Abstract

Dependence of output optical power, Stokes vector and degree of polarization on optical frequency is presented for an optical fiber system with both polarization mode dispersion and polarization-dependent loss or gain. The newly formulated equations are generalized for input light with arbitrary degree of polarization. The spectral resolved measurements of polarization mode dispersion using partially polarized light agree well with our theory.

© 2005 Optical Society of America

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References

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  1. Yi Li , and Amnon Yariv, �??Solutions to the dynamical equation of polarization-mode dispersion and polarization-dependent losses,�?? J.Opt.Soc.Am.B. 17, 1821-1827 (2000).
    [CrossRef]
  2. Liang Chen, Ou Chen, Saeed Hadjifaradji, and Xiaoyi Bao, �??Polarization-mode dispersion measurement in a system with polarization-dependent loss or gain,�?? IEEE Photonics Technol. Lett. 16, 206-208 (2004).
    [CrossRef]
  3. R.Simon, �??Nondepolarizing systems and degree of polarization,�?? Opt. Commun. 77, 349-354 (1990).
    [CrossRef]
  4. Shih-Yau Lu, and Russell A.Chipman, �??Interpretation of Mueller matrices based on polar decomposition,�?? J.Opt.Soc.Am.A. 13, 1106-1113 (1996).
    [CrossRef]
  5. Richard Barakat, �??Bilinear constraints between elements of the 4x4 Mueller-Jones transfer matrix of polarization theory,�?? Opt. Commun. 38, 159-161 (1981).
    [CrossRef]
  6. Shih-Yau lu, and Russell A.Chipman, �??Mueller matrices and the degree of polarization,�?? Opt. Commun. 146, 11-14 (1998).
    [CrossRef]
  7. N.Gisin, and B.Huttner, �??Combined effects of polarization mode dispersion and polarization-dependent losses in optical fibers,�?? Opt. Commun. 142, 119-125 (1997).
    [CrossRef]
  8. A.Bessa dos Santos, and J.P.von der weid, �??PDL effects in PMD emulators made out with HiBi fibers: Building PMD/PDL emulators,�?? IEEE Photonics Technol. Lett. 16, 452-454 (2004).
    [CrossRef]

IEEE Photonics Technol. Lett. (2)

Liang Chen, Ou Chen, Saeed Hadjifaradji, and Xiaoyi Bao, �??Polarization-mode dispersion measurement in a system with polarization-dependent loss or gain,�?? IEEE Photonics Technol. Lett. 16, 206-208 (2004).
[CrossRef]

A.Bessa dos Santos, and J.P.von der weid, �??PDL effects in PMD emulators made out with HiBi fibers: Building PMD/PDL emulators,�?? IEEE Photonics Technol. Lett. 16, 452-454 (2004).
[CrossRef]

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

Shih-Yau Lu, and Russell A.Chipman, �??Interpretation of Mueller matrices based on polar decomposition,�?? J.Opt.Soc.Am.A. 13, 1106-1113 (1996).
[CrossRef]

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

Yi Li , and Amnon Yariv, �??Solutions to the dynamical equation of polarization-mode dispersion and polarization-dependent losses,�?? J.Opt.Soc.Am.B. 17, 1821-1827 (2000).
[CrossRef]

Opt. Commun. (4)

R.Simon, �??Nondepolarizing systems and degree of polarization,�?? Opt. Commun. 77, 349-354 (1990).
[CrossRef]

Richard Barakat, �??Bilinear constraints between elements of the 4x4 Mueller-Jones transfer matrix of polarization theory,�?? Opt. Commun. 38, 159-161 (1981).
[CrossRef]

Shih-Yau lu, and Russell A.Chipman, �??Mueller matrices and the degree of polarization,�?? Opt. Commun. 146, 11-14 (1998).
[CrossRef]

N.Gisin, and B.Huttner, �??Combined effects of polarization mode dispersion and polarization-dependent losses in optical fibers,�?? Opt. Commun. 142, 119-125 (1997).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Experimental setup (PC: polarization controller, FUT: fiber under test)

Fig. 2.
Fig. 2.

Wavelength dependence of output optical power and DOP

Fig. 3.
Fig. 3.

Wavelength dependences of measured (a) DGD and (b) DAS

Equations (11)

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S = M S in
M T GM = det M G
M 1 = 1 det M G M T G = ( m 11 m 21 m 31 m 41 m 12 m 22 m 32 m 42 m 13 m 23 m 33 m 43 m 14 m 24 m 34 m 44 ) / det M
{ m 11 2 m 12 2 m 13 2 m 14 2 = det M m 21 2 m 22 2 m 23 2 m 24 2 = det M m 31 2 m 32 2 m 33 2 m 34 2 = det M m 41 2 m 42 2 m 43 2 m 44 2 = det M m 11 m 21 m 12 m 22 m 13 m 23 m 14 m 24 = 0 m 11 m 31 m 12 m 32 m 13 m 33 m 14 m 34 = 0 m 11 m 41 m 12 m 42 m 13 m 43 m 14 m 44 = 0 m 21 m 31 m 22 m 32 m 23 m 33 m 24 m 34 = 0 m 21 m 41 m 22 m 42 m 23 m 43 m 24 m 44 = 0 m 31 m 41 m 32 m 42 m 33 m 43 m 34 m 44 = 0
d S = d M M 1 S
d M M 1 = ( η ω ʌ 1 ʌ 2 ʌ 3 ʌ 1 η ω Ω 3 Ω 2 ʌ 2 Ω 3 η ω Ω 1 ʌ 3 Ω 3 Ω 1 η ω )
η ω = = d In det M 4
{ ʌ q 1 = ( m 11 m q 1 + m 12 m q 2 + m 13 m q 3 + m 14 m q 4 ) / det M q = 2,3,4 Ω 1 = ( m 41 m 31 + m 42 m 32 + m 43 m 33 + m 44 m 34 ) / det M Ω 2 = ( m 21 m 41 + m 22 m 42 + m 23 m 43 + m 24 m 44 ) / det M Ω 3 = ( m 31 m 21 + m 32 m 22 + m 33 m 23 + m 34 m 24 ) / det M
{ d s 0 = ʌ · S F + S 0 η ω d s F = S 0 ʌ + Ω × S F + η ω S F
{ ds N = Ω × s N + ʌ ( ʌ · s N ) · s N d s ̂ = Ω × s ̂ ( ʌ × s ̂ ) × s ̂ D dD = ( 1 D 2 ) ʌ · s ̂ = 1 D 2 D ʌ · s N
{ ʌ · [ S ̂ 2 D 1 + S ̂ 1 D 2 ( S ̂ 1 · S ̂ 2 ) ( S ̂ 1 D 1 + S ̂ 2 D 2 ) ] = S ̂ 1 · d s ̂ 2 + S ̂ 2 · d s ̂ 1 Ω · { [ D 2 D 1 ( S ̂ 1 · S ̂ 2 ) ] S ̂ 1 + [ D 2 D 1 ( S ̂ 1 · S ̂ 2 ) ] S ̂ 2 } = ( D 2 d s ̂ 2 D 1 d s ̂ 1 ) · ( S ̂ 1 × S ̂ 2 )

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