Abstract

The polarization properties of single-mode optical fibers are theoretically modeled with use of the Jones formalism. The fiber is described as an elliptical birefringent plate. The properties predicted by this model are discussed and lead to the development of a simple experimental method to extract the parameters that describe a real fiber. A magneto-optic method that measures the beat length of the fiber is also presented and gives a more complete description of the fiber. The validity of the model is then clearly established. Finally, the wavelength dependence of the parameters characteristic of the fiber is experimentally investigated.

© 2001 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, 15–22 (1981).
    [CrossRef]
  2. S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” IEEE J. Lightwave Technol. LT-1, 312–331 (1983).
    [CrossRef]
  3. D. Andresciani, F. Curti, F. Matera, B. Daino, “Measurement of the group-delay difference between the principal states of polarization on a low birefringence terrestrial fiber cable,” Opt. Lett. 12, 844–846 (1987).
    [CrossRef] [PubMed]
  4. C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” IEEE J. Lightwave Technol. 6, 1185–1190 (1988).
    [CrossRef]
  5. C. D. Poole, R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22, 1029–1030 (1986).
    [CrossRef]
  6. T. Chartier, F. Sanchez, G. Stéphan, P. Le Boudec, E. Delevaque, R. Leners, P. L. François, “Channeled spectrum of a fiber laser,” Opt. Lett. 18, 355–357 (1993).
    [CrossRef] [PubMed]
  7. U. Ghera, N. Friedman, M. Tur, “Polarization related phenomena in Nd-doped fiber lasers,” Opt. Mater. 4, 73–80 (1994).
    [CrossRef]
  8. H. Y. Kim, S. K. Kim, H. J. Jeong, H. K. Kim, B. Y. Kim, “Polarization properties of a twisted fiber laser,” Opt. Lett. 20, 386–388 (1995).
    [CrossRef] [PubMed]
  9. H. Y. Kim, E. H. Lee, B. Y. Kim, “Polarization properties of fiber lasers with twist-induced circular birefringence,” Appl. Opt. 36, 6764–6769 (1997).
    [CrossRef]
  10. R. Ulrich, A. Simon, “Polarization optics of twisted single-mode fibers,” Appl. Opt. 18, 2241–2251 (1979).
    [CrossRef] [PubMed]
  11. E. M. Frins, W. Dultz, “Rotation of the polarization plane in optical fibers,” IEEE J. Lightwave Technol. LT-14, 144–147 (1996).
  12. G. D. Van Wiggeren, R. Roy, “Transmission of linearly polarized light through a single-mode fiber with random fluctuations of birefringence,” Appl. Opt. 38, 3888–3892 (1999).
    [CrossRef]
  13. C. D. Poole, D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” IEEE J. Lightwave Technol. 12, 917–929 (1994).
    [CrossRef]
  14. M. Monerie, L. Jeunhomme, “Polarization mode coupling in long single-mode fibres,” Opt. Quantum Electron. 12, 449–461 (1980).
    [CrossRef]
  15. C. D. Poole, “Measurement of polarization-mode dispersion in single-mode fibers with random mode coupling,” Opt. Lett. 14, 523–525 (1989).
    [CrossRef] [PubMed]
  16. R. C. Jones, “A new calculus for the treatment of optical systems. I. Description and discussion of the calculus,” J. Opt. Soc. Am. 31, 488–493 (1941).
    [CrossRef]
  17. 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]
  18. S. Betti, F. Curti, B. Diano, G. De Marchis, E. Iannone, F. Matera, “Evolution of the bandwidth of the principal states of polarization in single-mode fibers,” Opt. Lett. 16, 467–469 (1991).
    [CrossRef] [PubMed]
  19. F. Maystre, R. Dandliker, “Polarimetric fiber optical sensor with high sensitivity using a Fabry–Perot structure,” Appl. Opt. 28, 1995–2000 (1989).
    [CrossRef] [PubMed]
  20. E. Hecht, A. Zajac, Optics, (Addison-Wesley, Reading, Mass., 1974).
  21. A. M. Smith, “Polarization and magnetooptic properties of single-mode optical fiber,” Appl. Opt. 17, 52–56 (1978).
    [CrossRef] [PubMed]
  22. G. W. Day, D. N. Payne, A. J. Barlow, J. J. Ramskov-Hansen, “Faraday rotation in coiled, monomode optical fibers: isolators, filters, and magnetic sensors,” Opt. Lett. 7, 238–240 (1982).
    [CrossRef] [PubMed]
  23. M. Turpin, M. Valentin, J. Dubos, J. Auge, “Mesure de la biréfringence des fibres optiques monomodes à maintien de polarisation linéaire,” Rev. Tech. Thomson-CSF 15, 1049–1071 (1983).
  24. P. G. Zhang, D. Irvine-Halliday, “Measurement of the beat length in high-birefringent optical fiber by way of magneto-optic modulation,” J. Lightwave Technol. 12, 597–602 (1994).
    [CrossRef]
  25. D. Irvine-Halliday, M. R. Khan, P. G. Zhang, “Beat-length measurement of high-birefringence polarization-maintaining optical fiber using the DC Faraday magneto-optic effect,” Opt. Eng. 39, 1310–1315 (2000).
    [CrossRef]
  26. H. Y. Kim, B. K. Kim, S. H. Yun, B. Y. Kim, “Response of fiber lasers to an axial magnetic field,” Opt. Lett. 20, 1713–1715 (1995).
    [CrossRef] [PubMed]
  27. A. Hideur, T. Chartier, F. Sanchez, “Yb-doped double-clad fiber laser in a unidirectional ring cavity,” in Optical Devices for Fiber Communication II, M. J. Digonnet, O. S. Gebizlioglu, R. A. Greenwell, D. N. Horwitz, D. K. Paul, eds., Proc. SPIE4216, 15–21 (2001).
    [CrossRef]

