Differential Attenuation Slope and Its Measurement Uncertainty due to Stokes Noise in a Longhaul Str

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Differential Attenuation Slope and Its
Measurement Uncertainty due to Stokes Noise in a
Long-haul Straight-line System

• Hua Jiao, H. Xu, L. Yan and G. M. Carter
• Department of Computer Science and Electrical
  Engineering, University of Maryland Baltimore
  County
• May 23, 2005

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Motivation

• Coupling between PMD and PDL can induce extra
  pulse broadening and increase performance
  variations.
• Measuring DGD alone cannot predict the combined
  penalty.
• Differential Attenuation Slope (DAS) is a direct
  result of this coupling.
• Analysis of DAS distribution in a long-haul
  system has not been done.
• Effect of noise on the DAS measurement
  uncertainty has not been studied.

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Goal of the study

• Through numerical simulation
• Correlate the DAS distributions to different PDL
  levels
• Investigate the measurement uncertainty of DAS
  due to Stokes noise.

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Combined effect of PMD and PDL (1)

• Anomalous pulse broadening and distortion1

1 B. Huttner and N. Gisin, Optics Lett., vol.
22, (1997).
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Combined effect of PMD and PDL (2)

• Complex principal state vectors
• Non-orthogonal real part of the two principal
  state vectors.

 

• A generalized Poincaré sphere method was proposed
  to measure the DGD and DAS 2.

2 L. Chen et al, Photon. Technol. Lett., vol.
16, (2004).
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Simulation model
50 sections
PDL element ( PDL 0, 0.3, 0.5, 0.75 or 1 dB)
107 km low PMD fiber (PMD 0.1 ps/km½)

• Fiber loss, chromatic dispersion, and
  nonlinearity neglected.
• 5,000 random fiber realizations.
• Propagation distance 5,000 km

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DAS distributions at different PDL levels
0.25
PDL 0.3 dB
PDL 0.5 dB
pdf
PDL 0.75dB
PDL 1.0 dB
0
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DAS (ps)
The distribution of DAS is symmetric and the mean
is zero.
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DAS as a function of PDL levels

• The Mean of DAS is zero.
• The standard deviation of DAS is proportional to
  PDL.

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Issues in real systems when measuring PMD

• ASE noise
• Fiber drift

Stokes noise angle

• How to simulate the effect of Stokes noise
• Propagate the noiseless signal.
• At the receiver, calculate the DAS using the
  noiseless signal to get DASreference.
• Perturb the noiseless signal at the receiver by a
  specified Stokes noise angle.
• Re-calculate the DAS to get DASperturbed.
• DAS uncertainty DASperturbed DASreference.

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Absolute measurement uncertainty of DAS caused
by Stokes noise
Standard deviation of DAS uncertainty vs. Stokes
noise angle
Distribution of DAS uncertainty (PDL 0.5 dB,
Stokes noise angle 0.01 rad.)
DAS uncertainty (ps)
DAS measurement uncertainty increases linearly
with Stokes noise angle !
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Relative measurement uncertainty of DAS caused
by Stokes noise
Ratio of the standard deviations of DAS
uncertainty and DAS
Std.( ) standard deviation
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Conclusions

• Simulated DAS distributions show symmetric shape
  in a 5,000 km straight-line system.
• The mean DAS is zero and the standard deviation
  of DAS is proportional to PDL.
• The measurement uncertainty of DAS is comparable
  to the magnitude of DAS for typical system
  parameters.