Nonlinear Fiber Research Articles

Extra-cavity modulating a dark bisoliton

Abstract Although the concept of modulating optical solitons out of fiber laser cavities has already been proposed, to more flexibly change optical solitons’ time or frequency domain properties, compared with traditional intra-cavity modulation. The extra-cavity modulation of dark bisolitons has seldom been touched upon. In this manuscript, we theoretically conduct the research about modulating a dark bisoliton at 1 μm wavelength regime, in an extra-cavity modulation system. The modulation system is composed of different modulation elements. In the simulation, we consider the variations of different parameters. And modulated dark bisoliton’s orthogonal polarization components will show unique variation properties as these soliton parameters vary. For example, as time delay in orthogonal directions varies, a new small pulse peak appears at the position of continuous wave background in vertical polarization direction at output port, when time delay reaches to a specific value. These simulation results further explore the extra-cavity modulation of dark pulses in nonlinear optical fiber modulation systems, which are useful to understand the dark bisolitons’ dynamics in extra-cavity modulation systems. And these results have potential applications in the field of high-speed and long-distance optical fiber communication.

Numerical Approaches in Nonlinear Fourier Transform‐Based Signal Processing for Telecommunications

ABSTRACTWe discuss applications of the inverse scattering transform, also known as the nonlinear Fourier transform (NFT) in telecommunications, both for nonlinear optical fiber communication channel equalization and time‐domain signal processing techniques. Our main focus is on the challenges and recent progress in the development of efficient numerical algorithms and approaches to NFT implementation.

The profile of soliton molecules for integrable complex coupled Kuralay equations

Abstract This study focuses on mathematically exploring the Kuralay equation, which is applicable in diverse fields such as nonlinear optics, optical fibers, and ferromagnetic materials. This study aims to investigate various soliton solutions and analyze the integrable motion of the induced space curves. This study employs traveling wave transformation, converting the partial differential equation (PDE) into an ordinary differential equation (ODE). Soliton solutions are derived utilizing both the generalized Jacobi elliptic function expansion (JEFE) method and novel extended direct algebraic (EDA) methods. The outcomes encompass a diverse range of soliton solutions, including double periodic waves, shock wave solutions, kink-shaped soliton solutions, solitary waves, bell-shaped solitons, and periodic wave solutions, obtained using Mathematica. In contrast, the EDA method produces dark, bright, singular, combined dark-bright solitons, dark-singular combined solitons, solitary wave solutions, etc. Visual representation of these soliton solutions is accomplished through 3D, 2D, and contour graphics, with a meticulous selection of parametric values. The graphical presentation underscores the influence of the parameters on the soliton propagation.

Concurrent multi-scale design optimization of fiber-reinforced composite material based on an adaptive normal distribution fiber optimization scheme for minimum structural compliance and additive manufacturing

Structural lightweight is a core technical requirement for the structural design of aerospace and new energy power equipment structures. For multi-scale variable stiffness design optimization of discrete fiber-reinforced composite laminates, one of the challenges is how to avoid the explosion of design variable combinations caused by the increase in the number of candidate discrete fiber laying angles. The Normal Distribution Fiber Optimization (NDFO) interpolation scheme has the numerical advantage that the number of design variables does not increase with an increase in the number of candidate discrete fiber laying angles. However, the traditional NDFO interpolation scheme uses uniform penalty parameters across all elements, which means that normalizing the penalty parameters for all the elements ignores the convergence differences of discrete fiber laying angles in different elements within the macro-scale structure topology. This leads to time-consuming and unstable optimization iteration of the macro-scale structural topology and micro-scale discrete fiber laying angle selection. Especially, it easily causes the micro-scale discrete fiber laying angle selection to fall into the local optimum prematurely. Therefore, considering the difficulties and challenges of the traditional NDFO interpolation scheme in the multi-scale variable stiffness design optimization of fiber-reinforced composites. This paper proposes an Adaptive Normal Distribution Fiber Optimization (ANDFO) interpolation scheme, and the feedback mechanism of the convergence rate of the element design variable and the objective function is introduced to achieve the adaptive reduction of the penalty parameters. Based on the proposed ANDFO interpolation scheme, a multi-scale design optimization model of fiber-reinforced composite laminates is established, considering the macro-scale structure topology and micro-scale discrete fiber laying angel selection. The explicit sensitivity of the objective function of minimizing structural compliance to the macro-scale topological design variables and the micro-scale fiber laying angle design variables is derived. Considering the manufacturability of additive manufacturing based on the optimized design results, a multi-scale nonlinear continuous filtering strategy for discrete fiber laying angle is adopted to improve the continuity of the local fiber laying path. Numerical examples systematically present the coupling effects of macro-scale structural topology and micro-scale fiber laying path, multi-scale nonlinear discrete fiber continuous filtering laying path structure, and continuous fiber additive manufacturing multi-scale optimized structure. The proposed ANDFO scheme provides a new theoretical and methodological approach for the lightweight and integrated multi-scale design and manufacturing of fiber-reinforced composite laminates through additive manufacturing technology.

