analysis of cross-polarization modulation in dispersion-managed dwdm systems marcus winter,...

Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems

Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann

LEOS Annual Meeting 2007

Hochfrequenztechnik-Photonik

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Fachgebiet Hochfrequenztechnik

Basics ofCross-Polarization Modulation

(XPolM)

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birefringence alters signal polarization

signal polarization can be described by Stokes vectors or SOPs (states of polarization)

XPolM results from birefringence modulation due to Kerr nonlinearity

XPolM manifests as rotation of Stokes vectors / SOPs and the PMD vector(rotation axis is the sum of all WDM Stokes vectors)

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gold: probe channel, green: WDM channels, silver: Stokes sum

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in WDM systems, each transmitted symbol experiences a quasi-unique sequence of elementary rotations

SOP / PMD vector diffusion

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SOP evolution of 213 bits

span 1

DOP = 0.987

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SOP evolution of 213 bits

span 2

DOP = 0.967

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SOP evolution of 213 bits

span 3

DOP = 0.948

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SOP diffusion (signal depolarization) can be detrimental for PolMUX systems

PMD vector diffusion can adversely affect PMD compensation

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Are these effects relevant for my system(s)?

1. measure - too late

2. simulate - WDM + PMD = tens of CPU days (per configuration)

3. analytical model - has to be sufficiently accurate

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Deriving the Model

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XPolM rotation axis (sum of many Stokes vectors) is a Gaussian random process

assuming isotropy, it is fully parameterized by the axis variance

the variance of a stochastic process is determined by (double) integration over its covariance function

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present model describes the covariance function of the Stokes sum taking into account - pulse profile (shape, length, magnitude) - attenuation - walk-off between channels - polarization decorrelation between channels

not included: - intrachannel linear and nonlinear distortions - depolarization in neighboring channels

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from the axis variance can be derived:

- the resulting SOP statistics (Roberts-Ursell distribution)

- a simple relation for the DOP DOP = exp (− ²/3 · σ²)

DOP/SOP statistics are well suited to test the model

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Verification of the Model

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10 × 10 Gbit/s NRZ + DC probe at center wavelength 50 GHz channel spacing 5 mW/ch SSMF full inline dispersion compensation DPMD = 0.5 ps/km0.5

split-step Fourier + coarse-step method 100 iterations (~8 CPU days on a 2.67 GHz Core2 PC)

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due to interaction ofSPM/XPM, PMD, XPolM

in copropagating channels

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Influence of Various System Parameters

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Summary / Outlook

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first-order model for XPolM has been developed

simple / usable in a non-numerical way symbol rate transparent approximation of the impact of XPolM comparison of system parameters/mitigation methods orders of magnitude faster than numerical simulations

(post-compensation) PMD vector statistics can also be derived

actual transmission penalties must still be derived

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http://www.marcuswinter.de/publications/leos2007