Abstract

We study the spectral properties of polarization-dependent loss (PDL) in fiber routes with multiple spans and amplifiers. In these systems, PDL stems from a small number of lumped WDM components interconnected by PDL-free fibers, a configuration that is poorly described by the popular model of distributed PDL. We derive transparent and practical analytical expressions for the autocorrelation functions of the PDL vector and of the square PDL magnitude and show that they are strongly affected by the order of the individual PDL elements.

© 2011 Optical Society of America

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  1. M. Shtaif, Opt. Express 16, 13918 (2008).
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    [CrossRef]
  7. M. Shtaif and A. Mecozzi, Opt. Lett. 25, 707 (2000).
    [CrossRef]
  8. S. Hadjifaradji, S. Yang, L. Chen, and X. Bao, IEEE Photon. Technol. Lett. 18, 2362 (2006).
    [CrossRef]
  9. N. Gisin, Opt. Commun. 114, 399 (1995).
    [CrossRef]
  10. J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. USA 97, 4541 (2000).
    [CrossRef] [PubMed]
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    [CrossRef]
  12. C. Antonelli and A. Mecozzi, Opt. Lett. 30, 1626 (2005).
    [CrossRef] [PubMed]
  13. M. Karlsson and J. Brentel, Opt. Lett. 24, 939 (1999).
    [CrossRef]
  14. L. Chen, S. Hadjifaradji, D. S. Waddy, and X. Bao, Proc. SPIE 5260, 377 (2003).
    [CrossRef]

2011 (1)

2009 (1)

J. Jiang, D. Richards, S. Oliva, P. Green, and R. Hui, Electron. Lett. 45, 123 (2009).
[CrossRef]

2008 (2)

J. Jiang, D. Richards, C. Allen, S. Oliva, and R. Hui, Opt. Commun. 281, 4631 (2008).
[CrossRef]

M. Shtaif, Opt. Express 16, 13918 (2008).
[CrossRef] [PubMed]

2006 (1)

S. Hadjifaradji, S. Yang, L. Chen, and X. Bao, IEEE Photon. Technol. Lett. 18, 2362 (2006).
[CrossRef]

2005 (1)

2003 (2)

A. Galtarossa and L. Palmieri, IEEE Photon. Technol. Lett. 15, 57 (2003).
[CrossRef]

L. Chen, S. Hadjifaradji, D. S. Waddy, and X. Bao, Proc. SPIE 5260, 377 (2003).
[CrossRef]

2002 (1)

A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 14, 313 (2002).
[CrossRef]

2000 (3)

M. Shtaif and A. Mecozzi, Opt. Lett. 25, 707 (2000).
[CrossRef]

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

B. Huttner, C. Geiser, and N. Gisin, IEEE J. Quantum Electron. 6, 317 (2000).
[CrossRef]

1999 (1)

1995 (1)

N. Gisin, Opt. Commun. 114, 399 (1995).
[CrossRef]

Allen, C.

J. Jiang, D. Richards, C. Allen, S. Oliva, and R. Hui, Opt. Commun. 281, 4631 (2008).
[CrossRef]

Antonelli, C.

Bao, X.

S. Hadjifaradji, S. Yang, L. Chen, and X. Bao, IEEE Photon. Technol. Lett. 18, 2362 (2006).
[CrossRef]

L. Chen, S. Hadjifaradji, D. S. Waddy, and X. Bao, Proc. SPIE 5260, 377 (2003).
[CrossRef]

Birk, M.

Brentel, J.

Chen, L.

S. Hadjifaradji, S. Yang, L. Chen, and X. Bao, IEEE Photon. Technol. Lett. 18, 2362 (2006).
[CrossRef]

L. Chen, S. Hadjifaradji, D. S. Waddy, and X. Bao, Proc. SPIE 5260, 377 (2003).
[CrossRef]

Galtarossa, A.

A. Galtarossa and L. Palmieri, IEEE Photon. Technol. Lett. 15, 57 (2003).
[CrossRef]

Geiser, C.

B. Huttner, C. Geiser, and N. Gisin, IEEE J. Quantum Electron. 6, 317 (2000).
[CrossRef]

Gisin, N.

B. Huttner, C. Geiser, and N. Gisin, IEEE J. Quantum Electron. 6, 317 (2000).
[CrossRef]

N. Gisin, Opt. Commun. 114, 399 (1995).
[CrossRef]

Gordon, J. P.

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

Green, P.

J. Jiang, D. Richards, S. Oliva, P. Green, and R. Hui, Electron. Lett. 45, 123 (2009).
[CrossRef]

Hadjifaradji, S.

S. Hadjifaradji, S. Yang, L. Chen, and X. Bao, IEEE Photon. Technol. Lett. 18, 2362 (2006).
[CrossRef]

L. Chen, S. Hadjifaradji, D. S. Waddy, and X. Bao, Proc. SPIE 5260, 377 (2003).
[CrossRef]

Hui, R.

J. Jiang, D. Richards, S. Oliva, P. Green, and R. Hui, Electron. Lett. 45, 123 (2009).
[CrossRef]

J. Jiang, D. Richards, C. Allen, S. Oliva, and R. Hui, Opt. Commun. 281, 4631 (2008).
[CrossRef]

Huttner, B.

B. Huttner, C. Geiser, and N. Gisin, IEEE J. Quantum Electron. 6, 317 (2000).
[CrossRef]

Jiang, J.

J. Jiang, D. Richards, S. Oliva, P. Green, and R. Hui, Electron. Lett. 45, 123 (2009).
[CrossRef]

J. Jiang, D. Richards, C. Allen, S. Oliva, and R. Hui, Opt. Commun. 281, 4631 (2008).
[CrossRef]

Karlsson, M.