Low-Complexity Fiber Nonlinearity Compensation Based on Operator Learning Over 12 075 km Single Model Fiber

Low-Complexity Fiber Nonlinearity Compensation Based on Operator Learning Over 12 075 km Single Model Fiber

The use of a supercontinuum light source for the characterization of passive fiber optic components

Abstract In this article, we report the application of a commercial supercontinuum light source for testing fiber optics components in a broad optical range. We demonstrate that this kind of light can be successfully used to measure the parameters of a number of passive fiber components, such as fiber Bragg gratings, fiber couplers, wavelength division multiplexers, and fibered isolators. We also show that near the double wavelength of the pulsed laser used to pump the nonlinear fiber generating the supercontinuum, the standard optical spectrum analyzers demonstrate the false spectral peak that affects the test results and that using a simple low-cost monochromator placed at the supercontinuum source output permits the elimination of this peak. The results of experiments related to the characterization of passive fiber devices in the broad optical range, from 1 μm to more than 2 μm, are discussed in detail as possible applications of the proposed technique.

An Mach-Zehnder interferometer refractive index sensor based on self-phase modulation effect in a tapered double-cladding highly nonlinear fiber

An Mach-Zehnder interferometer (MZI) sensor based on self-phase modulation (SPM) effect in a tapered double-cladding highly nonlinear fiber (DCHNLF) was proposed and experimentally verified for refractive index (RI) measurement. The DCHNLF was tapered and the SPM spectrum generated in its untapered region acted as the broadband light source for the sensor. The integration of the SPM effect and the RI detection not only simplified the structure of the sensor, but also enhanced its long-term stability and reliability. Since the effective RI of the outer cladding mode of the tapered DCHNLF was affected by the RI variation, a spectral shift would occur in interference spectrum between the core mode and the outer cladding mode. The tapering treatment enhanced the evanescent wave on the surface of DCHNLF, making the sensor more sensitive to external RI. In the external RI range of 1.3333 ∼ 1.3972, the sensor achieved an excellent sensitivity of 238.51 nm/RIU. In addition, the effect of average pump power and pump wavelength on the sensor performance were experimentally discussed. The results showed that the sensitivity was not affected by the pump condition. This MZI RI sensor has advantages of excellent performance, simple structure and easy fabrication, demonstrating broad application prospects in biomedical research, marine environment monitoring, and human health detection.

Various pulse nonlinear evolution and dynamics employing CuCrO2 nanocrystals as a promising saturable absorber

Considering that fiber lasers are a far richer nonlinear optical system, a systematical study on various pulse nonlinear evolution and dynamics by one SA has great significance. However, investigating these important pulse nonlinear dynamic evolution processes of CuCrO2 nanocrystals as new SAs applied in ultrafast fiber lasers has never been explored. Herein, we demonstrate the excellent nonlinear optical properties of CuCrO2 nanocrystals and investigate the potential of CuCrO2 nanocrystals for generating various pulse nonlinear dynamic evolution processes. Firstly, the output characteristics of the passively Q-switching pulsed fiber lasers have been regulated by using CuCrO2 nanocrystals-polyimide film and a tapered fiber. The pulse duration and repetition rate were simultaneously compressed by 10 and 222 times, the pulse energy and peak power were increased by 79 and 827 times, respectively. Secondly, we are able to generate chaotic multi-pulse wave packets and optical rogue waves by the polarization mode dispersion of single-mode fiber together with the non-instantaneous relaxation of CuCrO2 nanocrystals. Finally, the transition from chaotic multi-pulse wave packet to giant chirped mode-locked pulse is realized by introducing high nonlinear fibers. Our results show that CuCrO2 nanocrystals are an efficient nonlinear material for studying various nonlinear phenomena, and give a new impetus to the development of nonlinear optics and ultrafast photonics.