2000 (1)

D. Irvine-Halliday, M. R. Khan, P. G. Zhang, “Beat-length measurement of high-birefringence polarization-maintaining optical fiber using the DC Faraday magneto-optic effect,” Opt. Eng. 39, 1310–1315 (2000).
[CrossRef]

1999 (1)

1997 (1)

1996 (1)

E. M. Frins, W. Dultz, “Rotation of the polarization plane in optical fibers,” IEEE J. Lightwave Technol. LT-14, 144–147 (1996).

1995 (2)

1994 (3)

C. D. Poole, D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” IEEE J. Lightwave Technol. 12, 917–929 (1994).
[CrossRef]

U. Ghera, N. Friedman, M. Tur, “Polarization related phenomena in Nd-doped fiber lasers,” Opt. Mater. 4, 73–80 (1994).
[CrossRef]

P. G. Zhang, D. Irvine-Halliday, “Measurement of the beat length in high-birefringent optical fiber by way of magneto-optic modulation,” J. Lightwave Technol. 12, 597–602 (1994).
[CrossRef]

1993 (1)

1991 (1)

1989 (2)

1988 (1)

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” IEEE J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

1987 (1)

1986 (1)

C. D. Poole, R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22, 1029–1030 (1986).
[CrossRef]

1983 (2)

S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” IEEE J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

M. Turpin, M. Valentin, J. Dubos, J. Auge, “Mesure de la biréfringence des fibres optiques monomodes à maintien de polarisation linéaire,” Rev. Tech. Thomson-CSF 15, 1049–1071 (1983).

1982 (1)

1981 (1)

I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

1980 (1)

M. Monerie, L. Jeunhomme, “Polarization mode coupling in long single-mode fibres,” Opt. Quantum Electron. 12, 449–461 (1980).
[CrossRef]

1979 (1)

1978 (1)

1948 (1)

1941 (1)

Andresciani, D.

Auge, J.

M. Turpin, M. Valentin, J. Dubos, J. Auge, “Mesure de la biréfringence des fibres optiques monomodes à maintien de polarisation linéaire,” Rev. Tech. Thomson-CSF 15, 1049–1071 (1983).

Barlow, A. J.

Bergano, N. S.

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” IEEE J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Betti, S.

Chartier, T.

T. Chartier, F. Sanchez, G. Stéphan, P. Le Boudec, E. Delevaque, R. Leners, P. L. François, “Channeled spectrum of a fiber laser,” Opt. Lett. 18, 355–357 (1993).
[CrossRef] [PubMed]

A. Hideur, T. Chartier, F. Sanchez, “Yb-doped double-clad fiber laser in a unidirectional ring cavity,” in Optical Devices for Fiber Communication II, M. J. Digonnet, O. S. Gebizlioglu, R. A. Greenwell, D. N. Horwitz, D. K. Paul, eds., Proc. SPIE4216, 15–21 (2001).
[CrossRef]

Curti, F.

