Single-mode optical fibers (SMFs) have become the backbone of modern communication systems. However, their throughput is expected to reach its theoretical limit in the nearest future. Utilization of multimode fibers (MMFs) is considered as one of the most promising solutions rectifying this capacity crunch. Nevertheless, differential equations describing light propagation in MMFs are a way more sophisticated than those for SMFs, which makes numerical modelling of MMF-based systems computationally demanding and impractical for the most part of realistic scenarios. Physics-informed neural networks (PINNs) are known to outperform conventional numerical approaches in various domains and have been successfully applied to the nonlinear Schr\"odinger equation (NLSE) describing light propagation in SMFs. A comprehensive study on application of PINN to the multimode NLSE (MMNLSE) is still lacking though. To the best of our knowledge, this paper is the first to deploy the paradigm of PINN for MMNLSE and to demonstrate that a straightforward implementation of PINNs by analogy with NLSE does not work out. We pinpoint all issues hindering PINN convergence and introduce a novel scaling transformation for the zero-order dispersion coefficient that makes PINN capture all relevant physical effects. Our simulations reveal good agreement with the split-step Fourier (SSF) method and extend numerically attainable propagation lengths up to several hundred meters. All major limitations are also highlighted.
翻译:单模光光纤(SMFs)已成为现代通信系统的基石,但预计其输送量将在最近的将来达到其理论极限。多模纤维(MMFs)的利用被认为是纠正这种能力萎缩的最有希望的解决办法之一。然而,描述MMMF的光传播的不同方程比描述MMMMF系统(MMMF的光传播的公式比SMMF的系统(MMMMF的系统)的数字建模更加复杂,在多数现实情景中,这种模型的计算要求和不切实际情景大多是要求和不切实际情景的。物理知情神经网络(PNNNNNNNN)已知在不同领域超越常规数字方法,并成功地应用于说明描述SMFS的轻度传播的最有希望的解决方案。我们所有关于PINNINNNMMMLS系统(MNMMMNLSE)应用PINN的模型模型模型,以及表明通过与NLSSE类的类类比比的PINNNNNNN的简单实施PINNNNNNS类直接执行PIM(与MLSEMRMMMMMMMM(也无法使MF的物理、PSIM IM IM IM IM IM 和IM IM IM IM IM IM IM 所有的IM 和IM IM IM IM 所有的IM IM IM IM IM IM IM 的模型化改革 和 的模型 的模型化 的模型化化、所有序磨磨磨磨制 和 和 的全 和 的全 的全 的全 的全 的全 的