Vector theory of stimulated Raman scattering and its application to fiber-based Raman amplifiers

A vector theory of the stimulated Raman scattering process is developed for describing the polarization effects in fiber-based Raman amplifiers. We use this theory to show that polarization-mode dispersion (PMD) induces large fluctuations in an amplified signal. It is found that PMD-induced fluctuations follow a log-normal distribution. We also discuss the random nature of the polarization-dependent gain (PDG) in Raman amplifiers. Using the concept of a PDG vector, we find the probability distribution of PDG in an analytic form and use it to show that both the mean and the standard deviation of PDG depend on the PMD parameter inversely when the effective fiber length is much larger than the PMD diffusion length. We apply our theory to study how PDG can be reduced by scrambling pump polarization randomly and show that the mean value of PDG is directly proportional to the degree of pump polarization.