Abstract

We derive a compact equation characterizing the polarization property of an optical fiber with linear birefringence. Under particular conditions the solution of this equation gives the differential group delay as a simple functional of the birefringence autocorrelation function.

© 2008 Optical Society of America

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References

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  1. P. K. A. Wai and C. Menyuk, J. Lightwave Technol. 14, 148 (1996).
    [CrossRef]
  2. L. Palmieri, J. Lightwave Technol. 24, 4075 (2006).
    [CrossRef]
  3. J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. USA 97, 4541 (2000).
    [CrossRef] [PubMed]
  4. A. Galtarossa, L. Palmieri, and L. Schenato, Opt. Lett. 31, 2275 (2006).
    [CrossRef] [PubMed]
  5. A. Galtarossa, P. Griggio, L. Palmieri, and A. Pizzinat, Opt. Lett. 28, 1639 (2003).
    [CrossRef] [PubMed]
  6. A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, IEEE Photon. Technol. Lett. 15, 819 (2003).
    [CrossRef]
  7. M. Lax, Rev. Mod. Phys. 38, 541 (1966).
    [CrossRef]
  8. J. P. Gordon, J. Opt. Fiber. Commun. Rep. 1, 210 (2004).
    [CrossRef]

2006 (2)

2004 (1)

J. P. Gordon, J. Opt. Fiber. Commun. Rep. 1, 210 (2004).
[CrossRef]

2003 (2)

A. Galtarossa, P. Griggio, L. Palmieri, and A. Pizzinat, Opt. Lett. 28, 1639 (2003).
[CrossRef] [PubMed]

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, IEEE Photon. Technol. Lett. 15, 819 (2003).
[CrossRef]

2000 (1)

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

1996 (1)

P. K. A. Wai and C. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

1966 (1)

M. Lax, Rev. Mod. Phys. 38, 541 (1966).
[CrossRef]

Galtarossa, A.

Gordon, J. P.

J. P. Gordon, J. Opt. Fiber. Commun. Rep. 1, 210 (2004).
[CrossRef]

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

Griggio, P.

Kogelnik, H.

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

Lax, M.

M. Lax, Rev. Mod. Phys. 38, 541 (1966).
[CrossRef]

Marks, B. S.

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, IEEE Photon. Technol. Lett. 15, 819 (2003).
[CrossRef]

Menyuk, C.

P. K. A. Wai and C. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

Menyuk, C. R.

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, IEEE Photon. Technol. Lett. 15, 819 (2003).
[CrossRef]

Palmieri, L.

Pizzinat, A.

A. Galtarossa, P. Griggio, L. Palmieri, and A. Pizzinat, Opt. Lett. 28, 1639 (2003).
[CrossRef] [PubMed]

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, IEEE Photon. Technol. Lett. 15, 819 (2003).
[CrossRef]

Schenato, L.

Wai, P. K. A.

P. K. A. Wai and C. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Pizzinat, B. S. Marks, L. Palmieri, C. R. Menyuk, and A. Galtarossa, IEEE Photon. Technol. Lett. 15, 819 (2003).
[CrossRef]

J. Lightwave Technol. (2)

P. K. A. Wai and C. Menyuk, J. Lightwave Technol. 14, 148 (1996).
[CrossRef]

L. Palmieri, J. Lightwave Technol. 24, 4075 (2006).
[CrossRef]

J. Opt. Fiber. Commun. Rep. (1)

J. P. Gordon, J. Opt. Fiber. Commun. Rep. 1, 210 (2004).
[CrossRef]

Opt. Lett. (2)

Proc. Natl. Acad. Sci. USA (1)

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

Rev. Mod. Phys. (1)

M. Lax, Rev. Mod. Phys. 38, 541 (1966).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Ratio of the mean DGD obtained for a given Z, τ ( Z ) to that obtained with no spin τ un , versus the ratio of the period of the birefringence flips Z to the birefringence correlation length, for large z. Solid curve: Plot of Eq. (20); squares: Results of a Monte Carlo simulation performed with the random modulus model of the birefringence.

Equations (27)

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d τ d z = β ( z ) τ + β ( z ) ω ,
d τ 2 d z = 2 ω β ( z ) τ ( z ) .
β = β 1 e ̂ 1 + β 2 e ̂ 2 .
τ = τ + τ 3 e ̂ 3 .
d τ 2 d z = 2 ω β ( z ) τ ( z ) .
d τ 2 d z = 2 ω β ( z ) 0 z d z d τ ( z ) d z .
d τ d z = ( β 1 e ̂ 2 + β 2 e ̂ 1 ) τ 3 + β 1 e ̂ 1 + β 2 e ̂ 2 ω .
d τ 2 d z = 2 ω 2 0 z d z { [ β 1 ( z ) β 2 ( z ) β 2 ( z ) β 1 ( z ) ] ω τ 3 ( z ) + β 1 ( z ) β 1 ( z ) + β 2 ( z ) β 2 ( z ) } .
d τ 3 d z = e ̂ 3 β ( z ) 0 z d z τ ( z ) d z .
d τ 3 d z = 1 ω 0 z d z { [ β 1 ( z ) β 1 ( z ) + β 2 ( z ) β 2 ( z ) ] ω τ 3 ( z ) + β 1 ( z ) β 2 ( z ) β 2 ( z ) β 1 ( z ) } .
β ± = β 1 ± i β 2 .
d τ 2 d z = 2 ω 2 Re 0 z d z β ( z ) β + ( z ) [ 1 i ω τ 3 ( z ) ] ,
d τ 3 d z = 1 ω Im 0 z d z β ( z ) β + ( z ) [ 1 i ω τ 3 ( z ) ] .
T = ω 2 τ 2 2 + i ω τ 3 ,
d T d z = 0 z d z β ( z ) β + ( z ) [ 1 i Im T ( z ) ] .
T ( z ) = 0 z d z 0 z d z β ( z ) β + ( z ) [ 1 i Im T ( z ) ] .
β + ( z ) β ( z ) = β 0 2 exp ( z z L F ) .
T ( z ) = κ 1 ( z ) i n = 2 ( 1 ) n κ n ( z ) ,
κ n ( z ) = 0 z d z 1 0 z 2 n 1 d z 2 n β ( z 1 ) β + ( z 2 ) × Re [ β ( z 3 ) β + ( z 4 ) ] Re [ β ( z 2 n 3 ) β + ( z 2 n 2 ) ] × Im [ β ( z 2 n 1 ) β + ( z 2 n ) ] ,
2 i Im [ β ( z 2 n 1 ) β + ( z 2 n ) ] = β ( z 2 n 1 ) β + ( z 2 n ) β ( z 2 n ) β + ( z 2 n 1 ) ,
β + ( z k ) β ( z 2 n 1 ) β ( z h ) β + ( z 2 n ) = β 0 2 exp [ ( z k + z 2 n 1 z h + z 2 n ) L F ] .
β + ( z k ) β ( z 2 n ) β ( z h ) β + ( z 2 n 1 ) = β 0 2 exp [ ( z k + z 2 n z h + z 2 n 1 ) L F ] .
τ ( z ) 2 = 2 ω 2 0 z d z 0 z d z β ( z ) β ( z ) .
β ± ( z ) = exp [ ± 2 i A ( z ) ] β un , ± ( z ) .
A n ( z ) = ϑ + a n u ( z ) , a n = π 4 + n π 2 , n = 0 , 1 , 2 , ,
β ( z ) β + ( z ) = β 0 2 exp { 2 i [ A ( z ) A ( z ) ] z z L F } .
d T d z = 0 z d z β ( z ) β + ( z ) [ 1 i Im T ( z ) ] .

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