Abstract The potential for higher spectral efficiency has increased interest in mode division multiplexing (MDM) systems. However, the sensitivity of MDM to fiber nonlinearity and mode coupling, which induces nonlinear phase noise (NLPN), forms the main penalty. In this work, we developed an analytical model that describes the effects of fiber nonlinearity on the performance of m-array quadrature amplitude modulation (mQAM) MDM system based few-mode fiber (FMF). The random NLPN is mainly induced when Kerr nonlinearities such as self-phase modulation (SPM), cross-phase modulation (XPM) and four-wave mixing (FWM) as well as their interaction with optical amplifiers noise occur over an optical fiber link. FMF is proposed and designed to carry six spatial modes. The parameters of proposed FMF are used with the analytical model for evaluating the NLPN versus power and distance. To verify the analytical results, an MDM system, that uses proposed FMF without any nonlinear compensation, is demonstrated by numerical simulation. Each spatial mode is modulated by a 4QAM format with a symbol rate of 20 Gsymbol/s. The results are obtained for single-, two- and six–mode propagations to show the influence of fiber nonlinearity on the system performance. The results reveal that the XPM phase noise is the dominant effect that degrades the system performance, specifically when two degenerate spatial modes or modes within the same mode group are co-propagated. In addition, for six-mode transmission, FWM insignificantly induces the NLPN. Finally, the results confirm that the numerical and analytical results in good agreement.

中文翻译：

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存在非线性相位噪声的模分复用系统性能分析

摘要 更高频谱效率的潜力引起了对模分复用 (MDM) 系统的兴趣。然而，MDM 对光纤非线性和模式耦合的敏感性会导致非线性相位噪声 (NLPN)，这是主要的代价。在这项工作中，我们开发了一个分析模型，该模型描述了光纤非线性对基于多模光纤 (FMF) 的 m 阵列正交幅度调制 (mQAM) MDM 系统性能的影响。随机 NLPN 主要是在光纤链路上发生自相位调制 (SPM)、交叉相位调制 (XPM) 和四波混频 (FWM) 等克尔非线性及其与光放大器噪声的相互作用时引起的。提出并设计 FMF 以承载六种空间模式。建议的 FMF 的参数与分析模型一起使用，以评估 NLPN 与功率和距离的关系。为了验证分析结果，通过数值模拟演示了一个 MDM 系统，该系统使用没有任何非线性补偿的建议 FMF。每个空间模式由 4QAM 格式调制，符号率为 20 Gsymbol/s。获得了单模、二模和六模传播的结果，以显示光纤非线性对系统性能的影响。结果表明，XPM 相位噪声是降低系统性能的主要影响，特别是当两个退化空间模式或同一模式组中的模式共同传播时。此外，对于六模传输，FWM 对 NLPN 的影响微不足道。最后，