Abstract

We study the frequency autocorrelation of the differential group delay (DGD) in fibers with polarization mode dispersion (PMD). We show that the correlation bandwidth of the DGD is comparable with that of the orientation of the PMD vector. Furthermore, we show that all the most general statistical properties of polarization mode dispersion in long fibers are uniquely determined by the mean DGD. An estimate of the accuracy of measurements in which the mean DGD is extracted by frequency averaging in a single fiber is obtained as a function of the measured bandwidth.

© 2000 Optical Society of America

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References

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  1. C. D. Poole and J. Nagel, in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), Chap. 6.
  2. J. P. Gordon and H. Kogelnik, “PMD fundamentals,” Proc. Natl. Acad. Sci. USA (to be published).
  3. G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
    [CrossRef]
  4. M. Karlsson and J. Brentel, Opt. Lett. 24, 939 (1999).
    [CrossRef]
  5. M. Shtaif, A. Mecozzi, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
    [CrossRef]
  6. M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 433 (2000).
  7. C. W. Gardiner, Handbook of Stochastic Methods, 2nd ed., Vol. 13 of Springer Series in Synergetics (Springer-Verlag, Berlin, 1985).
  8. N. Gisin, B. Gisin, J. P. Von der Weid, and R. Passy, IEEE Photon. Technol. Lett. 8, 1671 (1996).
    [CrossRef]

2000 (2)

M. Shtaif, A. Mecozzi, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 433 (2000).

1999 (1)

1996 (1)

N. Gisin, B. Gisin, J. P. Von der Weid, and R. Passy, IEEE Photon. Technol. Lett. 8, 1671 (1996).
[CrossRef]

1991 (1)

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

Brentel, J.

Foschini, G. J.

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

Gardiner, C. W.

C. W. Gardiner, Handbook of Stochastic Methods, 2nd ed., Vol. 13 of Springer Series in Synergetics (Springer-Verlag, Berlin, 1985).

Gisin, B.

N. Gisin, B. Gisin, J. P. Von der Weid, and R. Passy, IEEE Photon. Technol. Lett. 8, 1671 (1996).
[CrossRef]

Gisin, N.

N. Gisin, B. Gisin, J. P. Von der Weid, and R. Passy, IEEE Photon. Technol. Lett. 8, 1671 (1996).
[CrossRef]

Gordon, J. P.

J. P. Gordon and H. Kogelnik, “PMD fundamentals,” Proc. Natl. Acad. Sci. USA (to be published).

Karlsson, M.

Kogelnik, H.

J. P. Gordon and H. Kogelnik, “PMD fundamentals,” Proc. Natl. Acad. Sci. USA (to be published).

Mecozzi, A.

M. Shtaif, A. Mecozzi, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 433 (2000).

Nagel, J.

C. D. Poole and J. Nagel, in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), Chap. 6.

Nagel, J. A.

M. Shtaif, A. Mecozzi, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 433 (2000).

Passy, R.

N. Gisin, B. Gisin, J. P. Von der Weid, and R. Passy, IEEE Photon. Technol. Lett. 8, 1671 (1996).
[CrossRef]

Poole, C. D.

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

C. D. Poole and J. Nagel, in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), Chap. 6.

Shtaif, M.

M. Shtaif, A. Mecozzi, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 433 (2000).

Tur, M.

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 433 (2000).

Von der Weid, J. P.

N. Gisin, B. Gisin, J. P. Von der Weid, and R. Passy, IEEE Photon. Technol. Lett. 8, 1671 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

M. Shtaif, A. Mecozzi, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 433 (2000).

N. Gisin, B. Gisin, J. P. Von der Weid, and R. Passy, IEEE Photon. Technol. Lett. 8, 1671 (1996).
[CrossRef]

J. Lightwave Technol. (1)

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

Opt. Lett. (1)

Other (3)

C. D. Poole and J. Nagel, in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic, San Diego, Calif., 1997), Chap. 6.

J. P. Gordon and H. Kogelnik, “PMD fundamentals,” Proc. Natl. Acad. Sci. USA (to be published).

C. W. Gardiner, Handbook of Stochastic Methods, 2nd ed., Vol. 13 of Springer Series in Synergetics (Springer-Verlag, Berlin, 1985).

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Figures (2)

Fig. 1
Fig. 1

(a) Autocorrelation function of the square DGD [Eq. (4)] as well as results of a Monte Carlo simulation of a fiber with 1000 independent sections (squares). (b) Auto-correlations of the DGD (thin curve) and of the PMD angle (thick curve). The vector autocorrelation is also shown for comparison (dashed curve). The curves were all normalized to their peak values.

Fig. 2
Fig. 2

(a) Normalized autocorrelation functions of DGD (dots) and of the square DGD (squares). To emphasize the resemblence we show the curves on a logarithmic scale. (b) Variance of the measured mean DGD when it is frequency averaged over an angular frequency bandwidth of B and divided by τdgd2. The dashed curve corresponds to the asymptotic dependence VarτB1.34τdgd/B.

Equations (8)

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dτz,ω=ωdWz×τz,ω+dWz,
dτ2=2τ·dτ+dτ·dτ=2τ·dW+γ2dz,
dτz,ω2τz,ω2=τz,ω2dτz,ω2+τz,ω2dτz,ω2+dτz,ω2dτz,ω2=2τz,ω2τz,ω·dW+2τz,ω2τz,ω·dW+γ2τz,ω2+τz,ω2dz+4γ23τz,ω·τz,ωdz.
τz,ω2τz,ω2=τ22+4τ2Δω2-12Δω4×1-exp-Δω2τ2/3,
τz,ω·τz,ω=3Δω21-exp-Δω2τ2/3.
dτNζ,ν=νdWNζ×τNζ,ω+dWNζ.
τz,ωτz,ω3π-8π2Δω2-6Δω4τ2×1-exp-Δω2τ2/3+83πτ2.
1B2-B/2B/2dω-B/2B/2dωτz,ωτz,ω-τdgd2.

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