Abstract

We describe a new time-domain method for determining the vector components of polarization-mode dispersion from measurements of the mean signal delays for four polarization launches. Using sinusoidal amplitude modulation and sensitive phase detection, we demonstrate that the PMD vector components measured with the new method agree with results obtained from the more traditional Müller Matrix Method.

© 2000 Optical Society of America

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References

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  1. C. D. Poole and J. A. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997), pp. 114–161.
  2. F. Heismann, “Polarization mode dispersion: fundamentals and impact on optical communication systems,” ECOC’98 Digest,  Vol. 2, Tutorials, pp. 51–79, Madrid, (1998).
  3. B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
    [Crossref]
  4. L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Müller matrix method for determining polarization mode dispersion vectors,” ECOC ’99 Digest,  Vol. II, pp. 10–11, Nice, (1999).
  5. R. M. Jopson, L. E. Nelson, and H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett. 11, 1153–1155 (1999).
    [Crossref]
  6. P. A. Williams, “Modulation phase-shift measurement of PMD using only four launched polarisation states: a new algorithm,” Electron. Lett. 35, 1578–1579 (1999).
    [Crossref]
  7. R. M. Jopson, L. E. Nelson, H. Kogelnik, and J. P. Gordon, “Polarization-dependent signal delay method for measuring polarization mode dispersion vectors,” LEOS’99 Postdeadline paper, PD1.1, San Francisco, CA (1999).
  8. L. F. Mollenauer and J. P. Gordon, “Birefringence-mediated timing jitter in soliton transmission,” Optics Lett. 19, 375–377 (1994).
  9. M. Karlsson, “Polarization mode dispersion-induced pulse broadening in optical fibers,” Optics Lett. 23, 688–690 (1998).
    [Crossref]
  10. W. Shieh, “Principal states of polarization for an optical pulse,” IEEE Photon. Technol. Lett. 11, 677–679 (1999).
    [Crossref]
  11. J. P. Gordon and H. Kogelnik, “PMD Fundamentals: Polarization mode dispersion in optical fibers,” Proceedings of the National Academy of Sciences, Vol. 97, April 25, 2000.
    [Crossref]

1999 (4)

L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Müller matrix method for determining polarization mode dispersion vectors,” ECOC ’99 Digest,  Vol. II, pp. 10–11, Nice, (1999).

R. M. Jopson, L. E. Nelson, and H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett. 11, 1153–1155 (1999).
[Crossref]

P. A. Williams, “Modulation phase-shift measurement of PMD using only four launched polarisation states: a new algorithm,” Electron. Lett. 35, 1578–1579 (1999).
[Crossref]

W. Shieh, “Principal states of polarization for an optical pulse,” IEEE Photon. Technol. Lett. 11, 677–679 (1999).
[Crossref]

1998 (2)

M. Karlsson, “Polarization mode dispersion-induced pulse broadening in optical fibers,” Optics Lett. 23, 688–690 (1998).
[Crossref]

F. Heismann, “Polarization mode dispersion: fundamentals and impact on optical communication systems,” ECOC’98 Digest,  Vol. 2, Tutorials, pp. 51–79, Madrid, (1998).

1994 (1)

L. F. Mollenauer and J. P. Gordon, “Birefringence-mediated timing jitter in soliton transmission,” Optics Lett. 19, 375–377 (1994).

1992 (1)

B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[Crossref]

Gordon, J. P.

L. F. Mollenauer and J. P. Gordon, “Birefringence-mediated timing jitter in soliton transmission,” Optics Lett. 19, 375–377 (1994).

J. P. Gordon and H. Kogelnik, “PMD Fundamentals: Polarization mode dispersion in optical fibers,” Proceedings of the National Academy of Sciences, Vol. 97, April 25, 2000.
[Crossref]

R. M. Jopson, L. E. Nelson, H. Kogelnik, and J. P. Gordon, “Polarization-dependent signal delay method for measuring polarization mode dispersion vectors,” LEOS’99 Postdeadline paper, PD1.1, San Francisco, CA (1999).

Heffner, B. L.

B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[Crossref]

Heismann, F.

F. Heismann, “Polarization mode dispersion: fundamentals and impact on optical communication systems,” ECOC’98 Digest,  Vol. 2, Tutorials, pp. 51–79, Madrid, (1998).

Jopson, R. M.

L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Müller matrix method for determining polarization mode dispersion vectors,” ECOC ’99 Digest,  Vol. II, pp. 10–11, Nice, (1999).

