Experimental validation of XPM mitigation using a generalizable multi-task learning neural network.

We address the development of efficient neural network (NN)-based post-equalizers in long-haul coherent-detection dense wavelength-division multiplexing (DWDM) optical transmission systems. To achieve a high level of generalization of the NN-based equalizers, we propose to employ multi-task learning (MTL). MTL refers to a single shared machine learning (NN) model that can perform multiple different (albeit related) tasks.

Robust neural networks using stochastic resonance neurons.

Various successful applications of deep artificial neural networks are effectively facilitated by the possibility to increase the number of layers and neurons in the network at the expense of the growing computational complexity. Increasing computational complexity to improve performance makes hardware implementation more difficult and directly affects both power consumption and the accumulation of signal processing latency, which are critical issues in many applications. Power consumption can be potentially reduced using analog neural networks, the performance of which, however, is limited by noise aggregation.

Raman dissipative soliton source of ultrashort pulses in NIR-III spectral window.

We present a novel fiber source of ultrashort pulses at the wavelength of 1660 nm based on the technique of external cavity Raman dissipative soliton generation. The output energy of the generated 30 ps chirped pulses is in the range of 0.5-3.

Soliton control in fiber lasers with a semiconductor optical amplifier by off-set filtering.

The path-averaged model is applied to described soliton characteristics in the anomalous cavity dispersion fiber laser with semiconductor optical amplifier. It is shown that, by off-setting the optical filter relative to the gain spectral maximum, it is possible to control velocity and frequency of both the fundamental optical soliton and chirped dissipative solitons.

Memory-aware end-to-end learning of channel distortions in optical coherent communications.

We implement a new variant of the end-to-end learning approach for the performance improvement of an optical coherent-detection communication system. The proposed solution enables learning the joint probabilistic and geometric shaping of symbol sequences by using auxiliary channel model based on the perturbation theory and the refined symbol probabilities training procedure. Due to its structure, the auxiliary channel model based on the first order perturbation theory expansions allows us performing an efficient parallelizable model application, while, simultaneously, producing a remarkably accurate channel approximation.

30-GBaud DP 16-QAM transmission in the E-band enabled by bismuth-doped fiber amplifiers.

We report the transmission of five 30-GBaud dual polarization 16-QAM signals over 160 km of standard single-mode fiber in the E-band (1410-1460 nm). The transmission line consists of two 80-km spans and three independent bismuth-doped fiber amplifiers. The developed amplifiers feature a maximum gain of 27.

Experimental implementation of a neural network optical channel equalizer in restricted hardware using pruning and quantization.

The deployment of artificial neural networks-based optical channel equalizers on edge-computing devices is critically important for the next generation of optical communication systems. However, this is still a highly challenging problem, mainly due to the computational complexity of the artificial neural networks (NNs) required for the efficient equalization of nonlinear optical channels with large dispersion-induced memory. To implement the NN-based optical channel equalizer in hardware, a substantial complexity reduction is needed, while we have to keep an acceptable performance level of the simplified NN model.

Neural networks for computing and denoising the continuous nonlinear Fourier spectrum in focusing nonlinear Schrödinger equation.

We combine the nonlinear Fourier transform (NFT) signal processing with machine learning methods for solving the direct spectral problem associated with the nonlinear Schrödinger equation. The latter is one of the core nonlinear science models emerging in a range of applications. Our focus is on the unexplored problem of computing the continuous nonlinear Fourier spectrum associated with decaying profiles, using a specially-structured deep neural network which we coined NFT-Net.

Intracavity incoherent supercontinuum dynamics and rogue waves in a broadband dissipative soliton laser.

Understanding dynamical complexity is one of the most important challenges in science. Significant progress has recently been made in optics through the study of dissipative soliton laser systems, where dynamics are governed by a complex balance between nonlinearity, dispersion, and energy exchange. A particularly complex regime of such systems is associated with noise-like pulse multiscale instabilities, where sub-picosecond pulses with random characteristics evolve chaotically underneath a much longer envelope.

Convolutional long short-term memory neural network equalizer for nonlinear Fourier transform-based optical transmission systems.

We evaluate improvement in the performance of the optical transmission systems operating with the continuous nonlinear Fourier spectrum by the artificial neural network equalisers installed at the receiver end. We propose here a novel equaliser designs based on bidirectional long short-term memory (BLSTM) gated recurrent neural network and compare their performance with the equaliser based on several fully connected layers. The proposed approach accounts for the correlations between different nonlinear spectral components.

Fast mode decomposition in few-mode fibers.

Retrieval of the optical phase information from measurement of intensity is of a high interest because this would facilitate simple and cost-efficient techniques and devices. In scientific and industrial applications that exploit multi-mode fibers, a prior knowledge of spatial mode structure of the fiber, in principle, makes it possible to recover phases using measured intensity distribution. However, current mode decomposition algorithms based on the analysis of the intensity distribution at the output of a few-mode fiber, such as optimization methods or neural networks, still have high computational costs and high latency that is a serious impediment for applications, such as telecommunications.

Author Correction: Analysis of laser radiation using the Nonlinear Fourier transform.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Soliton-sinc optical pulses.

We introduce a new, to the best of our knowledge, type of band-limited optical pulse-soliton-sinc tailored to the nonlinear Schrödinger (NLS) equation. The idea behind the soliton-sinc pulse is to combine, even if approximately, a property of a fundamental soliton to propagate without distortions in nonlinear systems governed by the NLS equation with a compact band-limited spectrum of a Nyquist pulse. Though the shape preserving propagation feature is not exact, such soliton-sinc pulses are more robust against nonlinear signal distortions compared to a Nyquist pulse.

