Analytical treatment of polarization-mode dispersion in single-mode fibers by means of the backscattered signal

We present analytical results on the polarization-mode dispersion characteristics of single-mode birefringent fibers based on statistical properties of the backscattered signal. In particular, we calculate exactly the relationship between polarization-mode dispersion characteristics in forward propagation with respect to round-trip propagation in terms of dynamical equations, differential group delays, correlation lengths, and second-order effects. The theory applies to fibers affected by superposition of linear and circular birefringence in both the short-length and the long-length regimes.