Investigating novel optical soliton solutions for a generalized (3+1)-dimensional q-deformed equation

In this study, we investigate the (3+1) q-deformed tanh-Gordon equation due to its importance in the context of mathematical physics. It describes solitonic solutions in quantum field theory; it can sometimes be used in condensed matter physics to describe interactions between particles in magnetic materials or superconductors; it can model light propagation in nonlinear optical fibers or photonic crystals where the refractive index has a q-deformed structure; and it also can be applied in studying shock waves, turbulence and rogue waves where the deformation introduces corrections to classical wave phenomena. Utilizing the (G′ωG′+G+r)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\frac{{\\mathfrak {G}}^{\\prime }}{\\omega {\\mathfrak {G}}^{\\prime }+{\\mathfrak {G}}+r})$$\\end{document}-expansion technique, we derive novel analytical solutions that enhance our understanding of the underlying dynamics. Additionally, we employ a finite element method (extended cubic B-spline method) to validate our analytical findings and explore the behavior of the q-deformed equation under different parameter regimes. Our results demonstrate the versatility of the q-deformed framework in generating rich optical phenomena, paving the way for future research in both theoretical and applied physics.

Spontaneous symmetry breaking and vortices in a tri-core nonlinear fractional waveguide

We introduce a waveguiding system composed of three linearly-coupled fractional waveguides, with a triangular (prismatic) transverse structure. It may be realized as a tri-core nonlinear optical fiber with fractional group-velocity dispersion (GVD), or, possibly, as a system of coupled Gross–Pitaevskii equations for a set of three tunnel-coupled cigar-shaped traps filled by a Bose–Einstein condensate of particles moving by Lévy flights. The analysis is focused on the phenomenon of spontaneous symmetry breaking (SSB) between components of triple solitons, and the formation and stability of vortex modes. In the self-focusing regime, we identify symmetric and asymmetric soliton states, whose structure and stability are determined by the Lévy index of the fractional GVD, the inter-core coupling strength, and the total energy, which determines the system’s nonlinearity. Bifurcation diagrams (of the supercritical type) reveal regions where SSB occurs, identifying the respective symmetric and asymmetric ground-state soliton modes. In agreement with the general principles of the SSB theory, the solitons with broken inter-component symmetry prevail, as stable states, with the increase of the energy in the weakly-coupled system. Three-components vortex solitons (which do not feature SSB) are studied too. Because the fractional GVD breaks the system’s Galilean invariance, we also address mobility of the vortex solitons, by applying a boost to them.

Improving Optical Transmission Performance in Multi-Channel Networks Utilizing Convolutional Neural Network-Enabled Digital Signal Processing to Mitigate Four-Wave Mixing

ABSTRACT The rapid growth of online services and the global transition to digital platforms, accelerated by the COVID-19 pandemic and the emergence of AI-based services, have led to a surge in demand for high-capacity optical communication networks (OCNs). However, this transition exacerbates the issue of fiber nonlinearity, notably four-wave mixing (FWM), which can significantly impact signal integrity in long-distance OCN transmissions with multiple channels. To address this challenge, this paper presents a novel approach leveraging a convolutional neural network (CNN)-based digital signal processing (DSP) model to mitigate the nonlinear effects of FWM on signal quality. The proposed CNN model, designed with three convolutional layers and trained on a comprehensive dataset of simulated OCN transmissions, demonstrates significant improvement in reducing nonlinear distortions caused by FWM. Our method is compared with traditional compensation techniques, such as digital back-propagation and Volterra series-based equalizers, showing a reduction in power penalties by 1 dB and an enhancement in the power budget by 2 dB. Simulation results indicate that the bit error rates (BERs) remain consistently below the critical threshold of 10−9 across various transmission distances, outperforming conventional methods. The simulation analysis, conducted on a 100 km multi-channel OCN testbed, confirms the CNN equalizer’s efficacy in reducing crosstalk and improving power efficiency, with a demonstrated 15% reduction in required launch power. Moreover, the analytical models used to evaluate the CNN-based DSP model show high accuracy in predicting performance, underscoring the model’s capability to achieve high-quality transmission with lower power requirements. These findings advocate for the integration of our CNN-based DSP model into OCNs, offering a fruitful solution for managing multi-channel, long-distance, and high-data-rate optical transmissions in real-world systems.

