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Cross-Polarization Modulationin DWDM Systems
Marcus WinterChristian-Alexander Bunge
Klaus Petermann
Hochfrequenztechnik-Photonik
TECHNISCHEUNIVERSITÄTBERLIN
Dario Setti
http://www.marcuswinter.de/publications/ecoc2008
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
what is cross-polarization modulation?
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
typical system in which XPolM may be relevant
nonlinear polarization effects
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
SOP of a fully polarized CW probe channel
10 × 10Gbps NRZ-modulated interfering
channels @ 8mW (50GHz grid)
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
visualization of numerical simulation data: fiber span 1
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
visualization of numerical simulation data: fiber span 2
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
visualization of numerical simulation data: fiber span 3
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TECHNISCHEUNIVERSITÄTBERLIN
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SOP of each sample moves seemingly at random
motion can be described by a rotation around the sum of the Stokes vectors of the interfering channels
(which have random length and orientation)
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
analyzing the random SOP motion
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
SOP movement is very similar to Brownian motion / diffusion on the surface of the Poincaré sphere
analytical description of the SOP distribution is known
symmetric around mean direction / given as distribution of deflection angles from mean
parameterized by either variance V or DOP
DOP = exp(-V/2)
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
deflection angle from mean direction
pro
ba
bili
ty d
en
sity
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
we want to derive the distribution(in terms of DOP or V)
analytically from the known system parameters
statistics of the probe SOPs and of the Stokes vector sum Σ are closely linked
Σ is approximately a 3D Gaussian
variance V is the integral over the autocovariance of Σ(with coefficients)
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
for 1st order approximation account only for the dominant effects on the Stokes vectors of the
interfering channels:
length → walk-off between channels
orientation → PMD .
both are pure interchannel effects(pulse shape and interferer DOP are ignored)
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
autocovariance function:walk-off
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
walk-off is caused by differing group velocities inDWDM channels due to GVD
→ decorrelation of Stokes vector lengths
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covariance decreases due to walk-off
dispersion comp.restores ACF
area under ACF determines V
channel spacing determines w-o length
propagation distance z
[no
rmal
ize
d] A
CF
(0
, z)
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
autocovariance function:polarization
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
PMD randomly rotates the polarization state of each channel relative to the probe
→ decorrelation of Stokes vector orientations
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
polarization effects are not compensated
propagation distance z
[no
rmal
ize
d] A
CF
(0
, z)
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
both ACFs depend on the fiber type
V also scales with the squares of optical power in the interfering channels and the nonlinear coefficient
straightforward to calculate power thresholds to keep nonlinear depolarization above e.g. DOP = 0.97
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
10 interfering 10Gbit/s channels in 50GHz grid
10 spans: resonant dispersion map of SSMF and (linear) DCF
target DOP = 0.97
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
summary
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TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
nonlinear channel depolarization due to cross-polarization modulation is a diffusion(-like) process
―
shape of the polarization states distribution is known
―
distribution can be fully parameterized by the DOP
―
DOP can be predicted analytically from system parameters