Abstract

We derive an analytical expression for differential group delay of spun and twisted fibers, which should provide valuable guidance for optimization of such parameters to produce low polarization mode dispersion fiber.

© 2003 Optical Society of America

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References

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  1. M. Karlsson, �??Polarization mode dispersion mitigation performance of various approaches,�?? in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), paper WI1, pp. 231�??232.
  2. B. W. Hakki, �??Polarization mode dispersion compensation by phase diversity detection,�?? IEEE Photon. Technol. Lett. 9, 121�??123 (1997).
    [CrossRef]
  3. F. Roy, C. Francia, F. Bruyere, and D. Penninckx, �??A simple dynamic polarization mode dispersion compensator,�?? in Optical Fiber Communication Conference, (Optical Society of America, Washington, D.C., 1999), TuS4-1, pp. 275 �??278.
  4. M. J. Li and D. A. Nolan, �??Fiber spin-profile designs for producing fibers with low polarization mode dispersion,�?? Opt. Lett. 23, 1659�??1661 (1998).
    [CrossRef]
  5. R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, and D. H. O. Bebbington, �??Theoretical analysis and measurement of effects of fiber twist on polarization mode dispersion of optical fibers,�?? Electron. Lett. 31, 1772�??1773 (1995).
    [CrossRef]
  6. X. Chen, M. Li, and D. A. Nolan, �??Analytical results for polarization mode dispersion of spun fibers,�?? in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), paper Th1, pp. 448�??449.
  7. C. D. Poole, J. H. Winters, and J. A. Nagel, �??Dynamical equation for polarization dispersion,�?? Opt. Lett. 16, 372�??374 (1991).
    [CrossRef] [PubMed]
  8. R. E. Schuh, A. Altuncu, X. Shan, and A. S. Siddiqui, �??Measurement and theoretical modeling of polarization mode dispersion in distributed erbium doped fibers,�?? in European Conference on Optical Communication, Edinburgh, U.K., 1997, Vol. 3, pp. 203�??206.
  9. A. Galtarossa, L. Palmieri, and A. Pizzinat, �??Optimized spinning design for low PMD fibers: an analytical approach,�?? J. Lightwave Technol. 19, 1502�??1512 (2001).
    [CrossRef]

Electron. Lett.

R. E. Schuh, E. S. R. Sikora, N. G. Walker, A. S. Siddiqui, L. M. Gleeson, and D. H. O. Bebbington, �??Theoretical analysis and measurement of effects of fiber twist on polarization mode dispersion of optical fibers,�?? Electron. Lett. 31, 1772�??1773 (1995).
[CrossRef]

European Conference on Optical Commun.

R. E. Schuh, A. Altuncu, X. Shan, and A. S. Siddiqui, �??Measurement and theoretical modeling of polarization mode dispersion in distributed erbium doped fibers,�?? in European Conference on Optical Communication, Edinburgh, U.K., 1997, Vol. 3, pp. 203�??206.

IEEE Photon. Technol. Lett.

B. W. Hakki, �??Polarization mode dispersion compensation by phase diversity detection,�?? IEEE Photon. Technol. Lett. 9, 121�??123 (1997).
[CrossRef]

J. Lightwave Technol.

Opt. Lett.

Optical Fiber Communication Conference

F. Roy, C. Francia, F. Bruyere, and D. Penninckx, �??A simple dynamic polarization mode dispersion compensator,�?? in Optical Fiber Communication Conference, (Optical Society of America, Washington, D.C., 1999), TuS4-1, pp. 275 �??278.

TOPS

M. Karlsson, �??Polarization mode dispersion mitigation performance of various approaches,�?? in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), paper WI1, pp. 231�??232.

X. Chen, M. Li, and D. A. Nolan, �??Analytical results for polarization mode dispersion of spun fibers,�?? in Optical Fiber Communication Conference, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), paper Th1, pp. 448�??449.

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Figures (5)

Fig. 1.
Fig. 1.

Evolution of DGD along the fiber with the same initial beat length of 15 m for two spin rate profiles: (a) sinusoidal spin function a 0=9.0617 m -1, p=3 m,γ=2 rad/m and (b) triangular asymmetrical spin rate function a 0=21.89 m-1 , p=1 m, r=0.1, γ=6rad/m. DGD is normalized to 1-m linear birefringence fiber.

Fig. 2
Fig. 2

DGD as a function of twist rate for different initial linear birefringence. The beat length was (a) 15 m and (b) 5 m.

Fig. 3.
Fig. 3.

Evolution of DGD along the fiber with the same initial beat length of 15 m and p=1 m, r=0.1:(a) a 0=21.89 m -1 and (b) a 0=25 m-1 . DGD is normalized to that of 1-m linear birefringence fiber.

Fig. 4
Fig. 4

Locus of (a 0,r) satisfied phase-matching conditions for a periodic DGD evolution.

Fig. 5.
Fig. 5.

PMD RF as a function of a 0 and r with a 1-m period.

Equations (17)

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Ω ' ( z , ω ) = β ( z , ω ) ω + β ( z , ω ) Ω ( z , ω )
β ( z , ω ) = [ β l cos ( 2 a ( z ) + 2 γ z ) , β l sin ( 2 a ( z ) + 2 γ z ) , g γ ]
β ( z , ω ) = [ β l , 0 , g γ ( 2 a ' ( z ) + 2 γ ) ]
Ω 1 ' = [ ( g 2 ) γ 2 a ' ( z ) ] Ω 2 + β ω ,
Ω 2 ' = [ ( g 2 ) γ 2 a ' ( z ) ] Ω 1 β l Ω 3 ,
Ω 3 ' = β l Ω 2 + g ω γ
[ Ω 1 Ω 2 ] = V ( z ) · 0 z V T ( t ) [ β ω β l g ω γ t ] · dt , Ω 3 = g ω γz
Δ τ = Ω = 0 z C ( t ) · exp ( i · ( A φ ) ) · dt 2 + ( g ω γ z ) 2
a = a 0 cos ( 2 π z p ) .
a = { a 0 r z , 0 z < r a 0 p 2 r ( 2 z + p ) , r z < p 2 , a ( z ) = a ( z p 2 ) , p 2 z < p
Δ τ = β ω · 0 z exp ( i · A ) dt ,
RF = 1 z · 0 z exp ( i · A ) dt .
Δ τ = n β ω · 0 p exp ( i · A ) dt , n = 0 , 1 , 2
Δ τ ( z ) = β ω L ( n ) + O ( z np ) , np z < ( n + 1 ) p
L ( n ) = n πi 2 a 0 { r [ ierf ( a 0 ri ) + exp ( i a 0 p 2 ) erf ( i a 0 r ) ] + p 2 r 2 [ ierf ( a 0 ( p 2 r ) i 2 )
+ exp ( i a 0 p 2 ) erf ( i a 0 ( p 2 r ) 2 ) ] }
O ( z ) = { πr 4 a 0 i erf ( a 0 i r z ) , 0 z < r O ( r ) + π ( p 2 r ) i 8 a 0 exp ( i a 0 p 2 ) erf ( 2 a 0 i p 2 r ( z r ) ) , r z < p 2 O ( p 2 ) + πri 4 a 0 exp ( i a 0 p 2 ) erf ( i a 0 r ( z p 2 ) , p 2 z < p 2 + r O ( p 2 + r ) + π ( p 2 r ) 8 a 0 i erf ( a 0 i p 2 r ( z p 2 r ) ) , p 2 + r z < p

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