Solitonic Analysis of the Newly Introduced Three-Dimensional Nonlinear Dynamical Equations in Fluid Mediums

The emergence of higher-dimensional evolution equations in dissimilar scientific arenas has been on the rise recently with a vast concentration in optical fiber communications, shallow water waves, plasma physics, and fluid dynamics. Therefore, the present study deploys certain improved analytical methods to perform a solitonic analysis of the newly introduced three-dimensional nonlinear dynamical equations (all within the current year, 2024), which comprise the new (3 + 1) Kairat-II nonlinear equation, the latest (3 + 1) Kairat-X nonlinear equation, the new (3 + 1) Boussinesq type nonlinear equation, and the new (3 + 1) generalized nonlinear Korteweg–de Vries equation. Certainly, a solitonic analysis, or rather, the admittance of diverse solitonic solutions by these new models of interest, will greatly augment the findings at hand, which mainly deliberate on the satisfaction of the Painleve integrability property and the existence of solitonic structures using the classical Hirota method. Lastly, this study is relevant to contemporary research in many nonlinear scientific fields, like hyper-elasticity, material science, optical fibers, optics, and propagation of waves in nonlinear media, thereby unearthing several concealed features.

Dissipative soliton resonance in a normal dispersion all-polarization-maintaining thulium-doped fiber laser

We report a first demonstration of dissipative soliton resonance (DSR) in a normal dispersion thulium-doped fiber laser (TDFL) constructed entirely of polarization-maintaining fibers. A nonlinear fiber loop mirror with a combination of normal and anomalous dispersion fibers inside the loop ensures a self-starting mode-locking operation in the DSR regime. The oscillator generated linearly polarized optical pulses with a fundamental repetition frequency of 5.735 MHz and a nearly constant peak power clamped at ∼ 4.35 W. The pulse duration extends from 217 ps to 6 ns, when the pump power increases from 417 mW to 1.86 W. The maximum average output power of the DSR pulses was 151 mW, corresponding to the single pulse energy of 26 nJ.

Jointly polar-coded probabilistic shaping scheme based on many-to-one mapping in IM/DD optical DMT interconnection.

A joint channel coding and probabilistic shaping (PS) scheme is proposed and experimentally demonstrated in an intensity modulation and direct-detection optical discrete multi-tone (DMT) interconnection. The PS-32 quadrature amplitude modulation (PS-32QAM) is probabilistically reshaped from a 6-bit/symbol 64QAM signal based on polar-coded many-to-one (MTO) mapping, enabling a Gaussian-like symbol probability distribution without shaping or forward error correction redundancy. A bit-interleaved polar-coded modulation iterative decoding system based on joint QAM demapping and polar decoding is employed to retrieve the multi-labeled PS symbols. Experimental results indicate that the polar-coded PS-32QAM DMT signal achieves a 1.5-dB receiver power sensitivity improvement and a 2.71-dB fiber nonlinearity tolerance enhancement over 10-km standard single-mode fiber transmission.

All-fiber coherent supercontinuum generation in a cascade of silica, fluoride, and chalcogenide fibers

Abstract We present an all-fiber coherent supercontinuum spanning the spectral range of 1.7–5.0 µm from a cascade of silica, ZBLAN, and chalcogenide (ChG) nonlinear fibers (NLFs). Coherence is maintained by the combined use of femtosecond pump pulses as well as by allowing deterministic spectral broadening mechanism at every stage of the cascade. The use of femtosecond pump pulses enables avoiding modulation instability (MI) at the onset of the supercontinuum generation process and thus prevent subsequent MI-seeded random noise. Once in the NLF cascade, the pump pulse is instead converted into a soliton of order maintained at N < 6 in the silica and ZBLAN NLFs, ensuring soliton fission followed by self-frequency shift of a few solitons. Finally, in the ChG NLF, spectral broadening is facilitated through self-phase modulation and dispersive wave generation. The deterministic nature of these nonlinear phenomena results in the generation of a coherent supercontinuum. The supercontinuum delivers an average power of 54 mW from an average pump power of 300 mW, yielding a power conversion efficiency of 18%. The experimental results closely align with numerical simulations, from which coherence is estimated. Such a coherent supercontinuum with a megahertz repetition rate is essential for spectroscopic systems based on optical frequency combs and applications in high-precision optical coherence tomography.

Non-Hermitian mode management in periodically modulated waveguide amplifiers

We propose an efficient mode management scheme in active nonlinear multimode fibers based on non-Hermitian potentials in the longitudinal direction with an antisymmetric transverse profile. The proposal takes advantage of the nonlinear saturation toward particular mode configurations, which can be tuned by the non-Hermitian potential. We demonstrate flexible control of the beam profile within the parameter space of the applied potential with various possibilities, such as improving the beam quality by condensing photons to the lowest order Hermite mode, exciting higher order modes, or engineering a desired mode profile as a combination of modes. The effect is also analytically predicted using a mode-expansion approach, showing good agreement with the full model calculations based on the complex Ginzburg–Landau equation. This study was performed for 1D planar guiding structures, yet the results can be extended to 2D fibers and could be very useful in applications of fiber amplifiers and lasers.

