Investigation of the combined effect of polarizationmode dispersion and polarizationdependent loss o

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Investigation of the combined effect of
polarization-mode dispersion and
polarization-dependent loss on system performance

• Hua Jiao
• Ph.D. dissertation defense
• Department of Computer Science and Electrical
  Engineering, University of Maryland Baltimore
  County
• Apr. 13 , 2007

2
Acknowledgements
3
Outline

• Motivation
• Introduction to PMD and PDL
• Literature review on receivers
• Our receiver model
• Validation of the receiver model
• Conclusions

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1. Motivation

• Polarization effects (PMD and PDL) are some of
  the major effects that cause impairments in high
  bit rate optical fiber communication systems.
• Polarization effects are random and may vary over
  time scales of milli-seconds to hours.
• The combined effects of PMD and PDL on system
  performance can be very complicated.
• It is important for system designers to
  understand how they interact together to affect
  system performance.

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Tools required and available

• Tools required
• The transmission modeling (available)
• The receiver model for a depolarized signal and
• partially polarized noise
• Available Receiver models
• Polarized signal and partially polarized noise
• e.g. systems with low bit-rate and long distance
• Depolarized signal and unpolarized noise
• e.g. systems with high bit-rate and short distance

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Goal of the dissertation

• Develop a receiver model for a depolarized
• signal and partially polarized noise
• Validate the receiver model

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2. Introduction Effect of PMD on signal
1. Equal power in two PSP
2. Unequal power in two PSP
PSP
PSP
PSP
PSP
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Effect of PDL

• Noise re-polarization

Electric field of noise at input
High loss axis
Electric field of noise at output
Low loss axis
out
in
PDL Device
DOP of the noise
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3. Literature Review on receivers

• Marcuse 1, Humblet and Azizoglu 2
  Rectangular optical
• filter, square-law photodetector and
  integrate-and-dump electrical filter
• Winzer et. al. 3 Format comparisons, optimum
  receiver bandwidth and receiver sensitivity
• Rebola and Cartaxo 4 Power penalty due to
  optical filtering, optical filter detuning,
  extinction ratio and eye closure
• Assumptions in their work
• Signal is polarized (no PMD effect)
• Noise is unpolarized or polarized and parallel
  with the signal

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Literature Review (cont)

• Yu Sun et. al.5 (Theory and experiments)
• Polarized signal and partially polarized noise
• Ivan Lima et. al. 6 (Theory and simulations)
• Polarized signal and partially polarized noise
• Depolarized signal and unpolarized noise
• In this dissertation
• Signal is depolarized
• Noise is partially polarized
• Model validated by simulations and experiments

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4. Our receiver model

• System and receiver structure
• System performance measure
• The formula for the variance of the received
  signal due
• to signal-noise beating

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System and receiver structure

• System structure

• Receiver structure

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System performance measure

• Q-factors obtained from the mean and variance of
  the received signal

R Responsivity of the photodetector ho, he
Impulse response of the optical and electrical
filter NASE Total power spectral density of the
noise Bo Noise equivalent bandwidth of the
optical filter
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Theory on the receiver model

• Signal pulse distortion due to PMD

Principal states of polarization in Jones space
t Differential group delay (First order
PMD) u(t) Electric field of the signal from the
transmitter
Power splitting ratios (
)
Principal state of polarization in Stokes space
(Slow mode)
Principal state of polarization in Stokes space
(Fast mode)
A complex vector

(i0, 1, 2, 3) are Pauli spin matrices
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Theory (cont)
The new formula for the variance due to
signal-noise beating
Stokes vector of the polarized part of the
noise
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Variables in the new formula

• Constants R, NASE (OSNR 15 dB), ? 36 ps,
  and S
• Variables
• Power-splitting-ratio
• DOP of the noise
• Angle between the SOP of the polarized part of
  the noise and the signal

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5. Validation of the receiver model

• How to vary the angle between the signal and the
  noise

(b) Parallel case, (c2 0.5)
(a) Orthogonal case, (c2 0.5)
z
z
?
?
a
a
y
y
x
x
Su Average Stokes vector of the signal
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Monte Carlo simulations

• Orthogonal case, (c2 0.5)

Symbols simulations Lines From formula
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Monte Carlo simulations (cont)
(b) Parallel case, (c2 0.5)
? 0
? p
? p/4
? 5p/8
Symbols simulations Lines From formula
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Monte Carlo simulations (cont)

• Orthogonal case, (c2 0.25)

Symbols simulations Lines From formula
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Monte Carlo simulations (cont)
(b) Parallel case, (c2 0.25)
? p/4 ---- ? 5p/8 - - ? p ? ?
p/4 ? ? 5p/8 ? ? p
Symbols simulations Lines From formula
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Summary of Monte Carlo simulations

• The agreement between theory and Monte
• Carlo simulations is excellent
• Two power-splitting-ratios
• Two schemes of varying the SOP of the noise
• A few angles for the average SOP of the signal

