulrich, Opt. Lett. 5, 354 (1980).
    [CrossRef] [PubMed]
  12. I. P. Kaminov, IEEE J. Quantum Electron. QE-17, 15 (1981).
    [CrossRef]

1981 (2)

M. Johnson, Appl. Opt. 20, 2075 (1981).
[CrossRef] [PubMed]

I. P. Kaminov, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

1980 (1)

1979 (4)

1978 (1)

1977 (2)

R. Ulrich, Opt. Lett. 1, 109 (1977).
[CrossRef] [PubMed]

Y. Namihira, M. Kudo, Y. Mushiako, Trans. Inst. Chem. Eng. 60C, 391 (1977); M. Johnson, Appl. Opt. 18, 1288 (1979). In Fig. 1(b) of the latter reference, the fast axis should be parallel to the direction of the force.
[CrossRef] [PubMed]

1976 (1)

W. Eickhoff, O. Krumpholz, Electron. Lett. 12, 405 (1976); A. Papp, H. Harms. Appl. Opt. 14, 2406 (1975).
[CrossRef] [PubMed]

Divino, M. D.

Eickhoff, W.

R. Ulrich, S. C. Rashleigh, W. Eickhoff, Opt. Lett. 5, 273 (1980); S. C. Rashleigh, R. Ulrich, Opt. Lett. 5, 354 (1980).
[CrossRef] [PubMed]

W. Eickhoff, O. Krumpholz, Electron. Lett. 12, 405 (1976); A. Papp, H. Harms. Appl. Opt. 14, 2406 (1975).
[CrossRef] [PubMed]

Hocker, G. B.

Johnson, M.

Kaminov, I. P.

I. P. Kaminov, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

Krumpholz, O.

W. Eickhoff, O. Krumpholz, Electron. Lett. 12, 405 (1976); A. Papp, H. Harms. Appl. Opt. 14, 2406 (1975).
[CrossRef] [PubMed]

Kudo, M.

Y. Namihira, M. Kudo, Y. Mushiako, Trans. Inst. Chem. Eng. 60C, 391 (1977); M. Johnson, Appl. Opt. 18, 1288 (1979). In Fig. 1(b) of the latter reference, the fast axis should be parallel to the direction of the force.
[CrossRef] [PubMed]

Love, J. D.

J. D. Love, R. A. Sammut, A. W. Snyder, Electron. Lett 15, 615 (1979); R. A. Sammut, Electron. Lett. 16, 728 (1980).
[CrossRef]

Mushiako, Y.

Y. Namihira, M. Kudo, Y. Mushiako, Trans. Inst. Chem. Eng. 60C, 391 (1977); M. Johnson, Appl. Opt. 18, 1288 (1979). In Fig. 1(b) of the latter reference, the fast axis should be parallel to the direction of the force.
[CrossRef] [PubMed]

Namihira, Y.

Y. Namihira, M. Kudo, Y. Mushiako, Trans. Inst. Chem. Eng. 60C, 391 (1977); M. Johnson, Appl. Opt. 18, 1288 (1979). In Fig. 1(b) of the latter reference, the fast axis should be parallel to the direction of the force.
[CrossRef] [PubMed]

Pleibel, W.

Ramachandran, G. N.

G. N. Ramachandran, S. Ramaseshan, Handbook of Physics, S. Flügge, Ed. (Springer, Berlin, 1961), Vol. 25/1, p.1.

Ramaseshan, S.

G. N. Ramachandran, S. Ramaseshan, Handbook of Physics, S. Flügge, Ed. (Springer, Berlin, 1961), Vol. 25/1, p.1.

Ramaswamy, V.

Rashleigh, S. C.

Sammut, R. A.

J. D. Love, R. A. Sammut, A. W. Snyder, Electron. Lett 15, 615 (1979); R. A. Sammut, Electron. Lett. 16, 728 (1980).
[CrossRef]

Simon, A.

Snyder, A. W.

J. D. Love, R. A. Sammut, A. W. Snyder, Electron. Lett 15, 615 (1979); R. A. Sammut, Electron. Lett. 16, 728 (1980).
[CrossRef]

Stolen, R. H.