Daino, B.

Dandliker, R.

Day, G. W.

De Marchis, G.

Delevaque, E.

Diano, B.

Dubos, J.

M. Turpin, M. Valentin, J. Dubos, J. Auge, “Mesure de la biréfringence des fibres optiques monomodes à maintien de polarisation linéaire,” Rev. Tech. Thomson-CSF 15, 1049–1071 (1983).

Dultz, W.

E. M. Frins, W. Dultz, “Rotation of the polarization plane in optical fibers,” IEEE J. Lightwave Technol. LT-14, 144–147 (1996).

Favin, D. L.

C. D. Poole, D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” IEEE J. Lightwave Technol. 12, 917–929 (1994).
[CrossRef]

François, P. L.

Friedman, N.

U. Ghera, N. Friedman, M. Tur, “Polarization related phenomena in Nd-doped fiber lasers,” Opt. Mater. 4, 73–80 (1994).
[CrossRef]

Frins, E. M.

E. M. Frins, W. Dultz, “Rotation of the polarization plane in optical fibers,” IEEE J. Lightwave Technol. LT-14, 144–147 (1996).

Ghera, U.

U. Ghera, N. Friedman, M. Tur, “Polarization related phenomena in Nd-doped fiber lasers,” Opt. Mater. 4, 73–80 (1994).
[CrossRef]

Hecht, E.

E. Hecht, A. Zajac, Optics, (Addison-Wesley, Reading, Mass., 1974).

Hideur, A.

A. Hideur, T. Chartier, F. Sanchez, “Yb-doped double-clad fiber laser in a unidirectional ring cavity,” in Optical Devices for Fiber Communication II, M. J. Digonnet, O. S. Gebizlioglu, R. A. Greenwell, D. N. Horwitz, D. K. Paul, eds., Proc. SPIE4216, 15–21 (2001).
[CrossRef]

Iannone, E.

Irvine-Halliday, D.

D. Irvine-Halliday, M. R. Khan, P. G. Zhang, “Beat-length measurement of high-birefringence polarization-maintaining optical fiber using the DC Faraday magneto-optic effect,” Opt. Eng. 39, 1310–1315 (2000).
[CrossRef]

P. G. Zhang, D. Irvine-Halliday, “Measurement of the beat length in high-birefringent optical fiber by way of magneto-optic modulation,” J. Lightwave Technol. 12, 597–602 (1994).
[CrossRef]

Jeong, H. J.

Jeunhomme, L.

M. Monerie, L. Jeunhomme, “Polarization mode coupling in long single-mode fibres,” Opt. Quantum Electron. 12, 449–461 (1980).
[CrossRef]

Jones, R. C.

Kaminow, I. P.

I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

Khan, M. R.

D. Irvine-Halliday, M. R. Khan, P. G. Zhang, “Beat-length measurement of high-birefringence polarization-maintaining optical fiber using the DC Faraday magneto-optic effect,” Opt. Eng. 39, 1310–1315 (2000).
[CrossRef]

Kim, B. K.

Kim, B. Y.

Kim, H. K.

Kim, H. Y.

Kim, S. K.

Le Boudec, P.

Lee, E. H.

Leners, R.

Matera, F.

Maystre, F.

Monerie, M.

M. Monerie, L. Jeunhomme, “Polarization mode coupling in long single-mode fibres,” Opt. Quantum Electron. 12, 449–461 (1980).
[CrossRef]

Payne, D. N.

Poole, C. D.

C. D. Poole, D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” IEEE J. Lightwave Technol. 12, 917–929 (1994).
[CrossRef]

C. D. Poole, “Measurement of polarization-mode dispersion in single-mode fibers with random mode coupling,” Opt. Lett. 14, 523–525 (1989).
[CrossRef] [PubMed]

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” IEEE J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

C. D. Poole, R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22, 1029–1030 (1986).
[CrossRef]

Ramskov-Hansen, J. J.

Rashleigh, S. C.

S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” IEEE J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

Roy, R.

Sanchez, F.

