Efficient Fiber-optic Data Transmission in the Nonlinear Regime**

世界上绝大多数的互联网和长途通信都是通过光纤网络传输的，这些光纤网络纵横交错，并通过超长海底电缆在它们之间跨越。尽管光纤对地球上的每个人和组织都很重要，但令人好奇的是，光纤的最终信息承载能力（在信息理论意义上）仍然未知。这意味着我们还不能确定我们是否能从光纤中挤出尽可能多的容量。这是一个具有重大实际意义的问题，因为在城市之间和跨越海洋铺设光纤的成本巨大，因此更倾向于优化现有光纤基础设施的使用。**建立光纤容量的理论困难在于，在远距离发送信息所需的非常高的光强度下，光纤通道是一种非线性介质。所谓的光学克尔效应导致光纤的二氧化硅玻璃材料的折射率随着入射光的强度而变化。光脉冲的传播是由一个众所周知的难以处理的随机偏微分方程控制的，这个方程被称为广义非线性薛定谔方程，它描述了色散、非线性和放大器噪声之间的物理效应和相互作用。由此产生的数学渠道模型远远超出了被充分研究的信息论教科书模型。**本项目的总体目标是研究光纤非线性减缓的基本限制和实际工程潜力，使用基于三种方法的技术：所谓的非线性傅立叶变换、球面编码和Kolmogorov-Zhakarov弱波湍流模型。如果成功，这项研究可能会产生有趣的新方法来协调宽带信道上的信息传输，特别是在高度非线性的传输机制中，有可能实现比现有方法更高的数据传输速率。******

The vast majority of the world's Internet and long-distance telecommunications is carried over fiber-optic networks that criss-cross the continents and span between them via ultra-long undersea cables. Despite their obvious importance to just about every person and organization on the planet, it is a curious fact that the ultimate information-carrying capacity (in an information-theoretic sense) of optical fibers remains unknown. This means that we are not yet sure that we are squeezing as much capacity out of a fiber as we possibly can. This is a question of great practical importance as---due to the immense cost of laying fibers between cities and across oceans---it is much preferred to optimize the use of the existing fiber infrastructure.** The theoretical difficulty in establishing the capacity of optical fibers is that, at the very high optical intensities needed to send information over vast distances, the fiber-optic channel is a nonlinear medium. The so-called optical Kerr effect causes the index of refraction of the silica glass material of a fiber to change in response to the intensity of the light impinging upon it. Light-pulse propagation is governed by a notoriously intractable stochastic partial differential equation called the generalized nonlinear Schroedinger equation, that describes the physical effects and interactions among chromatic dispersion, nonlinearity, and amplifier noise. The resulting mathematical channel model goes far beyond the well-studied information theory textbook models.** The overall goal of this project is to study the fundamental limits and practical engineering potential of fiber-optic nonlinearity mitigation using techniques based on three approaches: the so-called nonlinear Fourier transform, spherical codes, and the Kolmogorov-Zhakarov weak wave turbulence model. If successful, this research may yield interesting new methods to coordinate information transmission over wide-band channels, particularly in the highly nonlinear transmission regime, with the potential to achieve greater data transmission rates than existing approaches.******