Abstract

The polarization properties of concatenations of trunks of birefringent fibers and elements with polarization-dependent losses are analyzed. We show both theoretically and experimentally that the concatenation can have zero differential group delay over a whole range of wavelengths but that a pulse propagating down the concatenation can still experience significant pulse spreading. In this example the two main methods used for characterizing polarization mode dispersion in optical fiber systems, i.e., Jones matrix eigenanalysis and the interferometric method, give different results. This counterintuitive example underlines the need for a careful assessment of the basic concepts related to polarization effects in the presence of polarization-dependent losses.

© 1999 Optical Society of America

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References

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  1. C. D. Poole and R. E. Wagner, Electron. Lett. 22, 1029 (1986).
    [CrossRef]
  2. C. D. Poole and C. R. Giles, Opt. Lett. 13, 155 (1988).
    [CrossRef]
  3. N. Gisin, Opt. Commun. 86, 371 (1991).
    [CrossRef]
  4. B. L. Heffner, IEEE Photon. Technol. Lett. 4, 1066 (1992).
    [CrossRef]
  5. N. Gisin, J. P. von der Weid, and J. P. Pellaux, J. Lightwave Technol. 9, 821 (1991).
    [CrossRef]
  6. N. Gisin and J. P. Pellaux, Opt. Commun. 89, 316 (1992)B. Perny, C. Zimmer, F. Prieto, and N. Gisin, Electron. Lett. 32, 680 (1996).
    [CrossRef]
  7. B. Huttner and N. Gisin, Opt. Lett. 22, 504 (1997).
    [CrossRef] [PubMed]
  8. N. Gisin and B. Huttner, Opt. Commun. 142, 119 (1997).
    [CrossRef]
  9. A. Elamari, N. Gisin, B. Perny, H. Zbinden, and C. W. Zimmer, J. Lightwave Technol. 16, 332 (1998).
    [CrossRef]
  10. B. Huttner, B. Gisin, and N. Gisin, in Proceedings of the Symposium on Optical Fiber Measurements (National Institute of Standards and Technology, Boulder, Colo., 1998), pp. 49–52.
  11. R. Passy, N. Gisin, J. P. Pellaux, and P. Stamp, in Proceedings of the Optical Fiber Measurement Conference, 1991 (National Physical Laboratory, Teddington, UK), pp. 85–88.

1998 (1)

1997 (2)

B. Huttner and N. Gisin, Opt. Lett. 22, 504 (1997).
[CrossRef] [PubMed]

N. Gisin and B. Huttner, Opt. Commun. 142, 119 (1997).
[CrossRef]

1992 (2)

N. Gisin and J. P. Pellaux, Opt. Commun. 89, 316 (1992)B. Perny, C. Zimmer, F. Prieto, and N. Gisin, Electron. Lett. 32, 680 (1996).
[CrossRef]

B. L. Heffner, IEEE Photon. Technol. Lett. 4, 1066 (1992).
[CrossRef]

1991 (2)

N. Gisin, J. P. von der Weid, and J. P. Pellaux, J. Lightwave Technol. 9, 821 (1991).
[CrossRef]

N. Gisin, Opt. Commun. 86, 371 (1991).
[CrossRef]

1988 (1)

1986 (1)

C. D. Poole and R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

Elamari, A.

Giles, C. R.

Gisin, B.

B. Huttner, B. Gisin, and N. Gisin, in Proceedings of the Symposium on Optical Fiber Measurements (National Institute of Standards and Technology, Boulder, Colo., 1998), pp. 49–52.

Gisin, N.

A. Elamari, N. Gisin, B. Perny, H. Zbinden, and C. W. Zimmer, J. Lightwave Technol. 16, 332 (1998).
[CrossRef]

B. Huttner and N. Gisin, Opt. Lett. 22, 504 (1997).
[CrossRef] [PubMed]

N. Gisin and B. Huttner, Opt. Commun. 142, 119 (1997).
[CrossRef]

N. Gisin and J. P. Pellaux, Opt. Commun. 89, 316 (1992)B. Perny, C. Zimmer, F. Prieto, and N. Gisin, Electron. Lett. 32, 680 (1996).
[CrossRef]

N. Gisin, Opt. Commun. 86, 371 (1991).
[CrossRef]

N. Gisin, J. P. von der Weid, and J. P. Pellaux, J. Lightwave Technol. 9, 821 (1991).
[CrossRef]

B. Huttner, B. Gisin, and N. Gisin, in Proceedings of the Symposium on Optical Fiber Measurements (National Institute of Standards and Technology, Boulder, Colo., 1998), pp. 49–52.

R. Passy, N. Gisin, J. P. Pellaux, and P. Stamp, in Proceedings of the Optical Fiber Measurement Conference, 1991 (National Physical Laboratory, Teddington, UK), pp. 85–88.

Heffner, B. L.

B. L. Heffner, IEEE Photon. Technol. Lett. 4, 1066 (1992).
[CrossRef]

Huttner, B.

N. Gisin and B. Huttner, Opt. Commun. 142, 119 (1997).
[CrossRef]

B. Huttner and N. Gisin, Opt. Lett. 22, 504 (1997).
[CrossRef] [PubMed]

B. Huttner, B. Gisin, and N. Gisin, in Proceedings of the Symposium on Optical Fiber Measurements (National Institute of Standards and Technology, Boulder, Colo., 1998), pp. 49–52.