T. Chartier, F. Sanchez, G. Stéphan, P. Le Boudec, E. Delevaque, R. Leners, P. L. François, “Channeled spectrum of a fiber laser,” Opt. Lett. 18, 355–357 (1993).
[CrossRef] [PubMed]

A. Hideur, T. Chartier, F. Sanchez, “Yb-doped double-clad fiber laser in a unidirectional ring cavity,” in Optical Devices for Fiber Communication II, M. J. Digonnet, O. S. Gebizlioglu, R. A. Greenwell, D. N. Horwitz, D. K. Paul, eds., Proc. SPIE4216, 15–21 (2001).
[CrossRef]

Schulte, H. J.

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” IEEE J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Simon, A.

Smith, A. M.

Stéphan, G.

Tur, M.

U. Ghera, N. Friedman, M. Tur, “Polarization related phenomena in Nd-doped fiber lasers,” Opt. Mater. 4, 73–80 (1994).
[CrossRef]

Turpin, M.

M. Turpin, M. Valentin, J. Dubos, J. Auge, “Mesure de la biréfringence des fibres optiques monomodes à maintien de polarisation linéaire,” Rev. Tech. Thomson-CSF 15, 1049–1071 (1983).

Ulrich, R.

Valentin, M.

M. Turpin, M. Valentin, J. Dubos, J. Auge, “Mesure de la biréfringence des fibres optiques monomodes à maintien de polarisation linéaire,” Rev. Tech. Thomson-CSF 15, 1049–1071 (1983).

Van Wiggeren, G. D.

Wagner, R. E.

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” IEEE J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

C. D. Poole, R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22, 1029–1030 (1986).
[CrossRef]

Yun, S. H.

Zajac, A.

E. Hecht, A. Zajac, Optics, (Addison-Wesley, Reading, Mass., 1974).

Zhang, P. G.

D. Irvine-Halliday, M. R. Khan, P. G. Zhang, “Beat-length measurement of high-birefringence polarization-maintaining optical fiber using the DC Faraday magneto-optic effect,” Opt. Eng. 39, 1310–1315 (2000).
[CrossRef]

P. G. Zhang, D. Irvine-Halliday, “Measurement of the beat length in high-birefringent optical fiber by way of magneto-optic modulation,” J. Lightwave Technol. 12, 597–602 (1994).
[CrossRef]

Appl. Opt. (5)

Electron. Lett. (1)

C. D. Poole, R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22, 1029–1030 (1986).
[CrossRef]

IEEE J. Lightwave Technol. (4)

S. C. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” IEEE J. Lightwave Technol. LT-1, 312–331 (1983).
[CrossRef]

C. D. Poole, N. S. Bergano, R. E. Wagner, H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” IEEE J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

E. M. Frins, W. Dultz, “Rotation of the polarization plane in optical fibers,” IEEE J. Lightwave Technol. LT-14, 144–147 (1996).

C. D. Poole, D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” IEEE J. Lightwave Technol. 12, 917–929 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

J. Lightwave Technol. (1)

P. G. Zhang, D. Irvine-Halliday, “Measurement of the beat length in high-birefringent optical fiber by way of magneto-optic modulation,” J. Lightwave Technol. 12, 597–602 (1994).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Eng. (1)

D. Irvine-Halliday, M. R. Khan, P. G. Zhang, “Beat-length measurement of high-birefringence polarization-maintaining optical fiber using the DC Faraday magneto-optic effect,” Opt. Eng. 39, 1310–1315 (2000).
[CrossRef]

Opt. Lett. (7)

Opt. Mater. (1)

U. Ghera, N. Friedman, M. Tur, “Polarization related phenomena in Nd-doped fiber lasers,” Opt. Mater. 4, 73–80 (1994).
[CrossRef]

Opt. Quantum Electron. (1)

M. Monerie, L. Jeunhomme, “Polarization mode coupling in long single-mode fibres,” Opt. Quantum Electron. 12, 449–461 (1980).
[CrossRef]

Rev. Tech. Thomson-CSF (1)

M. Turpin, M. Valentin, J. Dubos, J. Auge, “Mesure de la biréfringence des fibres optiques monomodes à maintien de polarisation linéaire,” Rev. Tech. Thomson-CSF 15, 1049–1071 (1983).

