  A fourth-order Runge-Kutta in the interaction picture (RK4IP) method is
presented for solving the coupled nonlinear Schrodinger equation (CNLSE) that
governs the light propagation in optical fibers with randomly varying
birefringence. The computational error of RK4IP is caused by the fourth-order
Runge-Kutta algorithm, better than the split-step approximation limited by the
step size. As a result, the step size of RK4IP can have the same order of
magnitude as the dispersion length and/or the nonlinear length of the fiber,
provided the birefringence effect is small. For communication fibers with
random birefringence, the step size of RK4IP can be orders of magnitude larger
than the correlation length and the beating length of the fibers, depending on
the interaction between linear and nonlinear effects. Our approach can be
applied to the fibers having the general form of local birefringence and treat
the Kerr nonlinearity without approximation. For the systems with realistic
parameters, the RK4IP results are consistent with those using Manakov-PMD
approximation. However, increased interaction between the linear and nonlinear
terms in CNLSE leads to increased discrepancy between RK4IP and Manakov-PMD
approximation.
