An Analytic Formulation of PMD-Induced Pulse Distortion

We systematically analyze the pulse distortion resulting from polarization mode dispersion (PMD) by deriving an analytic expression for the characteristic function of the system bit error probability (BEP) density in terms of the lowest-order moments of the Fourier transformed input pulse shape. We determine the range of validity of our technique, which implements a second-order expansion of the Jones matrix, by comparing our results for chirped and unchirped input pulses with direct numerical simulations. Our method may be easily applied to analyze the role of the first- and second-order PMD in the interference between adjacent pulses.