Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives

Abstract

Fiber-optic communication systems are nowadays facing serious challenges due to fast growing demand on capacity from various new applications and services. It is now well recognised that nonlinear effects limit the spectral efficiency and transmission reach of modern fiber-optic communications. Nonlinearity compensation is therefore widely believed to be of paramount importance for increasing the capacity of future optical networks. Recently, there has been a steadily growing interest in the application of a powerful mathematical tool -the nonlinear Fourier transform (NFT) -in the development of fundamentally novel nonlinearity mitigation tools for fiber-optic channels. It has been recognized that, within this paradigm, the nonlinear crosstalk due to the Kerr effect is effectively absent, and fiber nonlinearity due to Kerr effect can enter as a constructive element rather than a degrading factor. The novelty and the mathematical complexity of the NFT, the versatility of the proposed system designs, and the lack of a unified vision of an optimal NFT-type communication system however constitute significant difficulties for communication researchers. In this paper, we therefore survey the existing approaches in a common framework and review the progress in this area with a focus on practical implementation aspects. First, an overview of existing key algorithms for the efficacious computation of the direct and inverse NFT is given, and the issues of accuracy and numerical complexity are elucidated. We then describe different approaches for the utilization of the NFT in practical transmission schemes. After that we discuss the differences, advantages and challenges of various recently emerged system designs employing the NFT, and the efficiency estimation available up-to-date. With many practical implementation aspects still being open, our minireview is aimed at helping researchers to assess the perspectives, understand the bottle-necks, and envision the development paths in the upcoming of NFT-based transmission technologies.

FNFT: A Software Library for Computing Nonlinear Fourier Transforms

“…In the last few years, there has been much interest in using NFTs for data transmission in optical fibers. We refer to Turitsyn et al (2017) for a recent review. Several invited papers and tutorials on the topic have been presented at major conferences such as the Optical Fiber Communication Conference and Exhibition (OFC) and the European Conference and Exhibition on Optical Communication (ECOC) in the last few years.…”

Soliton Content of Fiber-Optic Light Pulses

“…In the course of this renewed attention, several nonlinear transmission schemes and techniques for the nonlinear Fourier transform and its inverse transform have been (and still are) developed to overcome the linear capacity limits of fiber-optical transmission lines. An overview about the latest developments can be found in [63].…”

“…As an example, when setting A 0 = 3 and choosing P 0 and T 0 according to Equation (4), DST reveals that the pulse consists of two solitons and a small amplitude radiation part of nontrivial spectral shape (see Figure 8). Various schemes for numerical calculations of the DST are available [63,[65][66][67][68]. They all solve the Zakharov-Shabat eigenvalue problem of a discretized input field with M sample points and determine the nonlinear spectrum.…”

“…One can distinguish between matrix methods that calculate the eigenvalues directly from a M × M matrix and search methods in which the eigenvalues are found in an iterative manner. For a recent discussion, see, e.g., [63,[66][67][68].…”

“…Like the nonperiodic IST, this periodic case gained renewed interest in recent years. Different theoretical and numerical schemes have been developed with a view toward the application of nonlinear data transmission [63,66,67,[81][82][83]. A variant of the periodic DST based on the artificial periodization of field components was used to analyze rogue events and numerically to find the eigenvalue spectra of the breather solutions of Section 2.2 [84].…”