Cross-Polarization Modulation in DWDM Systems Marcus Winter Christian-Alexander Bunge Klaus...

Cross-Polarization Modulationin DWDM Systems

Marcus WinterChristian-Alexander Bunge

Klaus Petermann

Hochfrequenztechnik-Photonik

TECHNISCHEUNIVERSITÄTBERLIN

Dario Setti

http://www.marcuswinter.de/publications/ecoc2008


Fachgebiet Hochfrequenztechnik

what is cross-polarization modulation?



typical system in which XPolM may be relevant

nonlinear polarization effects



SOP of a fully polarized CW probe channel

10 × 10Gbps NRZ-modulated interfering

channels @ 8mW (50GHz grid)



visualization of numerical simulation data: fiber span 1



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)



analyzing the random SOP motion



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)



deflection angle from mean direction

pro

ba

bili

ty d

en

sity



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)



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)



autocovariance function:walk-off



walk-off is caused by differing group velocities inDWDM channels due to GVD

→ decorrelation of Stokes vector lengths



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)



autocovariance function:polarization



PMD randomly rotates the polarization state of each channel relative to the probe

→ decorrelation of Stokes vector orientations



polarization effects are not compensated

propagation distance z

[no

rmal

ize

d] A

CF

(0

, z)



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



10 interfering 10Gbit/s channels in 50GHz grid

10 spans: resonant dispersion map of SSMF and (linear) DCF

target DOP = 0.97



summary



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

Cross-Polarization Modulation in DWDM Systems Marcus Winter Christian-Alexander Bunge Klaus...

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