Tailoring of spatial coherence in a multimode fiber by selectively exciting groups of eigenmodes.

Control of the properties of speckle patterns produced by mutual interference of light waves is important for various applications of multimode optical fibers. It has been shown previously that a high signal-to-noise ratio in a multimode fiber can be achieved by preferential excitation of lower order spatial eigenmodes in optical fiber communication. Here we demonstrate that signal spatial coherence can be tailored by changing relative contributions of the lower and higher order multimode fiber eigenmodes for the research of speckle formation and spatial coherence.

Combining nonlinear Fourier transform and neural network-based processing in optical communications.

We propose a method to improve the performance of the nonlinear Fourier transform (NFT)-based optical transmission system by applying the neural network post-processing of the nonlinear spectrum at the receiver. We demonstrate through numerical modeling about one order of magnitude bit error rate improvement and compare this method with machine learning processing based on the classification of the received symbols. The proposed approach also offers a way to improve numerical accuracy of the inverse NFT; therefore, it can find a range of applications beyond optical communications.

Nonlinear Fourier transform for characterization of the coherent structures in optical microresonators.

We propose and demonstrate, in the framework of the generic mean-field model, the application of the nonlinear Fourier transform (NFT) signal processing based on the Zakharov-Shabat spectral problem to the characterization of the round trip scale dynamics of radiation in optical fiber- and microresonators.

Analysis of laser radiation using the Nonlinear Fourier transform.

Modern high-power lasers exhibit a rich diversity of nonlinear dynamics, often featuring nontrivial co-existence of linear dispersive waves and coherent structures. While the classical Fourier method adequately describes extended dispersive waves, the analysis of time-localised and/or non-stationary signals call for more nuanced approaches. Yet, mathematical methods that can be used for simultaneous characterisation of localized and extended fields are not yet well developed.

Gain-through-filtering enables tuneable frequency comb generation in passive optical resonators.

Optical frequency combs (OFCs), consisting of a set of phase-locked, equally spaced laser frequency lines, have enabled a great leap in precision spectroscopy and metrology since seminal works of Hänsch et al. Nowadays, OFCs are cornerstones of a wealth of further applications ranging from chemistry and biology to astrophysics and including molecular fingerprinting and light detection and ranging (LIDAR) systems, among others. Driven passive optical resonators constitute the ideal platform for OFC generation in terms of compactness and low energy footprint.

Rogue bioelectrical waves in the brain: the Hurst exponent as a potential measure for presurgical mapping in epilepsy.

Objective: Brain electromagnetic activity in patients with epilepsy is characterized by abnormal high-amplitude transient events (spikes) and abnormal patterns of synchronization of brain rhythms that accompany epileptic seizures. With the aim of improving methods for identifying epileptogenic sources in magnetoencephalographic (MEG) recordings of brain data, we applied methods previously used in the study of oceanic 'rogue waves' and other freak events in complex systems.

Approach: For data from three patients who were awaiting surgical treatment for epilepsy, we used a beamformer source model to produce volumetric maps showing areas with a high proportion of spikes that could be classified as 'rogue waves', and areas with high Hurst exponent (HE).

On the theory of adiabatic field dynamics in the Kerr medium with distributed gain and dispersion.

A general theory is presented for the adiabatic field evolution in a nonlinear Kerr medium with distributed amplification and varying dispersion. Analytical expression is derived linking parameters of the adiabaticity, gain distribution, and dispersion profile. As a particular example, an optical pulse compressor based on the adiabatic dynamics is examined.

Gain through losses in nonlinear optics.

Instabilities of uniform states are ubiquitous processes occurring in a variety of spatially extended nonlinear systems. These instabilities are at the heart of symmetry breaking, condensate dynamics, self-organisation, pattern formation, and noise amplification across diverse disciplines, including physics, chemistry, engineering, and biology. In nonlinear optics, modulation instabilities are generally linked to the so-called parametric amplification process, which occurs when certain phase-matching or quasi-phase-matching conditions are satisfied.

Polarization-multiplexed nonlinear inverse synthesis with standard and reduced-complexity NFT processing: erratum.

We correct a formula for the numerical nonlinear Fourier transform in [1]. The conclusions of our work are unchanged.

Contour integrals for numerical computation of discrete eigenvalues in the Zakharov-Shabat problem.

We propose a novel algorithm for the numerical computation of discrete eigenvalues in the Zakharov-Shabat problem. Our approach is based on contour integrals of the nonlinear Fourier spectrum function in the complex plane of the spectral parameter. The reliability and performance of the new approach are examined in application to a single eigenvalue, multiple eigenvalues, and the degenerate breather's multiple eigenvalue.

All-fiber highly chirped dissipative soliton generation in the telecom range.

A high-energy (0.93 nJ) all-fiber erbium femtosecond oscillator operating in the telecom spectral range is proposed and realized. The laser cavity, built of commercially available fibers and components, combines polarization maintaining (PM) and non-PM parts providing stable generation of highly chirped (chirp parameter 40) pulses compressed in an output piece of standard PM fiber to 165 fs.

Resonance optimization of polychromatic light in disordered structures.

Disorder offers rich possibilities for manipulating the phase and intensity of light and designing photonic devices for various applications including random lasers, light storage, and speckle-free imaging. Disorder-based optical systems can be implemented in one-dimensional structures based on random or pseudo-random alternating layers with different refractive indices. Such structures can be treated as sequences of scatterers, in which spatial light localization is characterized by random sets of spectral transmission resonances, each accompanied by a relatively high-intensity concentration.