A GPU-Accelerated Fourth-Order Runge–Kutta in the Interaction Picture Method for the Simulation of Nonlinear Signal Propagation in Multimode Fibers

Abstract

The nonlinear signal propagation in fibers can be described by the nonlinear Schrodinger equation and the Manakov equation. Most commonly, split-step Fourier methods (SSFM) are applied to solve these nonlinear equations. The numerical simulation of the nonlinear signal propagation is especially challenging for multimode fibers, particularly if the calculation of very small step sizes or a large number of steps is required. Instead of utilizing SSFM, the fourth-order Runge–Kutta in the Interaction Picture (RK4IP) method can be applied. This method has the potential to reduce the numerical error while simultaneously allowing an increased step size. These advantages come at the price of a higher numerical effort compared to the SSFM method for the same step size. Since the simulation of the signal propagation in multimode fibers is already quite challenging, parallelization becomes an even more interesting option. We demonstrate the adaptation of the RK4IP method to simulate the nonlinear signal propagation in multimode fibers, including its parallelization. Besides comparing the performance of a parallelized implementation for multicore CPUs and a GPU-accelerated version, we discuss efficient strategies to implement the RK4IP method on a GPU accelerator with CUDA. In addition, the RK4IP implementation is numerically compared with a conventional SSFM implementation.