Abstract

We derive a recursion relation for the frequency autocorrelation function of the polarization dispersion vector for polarization mode dispersion emulators with rotators. The autocorrelation function has a nonzero background for an emulator with a fixed number of sections. This background diminishes slowly as the number of sections grows. Randomizing the section lengths removes the autocorrelation periodicity exhibited by an emulator with equal sections, but it does not remove the finite background.

© 2002 Optical Society of America

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References

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  1. R. Khosravani, I. T. Lima, P. Ebrahimi, A. E. Willner, and C. R. Menyuk, IEEE Photon. Technol. Lett. 13, 127 (2001).
    [CrossRef]
  2. I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, J. Lightwave Technol. 19, 1872 (2001).
    [CrossRef]
  3. I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, in Optical Fiber Communications Conference, Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThB4.
  4. A. Djupsjöbacka, J. Lightwave Technol. 19, 285 (2001).
    [CrossRef]
  5. M. Karlsson, J. Lightwave Technol. 19, 324 (2001).
    [CrossRef]
  6. C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, J. Lightwave Technol. 6, 1185 (1988).
    [CrossRef]
  7. M. Karlsson and J. Brentel, Opt. Lett. 24, 939 (1999).
    [CrossRef]
  8. J. P. Gordon and H. Kogelnik, Proc. Natl. Acad. Sci. USA 97, 4541 (2000).
    [CrossRef]

2001 (4)

2000 (1)

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

1999 (1)

1988 (1)

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

Bergano, N. S.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

Brentel, J.

Djupsjöbacka, A.

Ebrahimi, P.

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, J. Lightwave Technol. 19, 1872 (2001).
[CrossRef]

R. Khosravani, I. T. Lima, P. Ebrahimi, A. E. Willner, and C. R. Menyuk, IEEE Photon. Technol. Lett. 13, 127 (2001).
[CrossRef]

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, in Optical Fiber Communications Conference, Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThB4.

Gordon, J. P.

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

Ibragimov, E.

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, J. Lightwave Technol. 19, 1872 (2001).
[CrossRef]

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, in Optical Fiber Communications Conference, Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThB4.

Karlsson, M.

Khosravani, R.

R. Khosravani, I. T. Lima, P. Ebrahimi, A. E. Willner, and C. R. Menyuk, IEEE Photon. Technol. Lett. 13, 127 (2001).
[CrossRef]

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, J. Lightwave Technol. 19, 1872 (2001).
[CrossRef]

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, in Optical Fiber Communications Conference, Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThB4.

Kogelnik, H.

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

Lima, I. T.

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, J. Lightwave Technol. 19, 1872 (2001).
[CrossRef]

R. Khosravani, I. T. Lima, P. Ebrahimi, A. E. Willner, and C. R. Menyuk, IEEE Photon. Technol. Lett. 13, 127 (2001).
[CrossRef]

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, in Optical Fiber Communications Conference, Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThB4.

Menyuk, C. R.

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, J. Lightwave Technol. 19, 1872 (2001).
[CrossRef]

R. Khosravani, I. T. Lima, P. Ebrahimi, A. E. Willner, and C. R. Menyuk, IEEE Photon. Technol. Lett. 13, 127 (2001).
[CrossRef]

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, in Optical Fiber Communications Conference, Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThB4.

Poole, C. D.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

Schulte, H. J.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

Wagner, R. E.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, J. Lightwave Technol. 6, 1185 (1988).
[CrossRef]

Willner, A. E.

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, J. Lightwave Technol. 19, 1872 (2001).
[CrossRef]

R. Khosravani, I. T. Lima, P. Ebrahimi, A. E. Willner, and C. R. Menyuk, IEEE Photon. Technol. Lett. 13, 127 (2001).
[CrossRef]

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, in Optical Fiber Communications Conference, Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThB4.

IEEE Photon. Technol. Lett. (1)

R. Khosravani, I. T. Lima, P. Ebrahimi, A. E. Willner, and C. R. Menyuk, IEEE Photon. Technol. Lett. 13, 127 (2001).
[CrossRef]

J. Lightwave Technol. (4)

Opt. Lett. (1)

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

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

Other (1)

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, in Optical Fiber Communications Conference, Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThB4.

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Figures (3)

Fig. 1
Fig. 1

Mean (solid curves) and mean plus and minus one standard deviation (dashed curves) of the autocorrelation function of emulators with rotators and an average DGD of 40 ps with different numbers N of sections. The sections’ DGDs are Gaussian distributed, with a variance of σ=1% of the mean DGD value. The center frequency, Δf=0 GHz, corresponds to the carrier wavelength, λ0=1.55 µm. Each autocorrelation function is normalized by the mean autocorrelation function at Δf=0 GHz.

Fig. 2
Fig. 2

Same as Fig. 1, except that σ=10%.

Fig. 3
Fig. 3

Same as Fig. 1, except that σ=20%.

Equations (12)

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Ωnω=τne^n+MnωΩn-1ω,
Ωnω=τneˆ1+RxγnωRzθnΩn-1ω,
fnω,ω0Ωnω·Ωnω0θ=τn2+Ωn-1ωTVnΩn-1ω0θ,
Vn=121+cos ΔγnI+0000000012cos Δγn-1,
fnω,ω0=τn2+Anfn-1ω,ω0+Bngn-1ω,ω0,
gnω,ω0=Cnfn-1ω,ω0+Dngn-1ω,ω0,
fnτ=τn2τ+Anτfn-1τ+Bnτgn-1τ,
gnτ=Cnτ+fn-1τ+Dnτgn-1τ,
Anτ=12hΔω+1,
Bnτ=12hΔω-1,
Cnτ=14hΔω-hω¯,
Dnτ=14hΔω+3hω¯,

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