The statistics of PMD-induced chromatic fiber dispersion

This paper presents a statistical description of polarization dependent chr omatic dispersion (PCD) in optical fibers due to second-order polarization mode dispersion (PMD). This chromatic dispersion is the cause of pulse broa dening and compression of the signal components propagating in the principa l states of polarization, We show here that, remarkably, the probability de nsity function of PCD has the form of the energy density of a first-order o ptical soliton. We report measurements that are in agreement with the predi ction of this soliton density. Moreover, since a large number of independen t experimental samples are difficult to obtain, me also report simulations of the experimental process and these serve to underscore the agreement bet ween 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 res pect to wavelength of a launched pulse is revealed to be 33% stronger than expected for spherical symmetry in the absence of dependence, while the mea n square PCD is weaker by 67%.