We experimentally investigate the problem of monitoring the Kerr-nonlinearity coefficient $\gamma$ from transmitted and received data for a single-mode fiber link of 1600 km length. We compare the accuracy and speed of three different approaches. First, a standard split-step Fourier method is used to predict the output at various $\gamma$ values, which are then compared to the measured output. Second, a recently proposed nonlinear Fourier transform (NFT)-based method, which matches solitonic eigenvalues in the transmitted and received signals for various $\gamma$ values. Third, a novel fast version of the NFT-based method, which only matches the highest few eigenvalues. Although the NFT-based methods do not scale with link length, we demonstrate that the SSFM-based method is significantly faster than the basic NFT-based method for the considered link of 1600 km, and outperforms even the faster version. However, for a simulated link of 8000 km, the fast NFT-based method is shown to be faster than the SSMF-based method, although at the cost of a small loss in accuracy.

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The shallow waters off the coast of Norderney in the southern North Sea are characterised by a higher frequency of rogue wave occurrences than expected. Here, rogue waves refer to waves exceeding twice the significant wave height. The role of nonlinear processes in the generation of rogue waves at this location is currently unclear. Within the framework of the Korteweg–de Vries (KdV) equation, we investigated the discrete soliton spectra of measured time series at Norderney to determine differences between time series with and without rogue waves. For this purpose, we applied a nonlinear Fourier transform (NLFT) based on the Korteweg–de Vries equation with vanishing boundary conditions (vKdV-NLFT). At measurement sites where the propagation of waves can be described by the KdV equation, the solitons in the discrete nonlinear vKdV-NLFT spectrum correspond to physical solitons. We do not know whether this is the case at the considered measurement site. In this paper, we use the nonlinear spectrum to classify rogue wave and non-rogue wave time series. More specifically, we investigate if the discrete nonlinear spectra of measured time series with visible rogue waves differ from those without rogue waves. Whether or not the discrete part of the nonlinear spectrum corresponds to solitons with respect to the conditions at the measurement site is not relevant in this case, as we are not concerned with how these spectra change during propagation. For each time series containing a rogue wave, we were able to identify at least one soliton in the nonlinear spectrum that contributed to the occurrence of the rogue wave in that time series. The amplitudes of these solitons were found to be smaller than the crest height of the corresponding rogue wave, and interaction with the continuous wave spectrum is needed to fully explain the observed rogue wave. Time series with and without rogue waves showed different characteristic soliton spectra. In most of the spectra calculated from rogue wave time series, most of the solitons clustered around similar heights, but the largest soliton was outstanding, with an amplitude significantly larger than all other solitons. The presence of a clearly outstanding soliton in the spectrum was found to be an indicator pointing towards the enhanced probability of the occurrence of a rogue wave in the time series. Similarly, when the discrete spectrum appears as a cluster of solitons without the presence of a clearly outstanding soliton, the presence of a rogue wave in the observed time series is unlikely. These results suggest that soliton-like and nonlinear processes substantially contribute to the enhanced occurrence of rogue waves off Norderney.@en

Fiber-optic transmission based on nonlinear frequency division multiplexing (NFDM) has received much attention in recent years. We introduce NFDMLab, an open source software package for simulating NFDM transmissions written in the Python language.@en

The recently proposed b-modulation method for nonlinear Fourier transform-based fiber-optic transmission offers explicit control over the duration of the generated pulses and therewith solves a longstanding practical problem. The currently used b-modulation however suffers from a fundamental energy barrier. There is a limit to the energy of the pulses, in normalized units, that can be generated. In this paper, we discuss how the energy barrier can be shifted by proper design of the carrier waveform and the modulation alphabet. In an experiment, it is found that the improved b-modulator achieves both a higher Q-factor and a further reach than a comparable conventional b-modulator. Furthermore, it performs significantly better than conventional approaches that modulate the reflection coefficient.

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Fiber-optic communication systems are nowadays facing serious challenges due to the fast growing demand on capacity from various new applications and services. It is now well recognized 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 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 the 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, as well as the spectral efficiency estimates available up-to-date. With many practical implementation aspects still being open, our mini-review is aimed at helping researchers assess the perspectives, understand the bottlenecks, and envision the development paths in the upcoming NFT-based transmission technologies.

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