This paper presents a statistical description of polarization dependent chromatic dispersion (PCD) in optical fibers due to second-order polarization mode dispersion (PMD). This chromatic dispersion is the cause of pulse broadening and compression of the signal components propagating in the principal states of polarization. We show here that, remarkably, the probability density function of PCD has the form of the energy density of a first-order optical soliton. We report measurements that are in agreement with the prediction of this soliton density. Moreover, since a large number of independent experimental samples are difficult to obtain, we also report simulations of the experimental process and these serve to underscore the agreement between theory and measurement. The probability density functions of first and second-order PMD vectors are spherically symmetric. However, these vectors are not statistically independent. The mean square depolarization with respect to wavelength of a launched pulse is revealed to be 33% stronger than expected for spherical symmetry in the absence of dependence, while the mean square PCD is weaker by 67%.
Gerard J. Foschini, R. M. Jopson, Lynn E. Nelson, and Herwig Kogelnik, "The Statistics of PMD-Induced Chromatic Fiber Dispersion," J. Lightwave Technol. 17, 1560- (1999)