Abstract

We describe how to calculate the Jones matrix transfer function of a fiber if its principal states of polarization and its differential group delay as functions of frequency are known. Using two counterexamples related to second-order polarization mode dispersion (PMD), we also show that a previous method used for the same purpose induces overestimation of second-order PMD effects by a factor of 2. Our new method is used to solve the problem for both counterexamples.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. D. Poole and R. E. Wagner, Electron. Lett. 22, 1029 (1986).
    [CrossRef]
  2. G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
    [CrossRef]
  3. F. Bruyère, Opt. Fiber Technol. 2, 269 (1996).
    [CrossRef]
  4. D. Penninckx and F. Bruyère, in Optical Fiber Communication Conference, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper ThR2.
  5. D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, San Diego, Calif., 1990), Chap. 5.
  6. C. Francia, F. Bruyère, D. Penninckx, and M. Chbat, IEEE Photon. Technol. Lett. 10, 1739 (1998).
    [CrossRef]

1998 (1)

C. Francia, F. Bruyère, D. Penninckx, and M. Chbat, IEEE Photon. Technol. Lett. 10, 1739 (1998).
[CrossRef]

1996 (1)

F. Bruyère, Opt. Fiber Technol. 2, 269 (1996).
[CrossRef]

1991 (1)

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

1986 (1)

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

Bruyère, F.

C. Francia, F. Bruyère, D. Penninckx, and M. Chbat, IEEE Photon. Technol. Lett. 10, 1739 (1998).
[CrossRef]

F. Bruyère, Opt. Fiber Technol. 2, 269 (1996).
[CrossRef]

D. Penninckx and F. Bruyère, in Optical Fiber Communication Conference, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper ThR2.

Chbat, M.

C. Francia, F. Bruyère, D. Penninckx, and M. Chbat, IEEE Photon. Technol. Lett. 10, 1739 (1998).
[CrossRef]

Foschini, G. J.

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

Francia, C.

C. Francia, F. Bruyère, D. Penninckx, and M. Chbat, IEEE Photon. Technol. Lett. 10, 1739 (1998).
[CrossRef]

Kliger, D. S.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, San Diego, Calif., 1990), Chap. 5.

Lewis, J. W.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, San Diego, Calif., 1990), Chap. 5.

Penninckx, D.

C. Francia, F. Bruyère, D. Penninckx, and M. Chbat, IEEE Photon. Technol. Lett. 10, 1739 (1998).
[CrossRef]

D. Penninckx and F. Bruyère, in Optical Fiber Communication Conference, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper ThR2.

Poole, C. D.

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

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

Randall, C. E.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, San Diego, Calif., 1990), Chap. 5.

Wagner, R. E.

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

Electron. Lett. (1)

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

IEEE Photon. Technol. Lett. (1)

C. Francia, F. Bruyère, D. Penninckx, and M. Chbat, IEEE Photon. Technol. Lett. 10, 1739 (1998).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Fiber Technol. (1)

F. Bruyère, Opt. Fiber Technol. 2, 269 (1996).
[CrossRef]

Other (2)

D. Penninckx and F. Bruyère, in Optical Fiber Communication Conference, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper ThR2.

D. S. Kliger, J. W. Lewis, and C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, San Diego, Calif., 1990), Chap. 5.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Assumed (solid line) and actual [DGDbω, dashed curve] DGD as a function of frequency for counter-example (b).

Fig. 2
Fig. 2

Assumed (filled circles) and actual (open circles) PSP’s over the Poincaré sphere as a function of frequency for counterexample (b). These values are typical for a fiber that exhibits 30-ps PMD. The circles are plotted every 1 GHz. The actual rotation rate of the PSP’s over the Poincaré sphere is equal not to 2k but to 4k, yielding an overestimation by a factor of 2 of second-order PMD effects.

Equations (10)

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

R=cos θ cos -i sin θ sin -sin θ cos +i cos θ sin sin θ cos +i cos θ sin cos θ cos +i sin θ sin ,  Pω=expi2ωdgd00exp-i2ωdgd,
DGDaω=ωωdgdω=dgd0+2 dgd1ω.
DGDbω=dgd0+16k2 sin2dgd0ω21/2.
Θbω=2kω+oω2,  Ebω=12k dgd0ω2+oω2.
Mωω=MωAω,
Mω=m1ωm2ω-m2*ωm1*ω,  Aω=a1ωa2ω-a2*ωa1*ω=Rωi2DGDω00-i2DGDωR-1ω.
m1ωm2ω=a1ω-a2*ωa1ωa1*ωm1ωm2ω,
m1ω=C1expiα-ω+2α-dgd0 exp-iα+ω+C2expiα+ω+2α+dgd0 exp-iα-ω,  m2ω=iC1-expiα-ω+2α-dgd0 exp-iα+ω+iC2-expiα+ω+2α+dgd0 exp-iα-ω,
α±=k±12dgd02+4k21/2.
C1=-12 exp-iπ41dgd02+4k21/2idgd02+α+,  C2=12exp+iπ41dgd02+4k21/2dgd02-iα-.

Metrics