Passy, R.

R. Passy, N. Gisin, J. P. Pellaux, and P. Stamp, in Proceedings of the Optical Fiber Measurement Conference, 1991 (National Physical Laboratory, Teddington, UK), pp. 85–88.

Pellaux, J. P.

N. Gisin and J. P. Pellaux, Opt. Commun. 89, 316 (1992)B. Perny, C. Zimmer, F. Prieto, and N. Gisin, Electron. Lett. 32, 680 (1996).
[CrossRef]

N. Gisin, J. P. von der Weid, and J. P. Pellaux, J. Lightwave Technol. 9, 821 (1991).
[CrossRef]

R. Passy, N. Gisin, J. P. Pellaux, and P. Stamp, in Proceedings of the Optical Fiber Measurement Conference, 1991 (National Physical Laboratory, Teddington, UK), pp. 85–88.

Perny, B.

Poole, C. D.

C. D. Poole and C. R. Giles, Opt. Lett. 13, 155 (1988).
[CrossRef]

C. D. Poole and R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

Stamp, P.

R. Passy, N. Gisin, J. P. Pellaux, and P. Stamp, in Proceedings of the Optical Fiber Measurement Conference, 1991 (National Physical Laboratory, Teddington, UK), pp. 85–88.

von der Weid, J. P.

N. Gisin, J. P. von der Weid, and J. P. Pellaux, J. Lightwave Technol. 9, 821 (1991).
[CrossRef]

Wagner, R. E.

C. D. Poole and R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

Zbinden, H.

Zimmer, C. W.

Electron. Lett. (1)

C. D. Poole and R. E. Wagner, Electron. Lett. 22, 1029 (1986).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

B. L. Heffner, IEEE Photon. Technol. Lett. 4, 1066 (1992).
[CrossRef]

J. Lightwave Technol. (2)

N. Gisin, J. P. von der Weid, and J. P. Pellaux, J. Lightwave Technol. 9, 821 (1991).
[CrossRef]

A. Elamari, N. Gisin, B. Perny, H. Zbinden, and C. W. Zimmer, J. Lightwave Technol. 16, 332 (1998).
[CrossRef]

Opt. Commun. (3)

N. Gisin and J. P. Pellaux, Opt. Commun. 89, 316 (1992)B. Perny, C. Zimmer, F. Prieto, and N. Gisin, Electron. Lett. 32, 680 (1996).
[CrossRef]

N. Gisin, Opt. Commun. 86, 371 (1991).
[CrossRef]

N. Gisin and B. Huttner, Opt. Commun. 142, 119 (1997).
[CrossRef]

Opt. Lett. (2)

Other (2)

B. Huttner, B. Gisin, and N. Gisin, in Proceedings of the Symposium on Optical Fiber Measurements (National Institute of Standards and Technology, Boulder, Colo., 1998), pp. 49–52.

R. Passy, N. Gisin, J. P. Pellaux, and P. Stamp, in Proceedings of the Optical Fiber Measurement Conference, 1991 (National Physical Laboratory, Teddington, UK), pp. 85–88.

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Figures (3)

Fig. 1
Fig. 1

Interferogram for a concatenation of three elements. The concatenation is made with one pure PDL element (7  dB), an axis along e^2, sandwiched between two opposite HiBi fibers, with PMD 0.7  ps, and axes along e^1 and -e^1. The axis of the PDL element is thus at 45° to the axes of the HiBi fibers. The setup is shown in the inset. The PMD value obtained from this measurement is 0.97  ps, in agreement with the result of a simulation with the same parameters (0.96  ps).

Fig. 2
Fig. 2

Measurement of the DGD for the same concatenation as in Fig.  1. The solid curve represents the DGD of the concatenation of Fig.  1, measured with JME. The average value of the DGD (dashed line) is 0.075  ps. This is to be compared with the value predicted by the interferometric method of 0.97 (dotted line). The value of the DGD for this concatenation, predicted by the analytic expression of Eqs.  (2) and (3), is zero.

Fig. 3
Fig. 3

Computer simulation with a more complicated concatenation. The concatenation is made with 27 elements: 14  HiBi fibers with 1-ps DGD and 13  PDL elements with PDL varying from 1 to 7  dB. The LED used has a FWHM of 50  nm. The DGD is zero over the full frequency range of the LED, but the interferogram clearly shows that there is pulse spreading. The calculated value of the PMD is 3.44  ps, which is confirmed by a simulation of pulse transmission through this device, as shown in the inset. The input pulse has a 7-ps FWHM and is represented by the dotted curve. The solid curve is the output pulse, which has been broadened by the concatenation. Its FWHM is 7.8  ps, in excellent agreement with the value calculated from the PMD measured with the interferometric method.

Equations (3)

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

ωΨoutω=ωTT-1Ψoutω=-iχ2Ψoutω,
χ2=β12+β32+2β1β3coshαe^1·e^3+1-coshα×e^1·e^2e^2·e^3-isinhαe^1·e^2×e^3,
χ2=-2β2coshα-1<0.

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