Abstract

We present a description and detailed uncertainty analysis of a polarization-mode dispersion (PMD) measurement system that uses the Jones matrix eigenanalysis measurement technique based on a rotating-wave-plate Stokes polarimeter. The uncertainty of the system is 3.2 fs (∼95% confidence interval) and is due primarily to PMD in the fiber leads of the measurement system.

© 1999 Optical Society of America

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References

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  1. P. A. Williams, “Mode-coupled artifact standard for polarization-mode dispersion: design, assembly, and implementation,” Appl. Opt. 38, 6498–6507 (1999).
    [CrossRef]
  2. B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
    [CrossRef]
  3. See “Polarization-mode dispersion measurement for single-mode optical fibers by Jones matrix eigenanalysis,” Fiber Optic Test Procedure (FOTP) 122Telecommunications Industry Association, 2500 Wilson Blvd., Suite 300, Arlington, VA 22201 USA.
  4. D. J. Ives, “Calibration of a polarisation state analyser for polarisation mode dispersion measurements,” in Technical Digest of the Fourth Optical Fibre Measurement Conference (Teddington, UK, 1997), pp. 213–216. The exact form of the Stokes polarimeter in this reference is unclear, however, a detailed error analysis is carried out.
  5. The terms type A and type B uncertainties refer to the ISO and the NIST convention and denote uncertainties that are (A) evaluated by statistical means and (B) evaluated by nonstatistical means. For details, see B. N. Taylor, C. E. Kuyatt, eds., “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” (National Institute of Standards and Technology, Boulder, Colo., 1994).
  6. P. A. Williams, A. H. Rose, C. M. Wang, “Rotating-polarizer polarimeter for accurate retardance measurement,” Appl. Opt. 36, 6466–6472 (1997).
    [CrossRef]
  7. P. D. Hale, G. W. Day, “Stability of birefringent linear retarders (waveplates),” Appl. Opt. 27, 5146–5153 (1988).
    [CrossRef] [PubMed]
  8. K. B. Rochford, A. H. Rose, P. A. Williams, C. M. Wang, I. G. Clarke, P. D. Hale, G. W. Day, “Design and performance of a stable linear retarder,” Appl. Opt. 36, 6458–6465 (1997).
    [CrossRef]
  9. E. Collette, ed., Polarized Light: Fundamentals and Applications (Marcel Dekker Inc., New York, 1993), p. 103.
  10. J. H. Shields, J. W. Ellis, “Dispersion of birefringence of quartz in the near infrared,” J. Opt. Soc. Am. 46, 263–265 (1956).
    [CrossRef]
  11. W. L. Wolfe, G. J. Zissis, eds., The Infrared Handbook (Environmental Research Institute of Michigan, Ann Arbor, 1985), pp. 7–57.
  12. B. L. Heffner, “Attosecond-resolution measurement of polarization mode dispersion in short sections of optical fiber,” Opt. Lett. 18, 2102–2104 (1993).
    [CrossRef] [PubMed]
  13. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 302.
  14. D. E. Gray, ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972), pp. 4–138.
  15. A. H. Rose, S. M. Etzel, National Institute of Standards and Technology, Boulder, Colo., 80303 (personal communication).

1999

1997

1993

1992

B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

1988

1956

Clarke, I. G.

Day, G. W.

Ellis, J. W.

Etzel, S. M.

A. H. Rose, S. M. Etzel, National Institute of Standards and Technology, Boulder, Colo., 80303 (personal communication).

Hale, P. D.

Heffner, B. L.

B. L. Heffner, “Attosecond-resolution measurement of polarization mode dispersion in short sections of optical fiber,” Opt. Lett. 18, 2102–2104 (1993).
[CrossRef] [PubMed]

B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

Ives, D. J.

D. J. Ives, “Calibration of a polarisation state analyser for polarisation mode dispersion measurements,” in Technical Digest of the Fourth Optical Fibre Measurement Conference (Teddington, UK, 1997), pp. 213–216. The exact form of the Stokes polarimeter in this reference is unclear, however, a detailed error analysis is carried out.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 302.

Rochford, K. B.

Rose, A. H.

Shields, J. H.

Wang, C. M.

Williams, P. A.

Appl. Opt.

IEEE Photon. Technol. Lett.

B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[CrossRef]

J. Opt. Soc. Am.

Opt. Lett.

Other

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), p. 302.

D. E. Gray, ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972), pp. 4–138.

A. H. Rose, S. M. Etzel, National Institute of Standards and Technology, Boulder, Colo., 80303 (personal communication).

W. L. Wolfe, G. J. Zissis, eds., The Infrared Handbook (Environmental Research Institute of Michigan, Ann Arbor, 1985), pp. 7–57.

See “Polarization-mode dispersion measurement for single-mode optical fibers by Jones matrix eigenanalysis,” Fiber Optic Test Procedure (FOTP) 122Telecommunications Industry Association, 2500 Wilson Blvd., Suite 300, Arlington, VA 22201 USA.

D. J. Ives, “Calibration of a polarisation state analyser for polarisation mode dispersion measurements,” in Technical Digest of the Fourth Optical Fibre Measurement Conference (Teddington, UK, 1997), pp. 213–216. The exact form of the Stokes polarimeter in this reference is unclear, however, a detailed error analysis is carried out.

The terms type A and type B uncertainties refer to the ISO and the NIST convention and denote uncertainties that are (A) evaluated by statistical means and (B) evaluated by nonstatistical means. For details, see B. N. Taylor, C. E. Kuyatt, eds., “Guidelines for evaluating and expressing the uncertainty of NIST measurement results,” (National Institute of Standards and Technology, Boulder, Colo., 1994).

E. Collette, ed., Polarized Light: Fundamentals and Applications (Marcel Dekker Inc., New York, 1993), p. 103.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the rotating-wave-plate Stokes polarimeter for measuring DGD.

Fig. 2
Fig. 2

Two possible types of wave-plate angular misalignment.

Fig. 3
Fig. 3

Schematic illustration that the distance ΔS between two Stokes vectors (Sa and Sb) is systematically biased by the presence of random Stokes noise (of amplitude η).

Fig. 4
Fig. 4

Normalized systematic error d(α) versus noise fraction α. Solid curve is theoretical prediction from Eq. (5), and circles are data points from two different quartz plates sampled at different wavelength step sizes.

Fig. 5
Fig. 5

Diagram of non-mode-coupled PMD test artifact. With removable polarizers that can be inserted to make a wavelength-scanning measurement independent of lead PMD.

Tables (2)

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Table 1 Estimated Random Uncertainties

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Table 2 Summary of Measurement Uncertainty for JME Measurement System

Equations (13)

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Δτg=argρ1/ρ2Δω,
Tω+ΔωT-1ω,
DOP=S0-S12+S22+S321/2S0.
S0=A-C/tan2δ/2, S1=2C/2 sin2δ/2, S2=2D/2 sin2δ/2, S3=B/sinδ,
dα=02π02π1+α cos θ-α cos φ2+1+α cos θ-α cos φ21/2 dθdφ02π02πdθdφ,
Iθ=12S0+S1 cos2 2θ+S2 sin 2θ cos 2θ+S3 sin 2θ,
A=1π02π Iθdθ,
B=2π02π Iθsin2θdθ.
C=2π02π Iθcos4θdθ,
D=2π02π Iθsin4θdθ.
S0=A-C, S1=2C, S2=2D, S3=B.
Δng=Δnp-λ dΔnpdλ.
γ=1/ΔnLdΔnL/dT=-1.232×10-4/°C.

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