Cross-Polarization Modulation in DWDM Systems

Präsentation zum Thema: "Cross-Polarization Modulation in DWDM Systems"—  Präsentation transkript:

1 Cross-Polarization Modulation in DWDM Systems
Marcus Winter Christian-Alexander Bunge Klaus Petermann Dario Setti TECHNISCHE UNIVERSITÄT BERLIN Hochfrequenztechnik-Photonik

2 what is cross-polarization modulation?

3 typical system in which XPolM may be relevant
nonlinear polarization effects

4 10 × 10Gbps NRZ-modulated interfering channels @ 8mW (50GHz grid)
SOP of a fully polarized CW probe channel

5 visualization of numerical simulation data: fiber span 1

6 visualization of numerical simulation data: fiber span 2

7 visualization of numerical simulation data: fiber span 3

8 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)

9 analyzing the random SOP motion

10 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)

11 probability density deflection angle from mean direction

12 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)

13 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)

14 autocovariance function: walk-off

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

16 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

17 autocovariance function: polarization

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

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

20 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

21 10 interfering 10Gbit/s channels in 50GHz grid
10 spans: resonant dispersion map of SSMF and (linear) DCF target DOP = 0.97

22 summary

23 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