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Experimental validations

• Issues in the experiments
• Drift of the SOP of the signal
• Measurement uncertainties
• Pulse width due to thermal drift of optical
  modulator (12ps)
• OSNR due to power fluctuations (up to 0.2 dB)
• Electrical bandwidth (a few GHz)
• Experimental results
• Sensitivity of the performance to the
  measurement
• uncertainties

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Experimental setup
Transmitter
PM Fiber
OSA
Tunable laser
EOM
EAM
Polarization controller
10 Gb/s
10 GHz
Receiver
Partially polarized noise
BERT
ASE
Polarimeter
Polarizer
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Q-factor in the experiment
Q-factor is estimated from the BER margin
measurement
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Valid BER
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Minimum BER
Optimum threshold
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Experimental cases

• Vary the angle between the SOP of the signal
• and the noise in the following cases
• Case 1 c2 0, DOPn 0.5 and 1
• Case 2 c2 0.5, DOPn 0.5 and 1
• Case 3 c2 0.3, DOPn 0.5 and 1

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Case 1 (c2 0)

• Signal is launched along the PSP
• SOP of the polarized part of the noise is varied

z
PSP
a
Su
y
x
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Experimental results (case 1)
(a) DOPn 0.5
(b) DOPn 1
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Case 2 (c2 0.5)

• SOP of the polarized part of the noise is fixed
• SOP of the signal drifts on the blue circle

z
Su
a
PSP
y
x
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Experimental results (case 2)
(a) DOPn 0.5
(b) DOPn 1
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Case 3 (c2 0.3)

• SOP of the polarized part of the noise is fixed
• SOP of the signal drifts on the blue circle

z
Su
a
PSP
y
x
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Experimental results (case 3)
(a) DOPn 0.5
(b) DOPn 1
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Inherent measurement uncertainty of the Q-factor

• Back-to-back measurement (no transmission fiber
  between the
• transmitter and the receiver)
• Polarized signal and unpolarized noise

?Q 0.3
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Sensitivity to pulse width
?Q 0.4
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Sensitivity to OSNR
?Q 0.3
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Sensitivity to electrical filter
?Q 0.1
?Q 0.1
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6. Conclusions

• We developed a new receiver model that can
  calculate the
• system performance of a depolarized signal and
  partially
• polarized noise
• We validated the new model through Monte Carlo
  simulations
• and experiments.
• Performance sensitivities to measurement
  uncertainties were
• investigated.

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• Thank you

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References

• D. Marcuse, IEEE J. Lightwave Technol., vol. 8,
  pp. 18161823, 1990.
• P. A. Humblet and M. Azizoglu, IEEE J. Lightwave
  Technol., vol. 9, pp. 15761582, 1991.
• P. J. Winzer et al., IEEE J. Lightwave Technol.,
  vol. 19, pp. 12631273, 2001.
• J. L. Rebola and A. V. T. Cartaxo, IEEE J.
  Lightwave Technol., vol. 20, pp. 401408, 2002.
• Yu Sun et al., IEEE Photon. Technol. Lett., vol.
  15, pp. 16481650, 2003.
• I. T. Lima Jr. et al., IEEE J. Lightwave
  Technol., vol. 23, pp. 14781490, 2005.

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Jones space

• Jones vector a two-element complex vector, with
  elements
• represented by the magnitude and phase of the
  electric
• field of the signal
• Jones matrix a complex 2?2 matrix for a device
• eout J ein.
• Simple in theory, not easy to measure in
  experiments

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Stokes space

• Stokes vector a three-element real vector, with
  elements
• represented by the powers of the signal
• S1 Power through linear horizontal polarizer
  (LHP)
• S2 Power difference between light transmitted
  through a linear 45o polarizer (L 45o) and
  through a linear 45o polarizer (L 45o)
• S3 Power difference between light transmitted
  through a right circular polarizer (RCP) and a
  left circular polarizer (LCP)

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Signal-noise beating for a depolarized signal and
partially polarized noise
(0,0,1)
(0,0, 1)
Average SOP of signal (1, 0,
0) Principal states (0, 0, 1) (0,
0, 1)
(1, 0, 0)
(1, 0, 0)
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Sensitivity to optical filter
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Poincaré sphere
Angle between two vectors in Stokes space is two
times of that in Jones space!
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Principal State of Polarization (PSP)

• Two orthogonal polarization states of the fiber
• Pulse un-distorted if launched in PSP
• Well defined in PM fiber

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Assumptions in our receiver model

• We ignore the transmission effects of chromatic
  dispersion
• and nonlinearity (can be included)
• We assume first order PMD dominate the penalties
  induced
• PMD.
• We ignore the PMD effect on the noise and the
  PDL effect
• on the signal (can be included in the model).

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Drift of the SOP of the signal

• Due to short beat length in PM fiber

Su
PSP
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Drift of the SOP of the signal

• Drift was effectively reduced by putting PM
  fiber in water

Su
PSP
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Future work

• Limitation of the new model to second-order PMD
• To determine the effect of second-order of PMD
  to the model.
• Study to be based on Monte Carlo simulations