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A fourth-order Runge-Kutta in the interaction picture (RK4IP) method ispresented for solving the coupled nonlinear Schrodinger equation (CNLSE) thatgoverns the light propagation in optical fibers with randomly varyingbirefringence. The computational error of RK4IP is caused by the fourth-orderRunge-Kutta algorithm, better than the split-step approximation limited by thestep size. As a result, the step size of RK4IP can have the same order ofmagnitude as the dispersion length and/or the nonlinear length of the fiber,provided the birefringence effect is small. For communication fibers withrandom birefringence, the step size of RK4IP can be orders of magnitude largerthan the correlation length and the beating length of the fibers, depending onthe interaction between linear and nonlinear effects. Our approach can beapplied to the fibers having the general form of local birefringence and treatthe Kerr nonlinearity without approximation. For the systems with realisticparameters, the RK4IP results are consistent with those using Manakov-PMDapproximation. However, increased interaction between the linear and nonlinearterms in CNLSE leads to increased discrepancy between RK4IP and Manakov-PMDapproximation.

A fourth-order Runge-Kutta in the interaction picture method for coupled nonlinear Schrodinger equation