Abstract

Using the Poincaré sphere and wavelength scanning it is possible to determine if the fiber birefringence corresponds to that of a linear, circular or elliptical retarder, as well as to obtain an approximate measurement of the polarization beatlength. This method is useful for low birefringence single-mode fibers. It is applied to erbium-doped fibers.

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References

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    [CrossRef]
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  3. A. J. Barlow, �??Optical-fiber birefringence measurement using a photo-elastic modulator,�?? J. Lightwave Technol. LT-3, 135-145, 1985.
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  6. 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.
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    [CrossRef]
  8. T. Chartier, A. Hideur, C. �?zkul, F. Sanchez, G. M. Stéphan, �??Measurement of the elliptical birefringence of single-mode optical fibers,�?? Appl. Opt. 40, 5343-5353, 2001.
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  9. M. Wegmuller, M. Legré, N. Gisin, �??Distributed beatlength measurement in single-mode fibers with optical frequency-domain reflectometry,�?? J. Lightwave Technol. 20, 828-835, 2002.
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  10. C. Tsao, �??Optical Fibre Waveguide Analysis�??(Oxford University Press, New York, p.101, 1992).
  11. K. Kikuchi, T. Okoshi, �??Wavelength-sweeping technique for measuring the beat length of linearly birefringent optical fibers,�?? Opt. Lett. 8, 122-123, 1983.
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  12. S.C. Rashleigh, �??Measurement of fiber birefringence by wavelength scanning effect of dispersion,�?? Opt. Lett. 8, 336-338, 1983.
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  13. T.I. Su, L. Wang, �??A cutback method for measuring low linear fibre birefringence using an electro-optic modulator,�?? Opt. Quantum Electron. 28, 1395-1405, 1996.
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  14. W. Eickhoff, Y. Yen, R. Ulrich, �??Wavelength dependence of birefringence in single-mode fiber�?? Appl. Opt. 20, 3428-3435, 1981.
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  15. V. Ramaswamy, R.D.Standley, D.Sze, W.G. French �??Polarization effects in short length, single mode fibers�?? Bell Sys. Tech. J. Vol. 57, No.3, 635-651, 1978.
  16. D. S. Kliger, J. W. Lewis, C. E. Randall, �??Polarized Light in Optics and Spectroscopy�?? (Academic Press, Inc., San Diego 1990).
  17. S.C. Rashleigh, �??Origins and control of polarization effects in single-mode fibers,�?? J. Lightwave Technol. LT-1, 312-331, 1983.
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  18. D. Tentori, C. Ayala-Díaz, F. Treviño-Martínez, M. Farfán-Sánchez, F.J. Mendieta-Jiménez, �??Birefringence evaluation of erbium doped optical fibers�?? Proc. SPIE, 5531, 359-366, 2004.
    [CrossRef]
  19. B. L. Heffner �??Accurate, Automated Measurement of Differential Group Delay Dispersion and Principal State Variation Using Jones Matrix Eigenanalysis�??, IEEE Photon. Technol. Lett. 5, 814-817, 1993.
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Appl. Opt. (5)

Bell Sys. Tech. J. (1)

V. Ramaswamy, R.D.Standley, D.Sze, W.G. French �??Polarization effects in short length, single mode fibers�?? Bell Sys. Tech. J. Vol. 57, No.3, 635-651, 1978.

Electron. Lett. (1)

M. Monerie, P. Lamouler, �??Birefringence measurement in twisted single-mode fibres,�?? Electron. Lett. 17, 252-253, 1981.
[CrossRef]

IEEE Photon. Technol. Lett. (1)

B. L. Heffner �??Accurate, Automated Measurement of Differential Group Delay Dispersion and Principal State Variation Using Jones Matrix Eigenanalysis�??, IEEE Photon. Technol. Lett. 5, 814-817, 1993.
[CrossRef]

J. Lightwave Technol. (2)

M. Wegmuller, M. Legré, N. Gisin, �??Distributed beatlength measurement in single-mode fibers with optical frequency-domain reflectometry,�?? J. Lightwave Technol. 20, 828-835, 2002.
[CrossRef]

S.C. Rashleigh, �??Origins and control of polarization effects in single-mode fibers,�?? J. Lightwave Technol. LT-1, 312-331, 1983.
[CrossRef]

J. Lightwave Technol. LT-3 (1)

A. J. Barlow, �??Optical-fiber birefringence measurement using a photo-elastic modulator,�?? J. Lightwave Technol. LT-3, 135-145, 1985.
[CrossRef]

J. Phys. E (1)

A.M. Smith, �??Automated birefringence measurement system�?? J. Phys. E 12, 927-930, 1979.
[CrossRef]

Opt. Lett. (3)

Opt. Quantum Electron. (1)

T.I. Su, L. Wang, �??A cutback method for measuring low linear fibre birefringence using an electro-optic modulator,�?? Opt. Quantum Electron. 28, 1395-1405, 1996.
[CrossRef]

Proc. SPIE (1)

D. Tentori, C. Ayala-Díaz, F. Treviño-Martínez, M. Farfán-Sánchez, F.J. Mendieta-Jiménez, �??Birefringence evaluation of erbium doped optical fibers�?? Proc. SPIE, 5531, 359-366, 2004.
[CrossRef]

Other (2)

D. S. Kliger, J. W. Lewis, C. E. Randall, �??Polarized Light in Optics and Spectroscopy�?? (Academic Press, Inc., San Diego 1990).

