**Impairments in Polarization-Multiplexed DWDM Channels due to Cross-Polarization Modulation
**

21th Annual Meeting of the IEEE Lasers and Electro-Optics Society 2008

**Abstract**: We derive the statistics of cross-polarization modulation-induced nonlinear crosstalk in polarization-multiplexed DWDM channels and an approximate relation between the degree of polarization and the associated noise terms.

**Reference**:

M. Winter, C.-A. Bunge, K. Petermann, D. Setti, “Impairments in Polarization-Multiplexed DWDM Channels due to Cross-Polarization Modulation,” *The 21th Annual Meeting of the IEEE Lasers and Electro-Optics Society*, 2008. LEOS 2008, paper WH3, 9-13 Nov. 2008

2008-Nov-26: corrected slides uploaded (no 3 dB “baseline” penalty for PolDM)

**Notes**:

A few notes on the *system simulation* slides, as these results were obtained after the paper was submitted and are not contained therein. There originally appeared an additional 3 dB penalty for all PolDM points. This would only be correct when calculating the PolDM OSNR penalty against the single-channel back-to-back OSNR value, as PolDM has this 3 dB penalty over SC. However, the penalty should be calculated versus the back-to-back PolDM OSNR value, so that this extra penalty does not appear. Thanks to M. O’Sullivan for pointing this out to me.

More general, the blue points in the graph show the OSNR penalties for CW-only probe channels when interpreting the output as an all-zero DQPSK signal (initially constant phase), one point for each iteration of the simulation (random initial polarizations of all channels, random bit patterns, phases and timings, random birefringence; all other parameters held constant between iterations). The power in the interfering channels was chosen so that the average penalty @ BER 10^{-4} is 1 dB. The penalties are not dependent on the DOP of the probe in the particular iteration (x-axis). Therefore, the reason for the penalty must be polarization-independent, which would point to XPM (in the Manakov sense of the NLSE).

The red points show the OSNR penalties when a (D)QPSK channel is added orthogonal to the probe at the same wavelength (PolDM) to each simulated system. The DOP shown on the x-axis, which makes no sense for a PolDM system, is the DOP of the corresponding CW-only system (see above). The increase in penalties is due to the crosstalk from the orthogonal channel. If this crosstalk were Gaussian in each iteration, all the red dots would lie along the dotted line (plus some variation similar to that due to XPM). But it is only Gaussian in the ensemble mean sense and may deviate considerably for each of the iterations — similar to the variations in XPM; however, not only dependent on the power of the interfering channels, but also on their polarization.

In general, the OSNR penalty does depend on the DOP (which is a measure of XPolM degradation of that particular iteration), but not in a deterministic way.

At this point it is not possible to predict the individual crosstalk (or, equivalently, SOP) distributions, or even the distribution of the DOPs for any particular system (comprising the set of fiber parameters and lengths of all spans). We can only predict the mean DOP of the polarization/PMD ensemble (see this publication). The DOP distribution around this mean depends much on the particular dispersion map used. With great simulation effort, it would be possible to give outage probabilities dependent on this mean DOP. These would, however, be valid only for a system, modulation format, and power values.

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