Solution of the Multimode Nonlinear Schrödinger Equation Using Physics-Informed Neural Networks

Single-mode optical fibers (SMFs) have become the foundation of modern communication systems. However, their capacity is expected to reach its theoretical limit in the near future. The use of multimode fibers (MMF) is seen as one of the most promising solutions to address this capacity deficit. The multimode nonlinear Schrödinger equation (MMNLSE) describing light propagation in MMF is significantly more complex than the equations for SMF, making numerical simulations of MMF-based systems computationally costly and impractical for most realistic scenarios. In this paper, we apply physics-informed neural networks (PINNs) to solve the MMNLSE. We show that a simple implementation of PINNs does not yield satisfactory results. We investigate the convergence of PINN and propose a novel scaling transformation for the zeroth-order dispersion coefficient that allows PINN to account for all important physical effects. Our calculations show good agreement with the Split-Step Fourier (SSF) method for fiber lengths of up to several hundred meters.