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.

SOA-based reservoir computing using upsampling.

We introduce a new, to the best of our knowledge, approach to reservoir computing based on upsampling and modulation, utilizing a semiconductor optical amplifier (SOA) and photodetector as nonlinear elements without conventionally used delay loop. We demonstrated the 400-step prediction capability of the proposed scheme for the Mackey-Glass (MG) time series test.

Nonlinear Optical Pulses in Media with Asymmetric Gain.

A generic novel model governing optical pulse propagation in a nonlinear dispersive amplifying medium with asymmetric (linear spectral slope) gain is introduced. We examine the properties of asymmetric optical pulses formed in such gain-skewed media, both theoretically and numerically. We derive a dissipative optical modification of the classical shallow water equations that highlights an analogy between this phenomenon and hydrodynamic wave breaking.

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.

Nonlinear beam tapering and two-dimensional ring solitons.

We examine a possibility to exploit the nonlinear lens effect-the initial stage of self-focusing to localize initially broad field distribution into the small central area where wave collapse is arrested-the nonlinear beam tapering. We describe two-dimensional localized solitary waves (ring solitons) in a physical system that presents a linear medium in the central core, surrounded by the cladding with the focusing Kerr nonlinearity. The standard variational analysis demonstrates that such solitons correspond to the minimum of the Hamiltonian.

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.

Nonlinear spectral tunability of pulsed fiber laser with semiconductor optical amplifier.

We examine spectral properties of radiation in the pulsed fiber lasers using the semiconductor optical amplifier (SOA) as the gain medium. The complex light dynamics that result from the interplay between the fiber propagation effects in the cavity, the nonlinear effects in the SOA and spectral filtering, shift the generated radiation from the central wavelength of the filter. The resulting wavelength of the output radiation depends on the SOA pump power and the bandwidth of the intracavity filter.

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.

Deep reinforcement learning for self-tuning laser source of dissipative solitons.

Increasing complexity of modern laser systems, mostly originated from the nonlinear dynamics of radiation, makes control of their operation more and more challenging, calling for development of new approaches in laser engineering. Machine learning methods, providing proven tools for identification, control, and data analytics of various complex systems, have been recently applied to mode-locked fiber lasers with the special focus on three key areas: self-starting, system optimization and characterization. However, the development of the machine learning algorithms for a particular laser system, while being an interesting research problem, is a demanding task requiring arduous efforts and tuning a large number of hyper-parameters in the laboratory arrangements.

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.

Intensity-only-measurement mode decomposition in few-mode fibers.

Recovery of optical phases using direct intensity detection methods is an ill-posed problem and some prior information is required to regularize it. In the case of multi-mode fibers, the known structure of eigenmodes is used to recover optical field and find mode decomposition by measuring intensity distribution. Here we demonstrate numerically and experimentally a mode decomposition technique that outperforms the fastest previously published method in terms of the number of modes while showing the same decomposition speed.

Nonlinear spectral blueshift in semiconductor optical amplifiers.

We demonstrate that spectral peak power of negatively chirped optical pulses can acquire a blueshift after amplification by a semiconductor optical amplifier. The central wavelength of a transform limited optical pulse translates over 20 nm towards a shorter wavelength after propagation in a single-mode fiber and semiconductor optical amplifier. A chirped Gaussian pulse with full width at half maximum 1 ps and dimensionless chirp parameter =-20 can be blueshifted by 5 THz.

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.

Inverse design of mode-locked fiber laser by particle swarm optimization algorithm.

A wide variety of laser applications, that often require radiation with specific characteristics, and relative flexibility of laser configurations offer a prospect of designing systems with the parameters on demand. The inverse laser design problem is to find the system architecture that provides for the generation of the desired laser output. However, typically, such inverse problems for nonlinear systems are sensitive to the computation of the gradients of a target (fitness) function making direct back propagation approach challenging.

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.

Nonlinear Fourier transform for analysis of optical spectral combs.

The nonlinear Fourier transform (NFT) is used to characterize the optical combs in the Lugiato-Lefever equation with both anomalous and normal dispersion. We demonstrate that the NFT signal processing technique can simplify analysis of the formation of dissipative dark solitons and regimes exploiting modulation instability for a generation of coherent structures, by approximating the comb with several discrete eigenvalues, providing a platform for the analytical description of dissipative coherent structures.

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.