Cross-Polarization Modulation in DWDM Systems Marcus Winter Christian-Alexander Bunge Klaus Petermann Dario Setti TECHNISCHE UNIVERSITÄT BERLIN Hochfrequenztechnik-Photonik http://www.marcuswinter.de/publications/ecoc2008

what is cross-polarization modulation?

typical system in which XPolM may be relevant nonlinear polarization effects

10 × 10Gbps NRZ-modulated interfering channels @ 8mW (50GHz grid) SOP of a fully polarized CW probe channel

visualization of numerical simulation data: fiber span 1

visualization of numerical simulation data: fiber span 2

visualization of numerical simulation data: fiber span 3

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

analytical description of the SOP distribution is known 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)

probability density deflection angle from mean direction

Σ is approximately a 3D Gaussian 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)

length → walk-off between channels 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

→ decorrelation of Stokes vector lengths walk-off is caused by differing group velocities in DWDM channels due to GVD → decorrelation of Stokes vector lengths

channel spacing determines w-o length covariance decreases due to walk-off area under ACF determines V dispersion comp. restores ACF [normalized] ACF (0, z) propagation distance z

autocovariance function: polarization

→ decorrelation of Stokes vector orientations PMD randomly rotates the polarization state of each channel relative to the probe → decorrelation of Stokes vector orientations

polarization effects are not compensated [normalized] ACF (0, z) propagation distance 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