Soliton solutions of nonlinear coupled Davey–Stewartson Fokas system using modified auxiliary equation method and extended (G′/G2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(G'/G^{2})$$\\end{document}-expansion method

The captivating realm of the nonlinear coupled Davey–Stewartson Fokas system is explored in this research paper. As a powerful tool, the proposed system is utilized for the realistic representation of various non-linear dynamical mechanisms in different fields of sciences and engineering including non-linear optical fibers, plasma physics and water waves theory. Two distinct exact methods, namely the modified auxiliary equation method and the extended (G′/G2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(G'/G^{2})$$\\end{document}-expansion method, are utilized to acquire the exact soliton solutions of the non-linear coupled Davey–Stewartson Fokas system. A plethora of novel soliton solutions containing anti-kink, kink, bright, dark, dark-bright, bright-dark and some other singular soliton solutions, have been obtained using the employed exact methods. The significance of proposed manuscript lies in the novelty of obtained solutions. Kink, dark and bright solitons have wide applications in optical fiber communications, plasma physics and water waves dynamics. The acquired nontrivial exact solutions contain exponential, trigonometric, rational and hyperbolic functions. Some obtained solutions are visually represented through graphical simulations of 3D, 2D-contour and 2D-line plots, providing a comprehensive visualization of the soliton dynamics.The modulation instability of the proposed nonlinear system has been investigated, which ensures the stability of the system.

Explicit solutions of the generalized Kudryashov’s equation with truncated M-fractional derivative

The main purpose of this article is to study the generalized Kudryashov’s equation with truncated M-fractional derivative, which is commonly used to describe the propagation of wide pulses in nonlinear optical fibers. By employing the complete discriminant system of fourth-order polynomials, various types of explicit solutions are systematically classified, which include periodic solutions, the trigonometric functions, the double-period solutions, and the elliptic function solutions. Additionally, a series of 2D, 3D, and contour plots are generated to visually depict the spatial distribution and evolution of various solutions. This not only advances the development of nonlinear equations in theory but also provides valuable guidance in practical applications.

Propagation of M-shaped and W-shaped similaritons in birefringent tapered graded-index nonlinear fiber amplifiers

We study the self-similar transmission of optical beams inside an inhomogeneous birefringent tapered graded-index nonlinear fiber amplifier within the framework of generalized coupled Schrödinger equations with spatially inhomogeneous nonlinearity, group velocity dispersion, tapering and gain or loss. New kinds of similariton solutions for the governing model are constructed by means of the similarity transformation method. Especially, the M-shaped and W-shaped similariton pulses are found successfully for the first time, which do not exist in single-mode waveguide amplifier. In addition, bright–dark similaritons are found in the presence of tapering effect. It is shown that these waveforms exhibit a quadratic phase structure, which leads to chirped self-similar pulses. In addition, we determine the relationships among the tapering profile, gain or loss distribution, nonlinearity, and similariton width, which provide the required conditions for controlling the self-similar wave dynamics. Moreover, we discuss the dynamical evolution of the similariton pulses under the influence of special tapering profiles, which are of physical importance in practical applications. The results show that through selecting the appropriate tapering, dispersion and nonlinearity profiles, we can control the dynamics of similaritons effectively.

Machine-learning-based impairment-aware dynamic RMSCA in multi-core elastic optical networks

This paper presents a routing, modulation, spectrum, and core assignment (RMSCA) algorithm for space-division-multiplexing-based elastic optical networks (SDM-EONs) comprising multi-core links. A network state-dependent route and core selection method is proposed using a deep neural network (DNN) classifier. The DNN is trained using a metaheuristic optimization algorithm to predict lightpath suitability, considering the quality of transmission and resource availability. Physical layer impairments, including inter-core crosstalk, amplified spontaneous emission, and Kerr fiber nonlinearities, are considered, and a random forest (RF)-based link noise estimator is proposed. A feature importance selection analysis is provided for all the features considered for the DNN classifier and the RF link noise estimator. The proposed machine-learning-enabled RMSCA approach is evaluated on three network topologies, USNET, NSFNET, and COST-239 with 7-core and 12-core fiber links. It is shown to be superior in terms of blocking probability, bandwidth blocking probability, and acceptable computational speed compared to the standard and published benchmarks at different traffic loads.