Abstract

I present a simple method for extracting the dispersive elements from a general unitary Jones matrix in such a way that the parts comprising the phase delays and higher-order dispersion in the two principal states of polarization are separated from those describing the frequency-dependent coupling between them. I then rigorously expand these two parts into power series in relative optical frequency, wherein the coefficients are explicit functions of the polarization mode dispersion vectors of various orders. This accurate expansion of the Jones matrix reveals in particular the amplitudes and phases of the cross-coupled components of the principal states of polarization, which are incorrectly described in most polarization mode dispersion models.

© 2003 Optical Society of America

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References

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  1. H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. Kaminow T. Li, eds. (Academic, San Diego, Calif., 2002), p. 725.
    [CrossRef]
  2. A. Eyal, W. K. Marshall, M. Tur, and A. Yariv, Electron. Lett. 35, 1658 (1999).
    [CrossRef]
  3. E. Forestieri and L. Vincetti, J. Lightwave Technol. 19, 1898 (2001).
    [CrossRef]
  4. H. Orlandini and L. Vincetti, IEEE Photon. Technol. Lett. 13, 1176 (2001).
    [CrossRef]
  5. H. Kogelnik, L. E. Nelson, and J. P. Gordon, J. Lightwave Technol. 21, 482 (2003).
    [CrossRef]
  6. D. Penninckx and V. Morénas, Opt. Lett. 24, 875 (1999).
    [CrossRef]
  7. H. Kogelnik, L. E. Nelson, J. P. Gordon, and R. M. Jopson, Opt. Lett. 25, 19 (2000).
    [CrossRef]

2003 (1)

H. Kogelnik, L. E. Nelson, and J. P. Gordon, J. Lightwave Technol. 21, 482 (2003).
[CrossRef]

2001 (2)

H. Orlandini and L. Vincetti, IEEE Photon. Technol. Lett. 13, 1176 (2001).
[CrossRef]

E. Forestieri and L. Vincetti, J. Lightwave Technol. 19, 1898 (2001).
[CrossRef]

2000 (1)

1999 (2)

D. Penninckx and V. Morénas, Opt. Lett. 24, 875 (1999).
[CrossRef]

A. Eyal, W. K. Marshall, M. Tur, and A. Yariv, Electron. Lett. 35, 1658 (1999).
[CrossRef]

Eyal, A.

A. Eyal, W. K. Marshall, M. Tur, and A. Yariv, Electron. Lett. 35, 1658 (1999).
[CrossRef]

Forestieri, E.

Gordon, J. P.

H. Kogelnik, L. E. Nelson, and J. P. Gordon, J. Lightwave Technol. 21, 482 (2003).
[CrossRef]

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

Jopson, R. M.

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

H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. Kaminow T. Li, eds. (Academic, San Diego, Calif., 2002), p. 725.
[CrossRef]

Kogelnik, H.

H. Kogelnik, L. E. Nelson, and J. P. Gordon, J. Lightwave Technol. 21, 482 (2003).
[CrossRef]

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

H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. Kaminow T. Li, eds. (Academic, San Diego, Calif., 2002), p. 725.
[CrossRef]

Marshall, W. K.

A. Eyal, W. K. Marshall, M. Tur, and A. Yariv, Electron. Lett. 35, 1658 (1999).
[CrossRef]

Morénas, V.

Nelson, L. E.

H. Kogelnik, L. E. Nelson, and J. P. Gordon, J. Lightwave Technol. 21, 482 (2003).
[CrossRef]

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

H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. Kaminow T. Li, eds. (Academic, San Diego, Calif., 2002), p. 725.
[CrossRef]

Orlandini, H.

H. Orlandini and L. Vincetti, IEEE Photon. Technol. Lett. 13, 1176 (2001).
[CrossRef]

Penninckx, D.

Tur, M.

A. Eyal, W. K. Marshall, M. Tur, and A. Yariv, Electron. Lett. 35, 1658 (1999).
[CrossRef]

Vincetti, L.

H. Orlandini and L. Vincetti, IEEE Photon. Technol. Lett. 13, 1176 (2001).
[CrossRef]

E. Forestieri and L. Vincetti, J. Lightwave Technol. 19, 1898 (2001).
[CrossRef]

Yariv, A.

A. Eyal, W. K. Marshall, M. Tur, and A. Yariv, Electron. Lett. 35, 1658 (1999).
[CrossRef]

Electron. Lett. (1)

A. Eyal, W. K. Marshall, M. Tur, and A. Yariv, Electron. Lett. 35, 1658 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. Orlandini and L. Vincetti, IEEE Photon. Technol. Lett. 13, 1176 (2001).
[CrossRef]

J. Lightwave Technol. (1)

H. Kogelnik, L. E. Nelson, and J. P. Gordon, J. Lightwave Technol. 21, 482 (2003).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Lett. (2)

Other (1)

H. Kogelnik, R. M. Jopson, and L. E. Nelson, in Optical Fiber Telecommunications IV B, I. Kaminow T. Li, eds. (Academic, San Diego, Calif., 2002), p. 725.
[CrossRef]

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Equations (18)

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Tω0+Δω=Wω0DΔωV-1ω0,
DΔω=W-1ω0Tω0+ΔωT-1ω0Wω0,
U1ω0Tωω0T-1ω0=-jτω0·σ,
eˆ±=±1±px/2exp-j/2tan-1pz/py1px/2expj/2tan-1pz/py,
d11=Reu11Δω-jpˆ·uΔω,
d12=juΔω-pˆ×uΔωx1-px2-1/2,
u=-Imu11ΔωImu12ΔωReu12Δω,
DΔω=n=0DnΔωn/n!,
Un=nΔωnTω0+ΔωΔω=0T-1ω0,
Un=-jτn-1·σ-m=1n-1n-1mUn-mUm,
D2=-τ2-jτω-τωexpjγ1τωexp-jγ1-τ2+jτω,
γ1=-tan-1τωx/pˆ×τωx,
u0=1-τ2Δω2/2-ττωΔω3/2-4τ·τωω+3τω2-τ4Δω4/24-,
up=τΔω+τωΔω2/2+pˆ·τωω-τ3Δω3/6+pˆ·τωωω-6τ2τωΔω4/24+,
d11=exp-jτΔω+τωΔω2/2+pˆ·τωωΔω3/6+pˆ·τωωωΔω4/24+,
d11=1-τω2Δω4/8-,
u=τωΔω2/2+τωω-τ×τωΔω3/6+τωωω-2τ×τωω-2τ2τωΔω4/24+,
d12=-τωexpjγ1Δω22×1-jτΔω3-τ2Δω26+-τωωexpjγ2Δω361-jτΔω2--τωωωexpjγ3Δω424-,

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