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![Page 1: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/1.jpg)
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
TECHNISCHEUNIVERSITÄTBERLIN
![Page 2: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/2.jpg)
TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
Basics ofCross-Polarization Modulation
(XPolM)
![Page 3: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/3.jpg)
TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
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)
![Page 4: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/4.jpg)
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gold: probe channel, green: WDM channels, silver: Stokes sum
![Page 5: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/5.jpg)
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Fachgebiet Hochfrequenztechnik
in WDM systems, each transmitted symbol experiences a quasi-unique sequence of elementary rotations
SOP / PMD vector diffusion
![Page 6: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/6.jpg)
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Fachgebiet Hochfrequenztechnik
SOP evolution of 213 bits
span 1
DOP = 0.987
![Page 7: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/7.jpg)
TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
SOP evolution of 213 bits
span 2
DOP = 0.967
![Page 8: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/8.jpg)
TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
SOP evolution of 213 bits
span 3
DOP = 0.948
![Page 9: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/9.jpg)
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Fachgebiet Hochfrequenztechnik
SOP diffusion (signal depolarization) can be detrimental for PolMUX systems
PMD vector diffusion can adversely affect PMD compensation
![Page 10: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/10.jpg)
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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
![Page 11: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/11.jpg)
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Fachgebiet Hochfrequenztechnik
Deriving the Model
![Page 12: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/12.jpg)
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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
![Page 13: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/13.jpg)
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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
![Page 14: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/14.jpg)
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Fachgebiet Hochfrequenztechnik
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
![Page 15: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/15.jpg)
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Verification of the Model
![Page 16: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/16.jpg)
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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)
![Page 17: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/17.jpg)
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due to interaction ofSPM/XPM, PMD, XPolM
in copropagating channels
![Page 18: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/18.jpg)
TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
![Page 19: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/19.jpg)
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Influence of Various System Parameters
![Page 20: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/20.jpg)
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![Page 21: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/21.jpg)
TECHNISCHEUNIVERSITÄTBERLIN
Fachgebiet Hochfrequenztechnik
![Page 22: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/22.jpg)
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Fachgebiet Hochfrequenztechnik
![Page 23: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/23.jpg)
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Summary / Outlook
![Page 24: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/24.jpg)
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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
![Page 25: Analysis of Cross-Polarization Modulation in Dispersion-Managed DWDM Systems Marcus Winter, Christian-Alexander Bunge, Dario Setti, Klaus Petermann LEOS.](https://reader038.fdocuments.us/reader038/viewer/2022110305/55204d7349795902118c8403/html5/thumbnails/25.jpg)
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Fachgebiet Hochfrequenztechnik
http://www.marcuswinter.de/publications/leos2007