DOP ellipsoids for systems with frequency-dependent principal states

The effects of polarization mode dispersion (PMD) in optical communication systems limit the practical length of fiber optic links. Characterization of the PMD of an optical system can be performed by observing the surface obtained from the vector whose length is the degree of polarization and direction is defined by the output state of polarization for a randomly varying input polarization. An analytical solution to the ellipsoid is derived for a simple higher order PMD system that is composed of two polarization-maintaining fibers. An approximate inverse relationship between the ellipsoid radii and the first- and second-order components of the PMD vector is also derived.