Abstract

We carry out a statistical characterization of Jones matrix eigenvalues and eigenmodes to gain deeper insight into recently proposed fiber models based on Jones matrix spectral decomposition. A set of linear dynamic equations for the Pauli coordinates of the Jones matrix is established. Using stochastic calculus, we determine the joint distribution of the retardation angle of the eigenmodes and, indirectly, their autocorrelation function. The correlation bandwidth of the eigenmodes is found to be 2/3 that of the polarization mode dispersion vector. The results agree well with simulations performed with the standard retarded plate model.

© 2001 Optical Society of America

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References

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  1. G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
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  2. M. Karlsson and J. Brentel, Opt. Lett. 24, 939 (1999).
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  3. M. Shtaif, A. Mecozzi, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
    [CrossRef]
  4. H. Kogelnik, L. E. Nelson, J. P. Gordon, and R. M. Jopson, Opt. Lett. 25, 19 (2000).
    [CrossRef]
  5. M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 434 (2000).
    [CrossRef]
  6. P. Ciprut, B. Gisin, N. Gisin, R. Passy, J. P. Von der Weid, F. Prieto, and C. W. Zimmer, J. Lightwave Technol. 16, 757 (1998).
    [CrossRef]
  7. M. Karlsson, Opt. Lett. 23, 688 (1998).
    [CrossRef]
  8. C. R. Menyuk and P. K. A. Wai, J. Opt. Soc. Am. B 11, 1288 (1994).
    [CrossRef]
  9. B. Øksendal, Stochastic Differential Equations, 5th ed. (Springer, New York, 1998).
    [CrossRef]
  10. M. O. Van Deventer, J. Lightwave Technol. 12, 2147 (1994).
    [CrossRef]
  11. M. Shtaif and A. Mecozzi, Opt. Lett. 25, 707 (2000).
    [CrossRef]

2000 (4)

M. Shtaif, A. Mecozzi, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

H. Kogelnik, L. E. Nelson, J. P. Gordon, and R. M. Jopson, Opt. Lett. 25, 19 (2000).
[CrossRef]

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 434 (2000).
[CrossRef]

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

1999 (1)

1998 (2)

1994 (2)

C. R. Menyuk and P. K. A. Wai, J. Opt. Soc. Am. B 11, 1288 (1994).
[CrossRef]

M. O. Van Deventer, J. Lightwave Technol. 12, 2147 (1994).
[CrossRef]

1991 (1)

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

Brentel, J.

Ciprut, P.

Foschini, G. J.

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

Gisin, B.

Gisin, N.

Gordon, J. P.

Jopson, R. M.

Karlsson, M.

Kogelnik, H.

Mecozzi, A.

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

M. Shtaif, A. Mecozzi, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 434 (2000).
[CrossRef]

Menyuk, C. R.

Nagel, J. A.

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 434 (2000).
[CrossRef]

M. Shtaif, A. Mecozzi, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

Nelson, L. E.

Øksendal, B.

B. Øksendal, Stochastic Differential Equations, 5th ed. (Springer, New York, 1998).
[CrossRef]

Passy, R.

Poole, C. D.

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

Prieto, F.

Shtaif, M.

M. Shtaif, A. Mecozzi, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 434 (2000).
[CrossRef]

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

Tur, M.

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 434 (2000).
[CrossRef]

Van Deventer, M. O.

M. O. Van Deventer, J. Lightwave Technol. 12, 2147 (1994).
[CrossRef]

Von der Weid, J. P.

Wai, P. K. A.

Zimmer, C. W.

IEEE Photon. Technol. Lett. (2)

M. Shtaif, A. Mecozzi, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 53 (2000).
[CrossRef]

M. Shtaif, A. Mecozzi, M. Tur, and J. A. Nagel, IEEE Photon. Technol. Lett. 12, 434 (2000).
[CrossRef]

J. Lightwave Technol. (3)

P. Ciprut, B. Gisin, N. Gisin, R. Passy, J. P. Von der Weid, F. Prieto, and C. W. Zimmer, J. Lightwave Technol. 16, 757 (1998).
[CrossRef]

G. J. Foschini and C. D. Poole, J. Lightwave Technol. 9, 1439 (1991).
[CrossRef]

M. O. Van Deventer, J. Lightwave Technol. 12, 2147 (1994).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (4)

Other (1)

B. Øksendal, Stochastic Differential Equations, 5th ed. (Springer, New York, 1998).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Probability density of (top) retardation angle Δϕ, (middle) eigenmode azimuth θ, (bottom) eigenmode ellipticity ϵ. Dashed curves and line, theory [Eq.  (4)]; circles, simulations.

Fig. 2
Fig. 2

top, ACF of (circles) vector u and other shapes its components, uk; bottom, ACF of (asterisks) the eigenmode vector b^ and (open circles) function Rc+RsRb^. Dashed curves, theory.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

Uz,ω=exp-iΔϕz,ω2b^z,ωσ=u0z,ωσ0-iuˇz,ωσ,
zu0z,ω=-12uˇz,ωWz,ω,zuˇz,ω=-12uˇz,ω×Wz,ω+12u0z,ωWz,ω,
cu-3ω2σ28u0uˇ,vuωσ2-uˇTu0σ0-uˇ×,
pΔϕ=1-cosΔϕ2π,pθ=1π,pϵ=cos2ϵ,
Eujz,ω1ukz,ω2=14exp-3σ2Δω2z8δjk,
EUω1Uω2=exp-3σ2Δω2z8σ0,
Ruω1,ω2Euz,ω1uz,ω2=exp-Δτ2Δω28.
Ruω1,ω2EcosΔϕz,ω1/2cosΔϕz,ω2/2+sinΔϕz,ω1/2sinΔϕz,ω2/2×b^z,ω1b^z,ω2,

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