Abstract

The effect of local PMD and PDL directional correlation is considered for the first time in a single mode fiber communication link. It is shown that the autocorrelation between the real and imaginary part of the complex principal state vector is nonzero in general. Experimental results verifying the local correlation between PMD and PDL directional are reported.

© 2003 Optical Society of America

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References

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  1. J.P. Gordon and H. Kogelnik, �??PMD fundamentals: Polarization mode dispersion in optical fibers,�?? Proc. Nat. Acad. Sci. 97, 4541 (2000).
    [CrossRef] [PubMed]
  2. N. Gisin and B. Huttner, �??Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers,�?? Opt. Commun. 142, 119 (1997).
    [CrossRef]
  3. Ricardo Feced, Seb J. Savory and Anagnostis Hadjifotiou, �??Interaction between polarization mode dispersion and polarization-dependent losses in optical communication links,�?? J. Opt. Soc. Am. B 20, 424 (2003).
    [CrossRef]
  4. Y. Li and A. Yariv, �??Solution to the dynamical equation of polarization-mode dispersion and polarization-dependent losses,�?? J. Opt. Soc. Am. B 17, 1821 (2000).
    [CrossRef]
  5. Liang Chen, Saeed Hadjifaradji, David S. Waddy and Xiaoyi Bao, �??Principal state vector autocorrelation in a fiber optic system having both polarization-mode dispersion and polarization dependent loss,�?? ICAPT�??2003, SPIE proceeding (in press).
  6. M. Karlsson and J. Brentel, �??Autocorrelation function of the polarization-mode dispersion vector,�?? Opt. Lett. 24, 939 (1999).
    [CrossRef]
  7. Liang Chen, Ou Chen, Saeed Hadjifaradji and Xiaoyi Bao, �??PMD Measurement method using the equation of motion for a system with PDL and PMD,�?? ICAPT�??2003 SPIE Proceeding (in press).

ICAPT???2003 (2)

Liang Chen, Saeed Hadjifaradji, David S. Waddy and Xiaoyi Bao, �??Principal state vector autocorrelation in a fiber optic system having both polarization-mode dispersion and polarization dependent loss,�?? ICAPT�??2003, SPIE proceeding (in press).

Liang Chen, Ou Chen, Saeed Hadjifaradji and Xiaoyi Bao, �??PMD Measurement method using the equation of motion for a system with PDL and PMD,�?? ICAPT�??2003 SPIE Proceeding (in press).

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

N. Gisin and B. Huttner, �??Combined effects of polarization mode dispersion and polarization dependent losses in optical fibers,�?? Opt. Commun. 142, 119 (1997).
[CrossRef]

Opt. Lett. (1)

Proc. Nat. Acad. Sci. (1)

J.P. Gordon and H. Kogelnik, �??PMD fundamentals: Polarization mode dispersion in optical fibers,�?? Proc. Nat. Acad. Sci. 97, 4541 (2000).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1.
Fig. 1.

The autocorrelation functions for a buried field fiber of 52km (thick lines) are compared with the analytical fitting curves (thin lines). (a), (b) and (c) are correspond to one instant, and (d), (e) and (f) to another instant. The overall agreement demonstrates the necessity of finite PMD and PDL directional correlation. Note: ω 1ω+ω 2 here.

Fig. 2.
Fig. 2.

The autocorrelation functions (lines with dots) of an emulator are compared with analytical fitting curves(solid lines). The overall agreement is very good.

Fig. 3.
Fig. 3.

The analytical autocorrelation functions are plotted for large PASPDL with finite PMD and PDL polarization directional correlation. Notice the oscillatory behavior.