C. Tsao, �??Optical Fibre Waveguide Analysis�??(Oxford University Press, New York, p.101, 1992).

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Figures (12)

Fig. 1.
Fig. 1.

Optical set-up used to work with the Poincaré sphere. Monochromatic signals come from a tunable diode laser. The azimuth angle of the input linear polarization is modified rotating the input linear polarizer. The Stokes vector of the output state of polarization is measured by a polarization analyzer.

Fig. 2.
Fig. 2.

These circular paths describe the evolution of the polarization state for a linear retarder. Each circle corresponds to a different azimuth angle of the input linear polarization. The symmetry axis lies on the equator plane. The fiber sample is aligned with the laboratory system.

Fig. 3.
Fig. 3.

This major circle describes the evolution of the polarization state for a circular retarder. This trajectory does not depend on the azimuth angle of the input linear polarization and/or the fiber sample. The symmetry axis crosses the Poincaré sphere through the north and south poles.

Fig. 4.
Fig. 4.

These circular trajectories describe the evolution of the polarization state for an elliptical retarder. The inclination angle between the symmetry axis and the equator plane depends on the circular to linear birefringence ratio of the fiber sample. The fiber sample is aligned with the laboratory system.

Fig. 5.
Fig. 5.

Fiber sample with elliptical retardation. Each circle corresponds to a different circular to linear birefringence ratio tanσ [(π/2 - σ)=ζ=5° to 30°]. For the trajectories shown in this figure, the azimuth angle of the input linear polarization state is φ=0°.

Fig. 6.
Fig. 6.

Wavelength scanning results obtained for the INO NOI 402K5 single-mode erbium-doped fiber. The sampling signal was scanned from 1511nm to 1571nm using 6nm steps. Each curve corresponds to a different azimuth angle of the input linear polarization state.

Fig. 7.
Fig. 7.

Lateral view of the curves shown in Fig. 6. In addition to the results in fig. 6, this orientation of the sphere allows us to include some other trajectories produced using different azimuth angles of the input polarizer. It is evident that each path is not a plane curve.

Fig. 8.
Fig. 8.

Wavelength scanning results obtained for the Photonetics EDOS-103 single-mode erbium-doped fiber. The sampling signal was scanned from 1511nm to 1571nm using 6nm steps. Each curve corresponds to a different azimuth angle of the input linear polarization state.

Fig. 9.
Fig. 9.

Lateral view of the curves shown in Fig. 8. In both figures, the same color was used for equivalent orientations of the input linear polarizer. It can be observed that when the signal wavelength is scanned, the trajectory described by the output polarization state is not a plane curve.

Fig. 10.
Fig. 10.

Results obtained for the average value of the elevation angle ζ, for the INO NOI sample. These values were calculated using consecutive values of the sampling wavelength ( ζ ¯ =-3.1°±2.4°).

Fig. 11.
Fig. 11.

Results obtained for the average value of the elevation angle ζ, for the Photonetics sample. These values were calculated using consecutive values of the sampling wavelength ( ζ ¯ =86°±1.1°).

Fig. 12.
Fig. 12.

The radii predicted by the value of the inclination angle determined from wavelength scanning data are compared with the real trajectories shown in fig. 8. The continuous line is the average value of the radius. The range of values produced by the standard deviation lies between the neighboring dotted lines.

Tables (2)

Tables Icon

Table I. Mueller matrices of the retarders used to describe the birefringence of single-mode fibers

Tables Icon

Table II. Stokes vectors at the output of the fiber sample

Equations (8)

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

Φ = 2 π s λ Δ n ;
S out = M S in ,
S in = ( 1 cos 2 φ sin 2 φ 0 ) t ;
S out = ( 1 cos 2 φ cos φ sin 2 φ sin φ sin 2 φ )
S out = ( 1 cos ( 2 φ θ ) sin ( 2 φ θ ) 0 )
S out = ( 1 cos 2 φ ( 1 2 cos 2 σ sin 2 δ ) sin 2 φ cos σ sin 2 δ cos 2 φ cos σ sin 2 δ + sin 2 φ cos 2 δ cos 2 φ sin 2 σ sin 2 δ sin 2 φ sin σ sin 2 δ )
S = ( cos 2 φ sin σ cos 2 φ cos σ sin 2 δ + sin 2 φ cos 2 δ cos 2 φ sin cos 2 φ cos σ cos 2 δ ) .
r = cos 2 2 φ cos 2 σ + sin 2 2 φ .

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