Polarization-Related Statistics of Raman Crosstalk in Single-Mode Optical Fibers

We present a novel comprehensive theory for the pump-to-probe interactions caused by the stimulated Raman scattering (SRS) in glass optical fibers. The developed theory applies to both the Raman gain with the undepleted pump assumption, and to the maximum loss induced by the Raman crosstalk (RXT loss). The latter is an effect that is the limiting propagation impairment in passive optical networks (PON). The main novelty of the paper is a rigorous mathematical analysis, describing the interaction of SRS with the polarization evolution due to polarization mode dispersion (PMD). The Raman gain (or the RXT loss) is modeled as a random process for which a comprehensive theory is developed, giving for the first time to our best knowledge, an exact closed-form expression for the mean and variance of the gain (or depletion), and a computationally efficient algorithm to numerically derive the gain probability density function. The developed theory is validated by the comparison with Monte Carlo analyses, based on the waveplate model for the optical fiber. The validation showed excellent agreement, confirming the validity of the developed theory. As an example of application, we used our theoretical results to analyze next-generation PON (NG-PON2) architectures, confirming that, in this scenario, RXT loss may be a limiting propagation effect.