Abstract

We give the exact analytical expression for the autocorrelation function of the polarization mode dispersion (PMD) vector of a fiber link in which first-order PMD is compensated for at the output. We use the result to obtain the mean-square width of a Gaussian pulse in the presence of a first-order PMD compensator.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Sunnerud, M. Karlsson, and P. A. Andrekson, IEEE Photon. Technol. Lett. 12, 50 (2000).
    [CrossRef]
  2. J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. U.S.A. 97, 4541 (2000).
    [CrossRef]
  3. M. Karlsson, Opt. Lett. 23, 688 (1998).
    [CrossRef]
  4. M. Karlsson and J. Brentel, Opt. Lett. 24, 939 (1999).
    [CrossRef]
  5. M. Shtaif, A. Mecozzi, and J. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
    [CrossRef]
  6. S. Kim, J. Lightwave Technol. 20, 1118 (2002).
    [CrossRef]

2002 (1)

2000 (3)

H. Sunnerud, M. Karlsson, and P. A. Andrekson, IEEE Photon. Technol. Lett. 12, 50 (2000).
[CrossRef]

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. U.S.A. 97, 4541 (2000).
[CrossRef]

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

1999 (1)

1998 (1)

Andrekson, P. A.

H. Sunnerud, M. Karlsson, and P. A. Andrekson, IEEE Photon. Technol. Lett. 12, 50 (2000).
[CrossRef]

Brentel, J.

Gordon, J. P.

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. U.S.A. 97, 4541 (2000).
[CrossRef]

Karlsson, M.

H. Sunnerud, M. Karlsson, and P. A. Andrekson, IEEE Photon. Technol. Lett. 12, 50 (2000).
[CrossRef]

M. Karlsson and J. Brentel, Opt. Lett. 24, 939 (1999).
[CrossRef]

M. Karlsson, Opt. Lett. 23, 688 (1998).
[CrossRef]

Kim, S.

Kogelnik, H.

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. U.S.A. 97, 4541 (2000).
[CrossRef]

Mecozzi, A.

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

Nagel, J.

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

Shtaif, M.

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

Sunnerud, H.

H. Sunnerud, M. Karlsson, and P. A. Andrekson, IEEE Photon. Technol. Lett. 12, 50 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

H. Sunnerud, M. Karlsson, and P. A. Andrekson, IEEE Photon. Technol. Lett. 12, 50 (2000).
[CrossRef]

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

J. Lightwave Technol. (1)

Opt. Lett. (2)

Proc. Natl. Acad. Sci. U.S.A. (1)

J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. U.S.A. 97, 4541 (2000).
[CrossRef]

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

Normalized autocorrelation functions of the PMD vector g c ( ω , ω ) L versus the dimensionless quantities ω L and ω L with the expression of Ref. [1] (top) and with the exact expression of Eq. (7) (bottom).

Fig. 2
Fig. 2

Normalized root-mean-square pulse width versus τ T 0 . Dotted curve, the case without compensation; solid curve, plot of Eq. (16); dashed curve, plot of the expression from Ref. [1]. Dots and squares refer to a Monte Carlo simulation over 2 × 10 3 fiber instances.

Equations (21)

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

τ out ( ω ) = i = 1 N R ω ( L , z i ) Δ β i ,
R ω ( L , z i ) = exp ( ω Δ β N × ) exp ( ω Δ β i × ) .
τ in ( ω ) = R ω τ out = i = 1 N R ω ( 0 , z i 1 ) Δ β i ,
τ c ( ω ) = τ in ( ω ) + R ω Δ β comp .
Δ β comp = τ ( 0 ) = i = 1 N Δ β i ,
g ( ω , ω ) = 3 ( ω ω ) 2 { 1 exp [ ( ω ω ) 2 L 3 ] } .
g c ( ω , ω ) = g ( ω , ω ) g 1 ( ω , ω ) g 1 ( ω , ω ) + g 2 ( ω , ω ) ,
g 2 ( ω , ω ) = i , j R ω Δ β i R ω Δ β j = i , j Δ β i R ω R ω Δ β j .
g 2 ( ω , ω ) = i Δ β i R ω R ω Δ β i .
exp ( ω Δ β k × ) exp ( ω Δ β k × ) = 1 3 { 1 + 2 cos [ ( ω ω ) Δ z ] } ,
g 2 ( ω , ω ) = exp [ ( ω ω ) 2 L 3 ] L .
g 1 ( ω , ω ) = 0 L exp [ ω 2 ( L z ) + ( ω ω ) 2 z 3 ] d z = 3 ω 2 ( ω ω ) 2 { exp [ ( ω ω ) 2 L 3 ] exp ( ω 2 L 3 ) } .
τ c ( ω ) = τ in ( ω ) τ ( 0 )
g c ( ω , ω ) = g ( ω , ω ) g 1 ( ω , 0 ) g 1 ( ω , 0 ) + L .
T 2 = T 0 2 + 1 4 d ω 2 π f ̃ ( ω ) 2 τ c 2 ( ω ) 1 4 d ω 2 π d ω 2 π f ̃ ( ω ) 2 f ̃ ( ω ) 2 [ τ c ( ω ) s ̂ ] [ τ c ( ω ) s ̂ ] .
T 2 = T 0 2 [ 1 + 1 4 ( I 0 I 1 ) ] ,
I 0 = 1 T 0 2 d ω 2 π f ̃ ( ω ) 2 g c ( ω , ω ) ,
I 1 = 1 3 T 0 2 d ω 2 π d ω 2 π f ̃ ( ω ) 2 f ̃ ( ω ) 2 g c ( ω , ω ) .
f ( t ) = 1 ( 2 π T 0 2 ) 1 4 exp ( t 2 4 T 0 2 ) ,
I 0 = 8 [ x 3 ( 1 + 2 3 x 1 ) ] ,
I 1 = 2 ( 1 + 4 3 x 1 ) + 4 3 x ( 1 + 4 3 x ) 1 2 4 [ tan 1 ( 3 + 2 x 2 9 + 6 x ) tan 1 ( 3 2 x 2 9 + 12 x ) ] .

Metrics