STATISTICAL-THEORY OF POLARIZATION DISPERSION IN SINGLE-MODE FIBERS

Small deviations from perfect circular symmetry in the core region of "single-mode" fibers cause optical pulses to become broadened as they propagate. Referred to as polarization dispersion, this effect, which causes intersymbol interference, looms as a potentially dominant source of pulse distortion in multigigabit-per-second lightwave transmission systems employing dispersion-shifted fibers. Over the last five years substantial effort (both laboratory measurement and computer simulation) has gone into determining the statistical character of this distortion. Through this effort, a three-dimensional polarization dispersion vector has been identified to characterize the effects of polarization dispersion on narrow-band sources. We present here the theoretical complement to the afore-mentioned experimental and simulation work. Specifically, we report the solution of Poole's stochastic dynamical equation for the evolution of the polarization dispersion vector with fiber length. In addition, we extend to a more complete description by considering small, but non-negligible, second-order dispersion effects through the frequency derivative of the dispersion vector. The work represents an unusually close interplay of theory with experiment and simulation. The complete analytical solution is seen, first of all, to accord with what were originally empirically derived features of the joint probability distribution of the polarization dispersion vector and its frequency derivative and, secondly, to point out hitherto unnoticed features. Among the analytically determined properties are the Gaussian probability densities of the three components of the dispersion vector, the hyperbolic secant (soliton shaped) probability densities of the components of the derivative of the dispersion vector, ten dimensionless constants involving the relative strength of first-order and second-order effects, and the square-root of fiber length dependence of the magnitude of the dispersion vector. The rich symmetry of the, at first, seemingly unwieldy, (six-dimensional) polarization dispersion vector statistics is also detailed. The full set of results serves to provide manageable formulas for representing dispersion for future lightwave transmission systems studies.