Kogelnik, H.

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

Magill, P.

Mecozzi, A.

Nelson, L. E.

Oliva, S.

J. Jiang, D. Richards, S. Oliva, P. Green, and R. Hui, Electron. Lett. 45, 123 (2009).
[CrossRef]

J. Jiang, D. Richards, C. Allen, S. Oliva, and R. Hui, Opt. Commun. 281, 4631 (2008).
[CrossRef]

Palmieri, L.

A. Galtarossa and L. Palmieri, IEEE Photon. Technol. Lett. 15, 57 (2003).
[CrossRef]

Rapp, L.

Richards, D.

J. Jiang, D. Richards, S. Oliva, P. Green, and R. Hui, Electron. Lett. 45, 123 (2009).
[CrossRef]

J. Jiang, D. Richards, C. Allen, S. Oliva, and R. Hui, Opt. Commun. 281, 4631 (2008).
[CrossRef]

Schex, A.

Shtaif, M.

Waddy, D. S.

L. Chen, S. Hadjifaradji, D. S. Waddy, and X. Bao, Proc. SPIE 5260, 377 (2003).
[CrossRef]

Yang, S.

S. Hadjifaradji, S. Yang, L. Chen, and X. Bao, IEEE Photon. Technol. Lett. 18, 2362 (2006).
[CrossRef]

Electron. Lett. (1)

J. Jiang, D. Richards, S. Oliva, P. Green, and R. Hui, Electron. Lett. 45, 123 (2009).
[CrossRef]

IEEE J. Quantum Electron. (1)

B. Huttner, C. Geiser, and N. Gisin, IEEE J. Quantum Electron. 6, 317 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

A. Mecozzi and M. Shtaif, IEEE Photon. Technol. Lett. 14, 313 (2002).
[CrossRef]

A. Galtarossa and L. Palmieri, IEEE Photon. Technol. Lett. 15, 57 (2003).
[CrossRef]

S. Hadjifaradji, S. Yang, L. Chen, and X. Bao, IEEE Photon. Technol. Lett. 18, 2362 (2006).
[CrossRef]

Opt. Commun. (2)

N. Gisin, Opt. Commun. 114, 399 (1995).
[CrossRef]

J. Jiang, D. Richards, C. Allen, S. Oliva, and R. Hui, Opt. Commun. 281, 4631 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

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

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

Proc. SPIE (1)

L. Chen, S. Hadjifaradji, D. S. Waddy, and X. Bao, Proc. SPIE 5260, 377 (2003).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Normalized ACF of PDL vector (left column) and square PDL magnitude (right column). Details are provided in the text.

Fig. 2
Fig. 2

The blue curves are the same as in Fig. 1. The red (green) curves show the same ACFs as the blue curves; however, the mean DGDs are sorted in ascending (descending) order and the PDL elements are sorted in descending (ascending) order.

Equations (15)

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T ( ω ) = M ( γ ) U ( ω ) = U ( ω ) [ U ( ω ) M ( γ ) U ( ω ) ] = U ( ω ) M [ R ( ω ) γ ] ,
T N ( ω ) = U N ( ω ) U 1 ( ω ) M [ γ N ( ω ) ] M [ γ 1 ( ω ) ] ,
γ k ( ω ) = R 1 ( ω ) R k ( ω ) γ k .
Γ ( ω ) · Γ ( ω ) = k , h = 1 N γ k ( ω ) · γ h ( ω ) ,
γ k ( ω ) · γ h ( ω ) = δ h , k γ k 2 exp [ t k Δ ω 2 τ 2 3 ] ,
f Γ ( Δ ω ) = ( k = 1 N γ k 2 ) 1 k = 1 N γ k 2 exp [ t k Δ ω 2 τ 2 3 ] .
Γ N 2 ( ω ) Γ N 1 2 ( ω ) + γ N 2 + 2 Γ N 1 ( ω ) · γ N ( ω ) .
Γ N 2 ( ω ) Γ N 2 ( ω ) = Γ N 1 2 ( ω ) Γ N 1 2 ( ω ) + Γ N 2 2 Γ N 1 2 2 + 4 Γ N 1 ( ω ) · γ N ( ω ) Γ N 1 ( ω ) · γ N ( ω ) ,
Γ N 2 ( ω ) Γ N 2 ( ω ) = Γ N 2 2 + 4 k = 2 N Γ k 1 ( ω ) · γ k ( ω ) × Γ k 1 ( ω ) · γ k ( ω ) .
γ k ( ω ) = R k ( ω ) γ k ,
Γ k ( ω ) = R k ( ω ) R 1 ( ω ) Γ k ( ω ) ,
Γ N 2 ( ω ) Γ N 2 ( ω ) = Γ N 2 2 + 4 3 k = 2 N γ k ( ω ) · γ k ( ω ) × Γ k 1 ( ω ) · Γ k 1 ( ω ) .
γ k ( ω ) · γ k ( ω ) = γ k 2 exp ( Δ ω 2 τ k 2 / 3 ) ,
Γ k ( ω ) · Γ k ( ω ) = h = 1 k γ h 2 exp [ t k t h 3 τ 2 Δ ω 2 ] .
f Γ 2 ( Δ ω ) = ( k = 2 N h = 1 k 1 γ k 2 γ h 2 ) 1 k = 2 N h = 1 k 1 γ k 2 γ h 2 × exp [ ( t k t h ) τ 2 Δ ω 2 / 3 ] .

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