Joint-characteristic Function of the First- and Second-order Polarization-mode-dispersion Vectors in Linearly Birefringent Optical Fibers

This paper presents the joint characteristic function of the first- and second-order polarization-mode-dispersion (PMD) vectors in installed optical fibers that are almost linearly birefringent. The joint characteristic function is a Fourier transform of the joint probability density function of these PMD vectors. We regard the random fiber birefringence components as white Gaussian processes and use a Fokker-Planck method. In the limit of a large transmission distance, our joint characteristic function agrees with the previous joint characteristic function obtained for highly of birefringent fibers. However, their differences can be noticeable for practical transmission distances.