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

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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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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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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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

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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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Fachgebiet Hochfrequenztechnik

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