R. M. Jopson, L. E. Nelson, and H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett. 11, 1153–1155 (1999).
[Crossref]

R. M. Jopson, L. E. Nelson, H. Kogelnik, and J. P. Gordon, “Polarization-dependent signal delay method for measuring polarization mode dispersion vectors,” LEOS’99 Postdeadline paper, PD1.1, San Francisco, CA (1999).

Karlsson, M.

M. Karlsson, “Polarization mode dispersion-induced pulse broadening in optical fibers,” Optics Lett. 23, 688–690 (1998).
[Crossref]

Kogelnik, H.

R. M. Jopson, L. E. Nelson, and H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett. 11, 1153–1155 (1999).
[Crossref]

L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Müller matrix method for determining polarization mode dispersion vectors,” ECOC ’99 Digest,  Vol. II, pp. 10–11, Nice, (1999).

R. M. Jopson, L. E. Nelson, H. Kogelnik, and J. P. Gordon, “Polarization-dependent signal delay method for measuring polarization mode dispersion vectors,” LEOS’99 Postdeadline paper, PD1.1, San Francisco, CA (1999).

J. P. Gordon and H. Kogelnik, “PMD Fundamentals: Polarization mode dispersion in optical fibers,” Proceedings of the National Academy of Sciences, Vol. 97, April 25, 2000.
[Crossref]

Mollenauer, L. F.

L. F. Mollenauer and J. P. Gordon, “Birefringence-mediated timing jitter in soliton transmission,” Optics Lett. 19, 375–377 (1994).

Nagel, J. A.

C. D. Poole and J. A. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997), pp. 114–161.

Nelson, L. E.

L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Müller matrix method for determining polarization mode dispersion vectors,” ECOC ’99 Digest,  Vol. II, pp. 10–11, Nice, (1999).

R. M. Jopson, L. E. Nelson, and H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett. 11, 1153–1155 (1999).
[Crossref]

R. M. Jopson, L. E. Nelson, H. Kogelnik, and J. P. Gordon, “Polarization-dependent signal delay method for measuring polarization mode dispersion vectors,” LEOS’99 Postdeadline paper, PD1.1, San Francisco, CA (1999).

Poole, C. D.

C. D. Poole and J. A. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997), pp. 114–161.

Shieh, W.

W. Shieh, “Principal states of polarization for an optical pulse,” IEEE Photon. Technol. Lett. 11, 677–679 (1999).
[Crossref]

Williams, P. A.

P. A. Williams, “Modulation phase-shift measurement of PMD using only four launched polarisation states: a new algorithm,” Electron. Lett. 35, 1578–1579 (1999).
[Crossref]

ECOC ’99 Digest (1)

L. E. Nelson, R. M. Jopson, and H. Kogelnik, “Müller matrix method for determining polarization mode dispersion vectors,” ECOC ’99 Digest,  Vol. II, pp. 10–11, Nice, (1999).

ECOC’98 Digest (1)

F. Heismann, “Polarization mode dispersion: fundamentals and impact on optical communication systems,” ECOC’98 Digest,  Vol. 2, Tutorials, pp. 51–79, Madrid, (1998).

Electron. Lett. (1)

P. A. Williams, “Modulation phase-shift measurement of PMD using only four launched polarisation states: a new algorithm,” Electron. Lett. 35, 1578–1579 (1999).
[Crossref]

IEEE Photon. Technol. Lett. (3)

B. L. Heffner, “Automated measurement of polarization mode dispersion using Jones matrix eigenanalysis,” IEEE Photon. Technol. Lett. 4, 1066–1069 (1992).
[Crossref]

R. M. Jopson, L. E. Nelson, and H. Kogelnik, “Measurement of second-order polarization-mode dispersion vectors in optical fibers,” IEEE Photon. Technol. Lett. 11, 1153–1155 (1999).
[Crossref]

W. Shieh, “Principal states of polarization for an optical pulse,” IEEE Photon. Technol. Lett. 11, 677–679 (1999).
[Crossref]

Optics Lett. (2)

L. F. Mollenauer and J. P. Gordon, “Birefringence-mediated timing jitter in soliton transmission,” Optics Lett. 19, 375–377 (1994).

M. Karlsson, “Polarization mode dispersion-induced pulse broadening in optical fibers,” Optics Lett. 23, 688–690 (1998).
[Crossref]

Other (3)

R. M. Jopson, L. E. Nelson, H. Kogelnik, and J. P. Gordon, “Polarization-dependent signal delay method for measuring polarization mode dispersion vectors,” LEOS’99 Postdeadline paper, PD1.1, San Francisco, CA (1999).