Ulrich, R.

Appl. Opt. (4)

Electron. Lett (1)

J. D. Love, R. A. Sammut, A. W. Snyder, Electron. Lett 15, 615 (1979); R. A. Sammut, Electron. Lett. 16, 728 (1980).
[CrossRef]

Electron. Lett. (1)

W. Eickhoff, O. Krumpholz, Electron. Lett. 12, 405 (1976); A. Papp, H. Harms. Appl. Opt. 14, 2406 (1975).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

I. P. Kaminov, IEEE J. Quantum Electron. QE-17, 15 (1981).
[CrossRef]

Opt. Lett. (3)

Trans. Inst. Chem. Eng. (1)

Y. Namihira, M. Kudo, Y. Mushiako, Trans. Inst. Chem. Eng. 60C, 391 (1977); M. Johnson, Appl. Opt. 18, 1288 (1979). In Fig. 1(b) of the latter reference, the fast axis should be parallel to the direction of the force.
[CrossRef] [PubMed]

Other (1)

G. N. Ramachandran, S. Ramaseshan, Handbook of Physics, S. Flügge, Ed. (Springer, Berlin, 1961), Vol. 25/1, p.1.

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Figures (6)

Fig. 1
Fig. 1

Poincaré sphere for the representation of birefringence effects. Points H, V, P, Q mark linear polarizations of horizontal, vertical, and ±45° azimuth, respectively, and , mark left and right circular states, respectively.

Fig. 2
Fig. 2

Frequency dependence of the three kinds of birefringence schematically.

Fig. 3
Fig. 3

Vectorial addition of the frequency independent shape birefringence βc and frequency-proportional stress-birefringence (a), (b). Output trajectories with untwisted fiber (c), with twisted fiber (d), (e).

Fig. 4
Fig. 4

Block diagram of the experimental setup.

Fig. 5
Fig. 5

Measured output trajectory C2(ν) represented here by its latitude and longitude as functions of frequency.

Fig. 6
Fig. 6

Total specific birefringence |ω0(ν)| of the fiber under test as a function of frequency. Also shown are the components of linear birefringence |βc + βs| and of circular birefringence |α − 2τ|.

Equations (19)

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ω ( ν , z ) = β c ( ν , z ) + β c ( ν , z ) + α ( ν , z )
β c ( β ) β c , max = 0.13 ( e 2 / b ) ( 2 Δ ) 3 / 2 ,
β s ( ν ) = 2 π n 3 p 44 ( 1 + N ) ( σ / E ) ν
α ( ν ) = - n 2 p 44 τ e l Z ^ .
Ω ( ν ) = L ω ( ν ) = L [ β c + β s ( ν ) ] ,
ϕ β ( ν , z ) = ϕ β ( ν , 0 ) + τ z .
ω 0 = ω - 2 τ .
γ = arctan [ ( α - 2 τ ) Z ^ / β c + β s ]
Ω 0 ( ν ) = L ω 0 ( ν ) .
T ± = ( 2 π ) - 1 d θ ± ( ν ) / d ν .
Δ T = T - - T + = ( 2 π ) - 1 d Ω 0 ( ν ) / d ν ,
θ - ( ν ) - θ + ( ν ) = Ω 0 ( ν ) .
2 ψ = ± arccos [ 2 ( A 2 + B 2 ) 1 / 2 / I 0 ] ;
2 ϕ = arctan ( B / A ) + 2 ϕ 0 .
γ ( ν ) = arccos { [ 1 - sin 2 ψ 2 - sin 2 2 ϕ ( 1 + sin 2 ψ ) ] 1 / 2 } ,
Ω 0 ( ν ) = arccos ( sin 2 ψ sin 2 2 ϕ - cos 2 2 ϕ ) .
β c + β s = ω 0 cos γ ;
α - 2 τ = ω 0 sin γ .
β c + β s ( ν ) = 1.085 × 10 - 3 ν - 2.52 ( rad / m ) .

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