Other (2)

A. Hideur, T. Chartier, F. Sanchez, “Yb-doped double-clad fiber laser in a unidirectional ring cavity,” in Optical Devices for Fiber Communication II, M. J. Digonnet, O. S. Gebizlioglu, R. A. Greenwell, D. N. Horwitz, D. K. Paul, eds., Proc. SPIE4216, 15–21 (2001).
[CrossRef]

E. Hecht, A. Zajac, Optics, (Addison-Wesley, Reading, Mass., 1974).

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Figures (11)

Fig. 1
Fig. 1

Description of the fiber as a concatenation of birefringent plates M i oriented along θ i .

Fig. 2
Fig. 2

Eigenvectors V ± of M f on the Poincaré sphere.

Fig. 3
Fig. 3

Representation on the Poincaré sphere of the LSP and the ESP and the paths (a) and (b) representing their transformation by the fiber.

Fig. 4
Fig. 4

Experimental setup for the measurement of the LSP and the ESP.

Fig. 5
Fig. 5

Possible paths describing the evolution of an input LSP and ESP of the fiber for (a) ∊ = 1.24 rad/m and (b) ∊ = 2.53 rad/m. Note that the angles mentioned on the figure are real values of the azimuth.

Fig. 6
Fig. 6

Setup of (a) the magneto-optic method and (b) modeling of the fiber.

Fig. 7
Fig. 7

Measurement of the beat length of the fiber at 1064 nm with the magneto-optic method.

Fig. 8
Fig. 8

Measurement of ∊ as a function of wavelength by use of the magneto-optic method (squares) and the LSP–ESP method (circles).

Fig. 9
Fig. 9

Experimental measurement of ϕin, ϕout, and ψ as a function of wavelength.

Fig. 10
Fig. 10

Wavelength dependence of α, β, and ∊.

Fig. 11
Fig. 11

Evolution of the azimuth and the ellipticity of the output state of polarization versus the input azimuth at (a) 1048, (b) 1064, and (c) 1096 nm.

Tables (1)

Tables Icon

Table 1 Parameters Used in the Model

Equations (57)

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

Mf=RθnMnR-θn×Rθ2M2R-θ2Rθ1M1R-θ1,
Rθ=cos θ-sin θsin θcos θ.
Mi=expi φi200exp-i φi2,
Mf=ab-b*a*,
a=cosL2+i βsinL2,
b=-α+iγsinL2,
=α2+β2+γ21/2.
sin 2χ=α,
tan 2φ=-γβ.
Mf=ab-ba*,
a=cosL2+i βsinL2,
b=-αsinL2,
=α2+β21/2.
sin 2χ=α.
Lin=cosϕinsinϕin,
Lout=MfLin.
ϕout=-ϕin=ϕ,
tan 2ϕ=αtanL2.
Eout=MfEin,
Ein=cos ξi sin ξ.
tan 2ψ=αtan L
tan 2ξ=αβ1-cos Lα2+β2 cos L.
OA=cos 2ψ,
AC=sin 2ψ,
AB=OA sin 2χ=αcos 2ψ.
tan L=ACAB=αtan 2ψ.
tanL2=±1-2 tan 2ϕtan 2ψ1/2=±m,
=2L±arctan m±kπ,
α=±mtan 2ϕ,
β=±2-α21/2,
=2Lkπ±arctan m,
α=±mtan 2ϕ,
β=2-α21/2.
M1=a1b1-b1a1*,
a1=cosz-l2+i βsinz-l2,
b1=-αsinz-l2.
h=2VH,
αh=α+h,
h=β2+αh21/2,
M2=a2b2-b2a2*,
a2=coshl2+i βhsinhl2,
b2=-αhhsinhl2.
M3=a3b3-b3a3*,
a3=cosL-z2+i βsinL-z2,
b3=-αsinL-z2.
Mh=AhBh-Bh*Ah*,
Ah=cosL2+i βsinL2-ih αβ31-h α2×sinhl2cosL+l-2z2,
Bh=-αsinL2-h β23sinhl2cosL+l-2z2-ih β21-h α2sinhl2sinL+l-2z2.
Vout=Mpϕ+π/4MhEin,
Iout=12+h β23sinhl2cos2L+l-2z2.
V=a+ibc+id.
s0=a2+b2+c2+d2,
s1=a2+b2-c2-d2,
s2=2ac+bd,
s3=2ad-bc.
sin 2χ=s3s0,
tan 2φ=s2s1.

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