J. P. Gordon and H. Kogelnik, “PMD Fundamentals: Polarization mode dispersion in optical fibers,” Proceedings of the National Academy of Sciences, Vol. 97, April 25, 2000.
[Crossref]

C. D. Poole and J. A. Nagel, “Polarization effects in lightwave systems,” in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, eds. (Academic Press, San Diego, 1997), pp. 114–161.

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Figures (5)

Fig. 1.
Fig. 1.

Mean signal delay of a fiber having a dispersion of +124 ps/nm. The green curve shows the delay that would be obtained if the fiber had no PMD. The red curves show the green curve plus and minus half the differential group delay. The markers show the measured delay for a specific launch polarization state.

Fig. 2.
Fig. 2.

Apparatus used for the Polarization-Dependent Signal Delay Method measurement of PMD. MOD: Lithium Niobate amplitude modulator, A: optical amplifier, PC: polarization controller, Rx: receiver.

Fig. 3.
Fig. 3.

Measured wavelength dependence of the signal delay of a single-mode fiber span having 35-ps mean DGD for four fixed input polarizations.

Fig. 4.
Fig. 4.

Wavelength dependence of the first-order input PMD vector, τ (ω), including magnitude (DGD) and components, and the relative polarization independent delay, τ0R , for the single-mode fiber span with 35-ps mean DGD. Markers show the Polarization-Dependent Signal Delay Method (PSD) results using 1-GHz modulation frequency; curves without markers show the results obtained from the Müller Matrix Method (MMM).

Fig. 5.
Fig. 5.

PSD measurement using 3-GHz modulation frequency of τ (ω) and τ0R for the same single-mode fiber span as in Fig. 4. Red curves show the PSD results for τ0R and magnitude and components of τ (ω) computed with the linear approximation; blue curves show the results obtained from the exact expressions. The markers show measured data, while the lines serve to guide the eye.

Equations (28)

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τ g = τ o + 1 2 τ · s .
τ g = W 1 ( z ) W 1 ( 0 ) W ,
τ o = 1 2 ( τ g 1 + τ g ( 1 ) ) ; τ i = 2 ( τ gi τ 0 )
X = 1 2 2 s 11 s 12 s 13 2 s 21 s 22 s 23 2 s 31 s 32 s 33 2 s 41 s 42 s 43 .
tan ω m ( τ ϕ τ o ) = p · s tan ( ω m Δ τ 2 ) ,
Ŝ i = α i s a + β i s b + γ i s c ( i = 1 , 2 , 3 ) ,
α 1 β 1 γ 1 α 2 β 2 γ 2 α 3 β 3 γ 3 = a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 1 .
tan ω m ( τ ϕ 1 τ 0 ) = p ̂ · ( α 1 s a + β 1 s b + γ 1 s c ) tan ( ω m Δ τ 2 ) ,
tan ω m ( τ ϕ 1 τ 0 ) = α 1 tan ω m ( τ ϕ a τ 0 ) + β 1 tan ω m ( τ ϕ b τ 0 ) + γ 1 tan ω m ( τ ϕ c τ 0 ) .
τ 0 = τ ϕ 1 α 1 τ ϕ a β 1 τ ϕ b γ 1 τ ϕ c 1 α 1 β 1 γ 1 .
tan 2 ( ω m Δ τ 2 ) = i [ α i tan ω m ( τ ϕ a τ 0 ) + β i tan ω m ( τ ϕ b τ 0 ) + γ i tan ω m ( τ ϕ c τ 0 ) ] 2 .
p i = α i tan ω m ( τ ϕ a τ 0 ) + β i tan ω m ( τ ϕ b τ 0 ) + γ i tan ω m ( τ ϕ c τ 0 ) tan ( ω m Δ τ 2 ) .
τ = ( τ 1 τ 2 τ 3 )
and Ω = ( τ 1 τ 2 τ 3 ) .
R Δ = R + R ˜ 0
τ s = R ˜ ( ω ) τ ,
R ( ω ) = R Δ · R 0 = R ˜ Δ · R + ,
R Δ s = R ˜ ( ω ) R Δ R ( ω ) ,
R Δ s = R ˜ 0 R + .
τ = Δ τ p
Ω = Δ τ q ,
R Δ = ( cos ϕ ) I + ( 1 cos ϕ ) r r + ( sin ϕ ) r ×
R Δ = ( cos ϕ ) I + ( 1 cos ϕ ) r r ( sin ϕ ) r × ,
2 sin ϕ ( r × ) = R Δ R ˜ Δ
2 sin ϕ ( r × ) = R ˜ Δ R Δ ,
Δ τ = ϕ Δ ω
p = r
q = r .

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