Efficient Fiber-optic Data Transmission in the Nonlinear Regime

世界上绝大多数的互联网和长途电信都是通过光纤网络进行的，这些网络纵横交错，并通过超长的海底电缆跨越各大洲。 尽管光纤对地球上的每个人和组织都有着明显的重要性，但一个奇怪的事实是，光纤的最终信息承载能力（从信息理论的角度来看）仍然是未知的。 这意味着我们还不确定我们是否尽可能多地从光纤中挤出容量。 这是一个非常重要的实际问题，因为-由于在城市之间和跨海洋铺设光纤的巨大成本-最好是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，光纤信道是一种非线性介质。 所谓的光学克尔效应是指光纤中石英玻璃材料的折射率随入射光强度的变化而变化。光脉冲的传播受一个非常难处理的随机偏微分方程控制，该方程称为广义非线性薛定谔方程，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。 由此产生的数学信道模型远远超出了经过充分研究的信息论教科书模型。 该项目的总体目标是研究光纤非线性缓解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，球形代码和Kolmogorov-Zhakarov弱波湍流模型。 如果成功的话，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制度，有可能实现更大的数据传输速率比现有的方法。

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.