Equations (27)

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E out ( ω ) = A N e i φ CD ( ω ) T N ( ω ) E in ( ω )
= A N e i φ CD ( ω ) e i ω β N · σ 2 e α N · σ 2 e i ω β 1 · σ 2 e α 1 · σ 2 E in ( ω )
i 2 W N ( ω ) · σ = T N ( ω ) ω T N 1 ( ω )
= i 2 β N · σ + e i ω β N · σ 2 e α N · σ 2 ( T N 1 ω T N 1 1 ) e α N · σ 2 e i ω β N · σ 2
= i 2 β N · σ + e i ω β N · σ 2 e α N · σ 2 ( i 2 W N 1 · σ ) e α N · σ 2 e i ω β N · σ 2
W N ( ω ) = β ̂ N { β N + ( 1 cos β N ω ) [ cosh α N ( β ̂ N · W N 1 ( ω ) )
+ i sinh α N ( β ̂ N · ( α ̂ N × W N 1 ( ω ) ) )
( cosh α N 1 ) ( α ̂ N · β ̂ N ) ( α ̂ N · W N 1 ( ω ) ) ] }
+ α ̂ N { i sinh α N sin β N ω ( β ̂ N · W N 1 ( ω ) )
( cosh α N 1 ) cos β N ω ( α ̂ N · W ̂ N 1 ( ω ) ) }
+ W ̂ N 1 ( ω ) { cosh α N cos β N ω i sinh α N sin β N ω ( α ̂ N · β ̂ N ) }
+ ( α ̂ N × β ̂ N ) { ( cosh α N 1 ) sin β N ω ( α ̂ N · W N 1 ( ω ) ) }
+ i sinh α N cos β N ω ( α ̂ N × W N 1 ( ω ) ) + cosh α N sin β N ω ( β ̂ N × W N 1 ( ω ) ) .
n ̂ · A n ̂ · B
( n ̂ · A ) ( n ̂ · B ) = 1 3 ( A · B ) .
( α ̂ j · A ) ( β ̂ j · B ) = 1 3 α ̂ j · β ̂ j ( A · B )
W N ( ω ) · W N ( ω ) = β 2 + q W N 1 ( ω ) · W N 1 ( ω ) = β 2 1 q N 1 q
W ( ω ) · W ( ω ) = lim N W N ( ω ) · W N ( ω ) = 3 ( Δ ω ) 2 [ 1 e Δ τ 2 ( Δ ω ) 2 3 ]
W N ( ω ) · W N * ( ω ) = β 2 + q W N 1 ( ω ) · W N 1 * ( ω ) = β 2 1 p N 1 p
p = 1 3 [ cosh 2 α ( 1 + cos β Δ ω ) + cos β Δ ω 2 i α ̂ · β ̂ sinh 2 α sin β Δ ω
+ ( α ̂ · β ̂ ) 2 ( cosh 2 α 1 ) ( cos β Δ ω 1 ) ] .
W ( ω ) · W * ( ω ) = lim N W N ( ω ) · W N * ( ω ) = Δ τ 2 g ih [ e g ih 1 ]
Ω ( ω ) · Ω ( ω ) = 3 2 ( Δ ω ) 2 [ 1 e Δ τ 2 ( Δ ω ) 2 3 ] + Δ τ 2 2 ( g 2 + h 2 ) [ g e g cos h g + h e g sin h ]
Λ ( ω ) · Λ ( ω ) = 3 2 ( Δ ω ) 2 [ 1 e Δ τ 2 ( Δ ω ) 2 3 ] + Δ τ 2 2 ( g 2 + h 2 ) [ g e g cos h g + h e g sin h ]
Λ ( ω ) · Ω ( ω ) = Δ τ 2 2 ( g 2 + h 2 ) [ h e g cos h h + g e g sin h ] = Ω ( ω ) · Λ ( ω ) .
{ Ω ( ω ) · Ω ( ω ) = Δ τ 2 [ 1 2 + 3 8 η 2 ( e 4 η 2 3 1 ) ] Λ ( ω ) · Λ ( ω ) = Δ τ 2 [ 1 2 3 8 η 2 ( e 4 η 2 3 1 ) ] .
d Λ ( ω + Δ ω ) · Ω ( ω ) d Δ ω | Δ ω = 0 = 3 8 α ̂ · β ̂ [ Δ τ 2 η 2 ] 3 2 [ e 4 η 2 3 ( 1 4 3 η 2 ) 1 ] .

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