Optimal Polarization Launch for Raman Depletion Minimization in GPON and TWDM-PON Coexistence

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

“…In particular, in [33], a complete analysis of the statistics of Raman gain for random input SOPs is carried out, and it is shown that the probability density function (PDF) of the Raman gain in that case is given by a log-normal, Gaussian in dB, distribution with known mean and variance. For the RXT-loss, such a result, among others, is confirmed in [23], [24]. In [33], the case of known input SOPs is not analyzed while it is done in [32].…”

“…In the last couple of years, the ongoing standardization process of NG-PON2 has required to study in details the effects of SRS in the full-coexistence scenario, in order to understand under what circumstances compatibility among different PON standards may exist. The works existing in literature [21], [24], [38] have always made use of simulations in order to take into account the stochastic nature of SRS. Such simulations are long and computational intensive, that may require several weeks of CPU time in order to produce reliable results.…”

“…On the contrary, in some recent implementation of passive optical networks (PON), RXT is already a limiting issue, as analyzed in [18]- [21], since different services are placed on different wavelengths in both the C-and L-band simultaneously, and may thus have a spectral separation close to the Raman peak. In particular, in NG-PON2 [22], the activation of TWDM-PON channels at 1600 nm may strongly deplete the already operating GPON channel at 1500 nm, possibly causing its out-of-service [23], [24]. SRS depends on the evolution with propagation of the states of polarization (SOP) of the signals involved in the process, as it is mainly effective among signals locally characterized by the same SOP [25].…”

“…Therefore, any variation of signal SOPs with time and distance makes the RXT vary consequentially. Since the variation of SOPs is a random process, the RXT loss is stochastic as well, and its characterization is required in order to estimate the probability of out-of-service they may induce [23], [24]. It is well known that in optical fibers, the main physical effects causing change of SOPs are the birefringence and the phenomenon generated by its random variation, i.e., the polarization mode dispersion (PMD).…”

“…A one dimensional version of this problem, namely the integral of the component of a particle freely diffusing on a circle, has been solved, in the small noise limit, in a seminal paper by Foschini and Vannucci in the context of the analysis of the noise of an integrate and dump receiver with a local oscillator of finite linewidth [34]. Thanks to the obtained results, we are able to statistically fully characterize the RXT loss with the possibility to estimate the related outage probability in PONs [23], [24]. In addition, we also provide an analytical approximation able to give the PDF of the Raman gain for very small values of PMD.…”