cross-polarization modulation in dwdm systems marcus winter christian-alexander bunge klaus...
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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
TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
what is cross-polarization modulation?
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Fachgebiet Hochfrequenztechnik
typical system in which XPolM may be relevant
nonlinear polarization effects
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SOP of a fully polarized CW probe channel
10 × 10Gbps NRZ-modulated interfering
channels @ 8mW (50GHz grid)
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Fachgebiet Hochfrequenztechnik
visualization of numerical simulation data: fiber span 1
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visualization of numerical simulation data: fiber span 2
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Fachgebiet Hochfrequenztechnik
visualization of numerical simulation data: fiber span 3
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Fachgebiet Hochfrequenztechnik
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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Fachgebiet Hochfrequenztechnik
analyzing the random SOP motion
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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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deflection angle from mean direction
pro
ba
bili
ty d
en
sity
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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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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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autocovariance function:walk-off
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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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Fachgebiet Hochfrequenztechnik
autocovariance function:polarization
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Fachgebiet Hochfrequenztechnik
PMD randomly rotates the polarization state of each channel relative to the probe
→ decorrelation of Stokes vector orientations
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polarization effects are not compensated
propagation distance z
[no
rmal
ize
d] A
CF
(0
, z)
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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
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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summary
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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