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

TL;DR

The paper introduces a fourth-order Runge-Kutta in the interaction picture (RK4IP) method for solving coupled nonlinear Schrödinger equations in optical fibers, enabling larger step sizes and improved accuracy over traditional methods.

Contribution

The paper presents a novel RK4IP method that efficiently solves the CNLSE with larger step sizes and without approximations, improving computational accuracy for fiber optics modeling.

Findings

RK4IP achieves higher accuracy than split-step methods.

Step size can be comparable to dispersion and nonlinear lengths.

Method is consistent with Manakov-PMD approximation for realistic parameters.

Abstract

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.