Nonlinear Fiber Research Articles

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.

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.

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.

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 principle of the SSB theory, the solitons with broken inter-component symmetry prevail 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.

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.

Characterizing nonlinear constitutive behaviors of fiber metal laminates

Abstract This study characterized the nonlinear tensile behavior of fiber metal laminates (FMLs). FMLs comprise layers of thin metallic sheets and fiber-reinforced composite layers, and a constitutive FML model includes the constitutive relationships of the FML’s constituent materials; however, nonlinear behavior is typically only considered for the metal components of an FML. In this study, a nonlinear constitutive relationship for the unidirectional fiber composites was modeled using a one-parameter plastic model. The nonlinear constitutive law for the metal was formulated using the J2 flow rule. These relationships were summed for each layer in accordance with laminated plate theory to obtain a constitutive FML model, which was then used for numerical predictions of nonlinear stress–strain curves. The model was validated by comparing its predictions with experimental results from the literature. Moreover, the effect of the inclusion of nonlinear fiber composite behavior on the model predictions was investigated. Results revealed that the difference between the model predictions and the experimental results was less than 4%. These predictions with nonlinear fiber composite behavior were substantially more accurate than those of the model without this behavior for FMLs with angle-ply fiber composites.

A multiscale discrete fiber model of failure in heterogeneous tissues: Applications to remodeled cerebral aneurysms

Damage-accumulation failure models are broadly used to examine tissue property changes caused by mechanical loading. However, damage accumulation models are purely phenomenological. The underlying justification in using this type of model is often that damage occurs to the extracellular fibers and/or cells which changes the fundamental mechanical behavior of the system. In this work, we seek to align damage accumulation models with microstructural models to predict alterations in the mechanical behavior of biological materials that arise from structural heterogeneity associated with nonuniform remodeling of tissues. Further, we seek to extend this multiscale model toward assessing catastrophic failure events such as cerebral aneurysm rupture. First, we demonstrate that a model made up of linear elastin and actin and nonlinear collagen fibers can replicate bot the pre-failure and failure tissue-scale mechanics of uniaxially-stretched cerebral aneurysms. Next, we investigate how mechanical heterogeneities, like those observed in cerebral aneurysms, influence fiber and tissue failure. Notably, we find that failure occurs and the interface between regions of high and low material stiffness, suggesting that spatial mechanical heterogeneity influences aneurysm failure behavior. This model system is a step toward linking structural changes in growth and remodeling to failure properties.

A versatile 5-axis melt electrowriting platform for unprecedented design freedom of 3D fibrous scaffolds

Melt electrowriting (MEW) is an electrohydrodynamic additive manufacturing technology for the fabrication of precise microfiber scaffold architectures but is so far restricted to printing onto simple collector geometries and, therefore, constrained in design freedom. This is due to current limitations in print head designs, kinematic systems, and software to generate motion commands. We address these aspects by upgrading a low-cost 5-axis kinematic system and complete it with a custom-designed print head and a collector fabrication workflow to enable collision-free MEW onto arbitrarily shaped multicurvature 3D geometries. A universal graphical approach enables generation of Gcodes customized to the 5-axis MEW requirements. The print head is validated by producing polycaprolactone fibers with diameters ranging from 5.6 ± 1.7 µm to 50.7 ± 5.5 µm and by writing both linear and non-linear fiber patterns onto collectors featuring concave and convex surfaces. Stable printing conditions are achieved by continuously reorienting the print head and collector surface perpendicular to each other at a constant working distance. Ultimately, we demonstrate the system’s potential in shaping anatomically relevant scaffold geometries by stacking microfibers onto collectors resembling a trileaflet valve and a bifurcating vessel. This multi-axis MEW platform unlocks exciting avenues towards unprecedented design freedom for MEW scaffolds.

Unseeded one-third harmonic generation in optical fibers

We propose a new concept to generate efficient one-third harmonic light from an unseeded third harmonic process in optical fibers. Our concept is based on the dynamic constant (Hamiltonian) of the nonlinear third harmonic generation in optical fibers and includes a periodic array of nonlinear fibers and phase compensation elements. We test our concept with a simulation of the nonlinear interaction between the fundamental and third harmonic modes of a realistic optical fiber, demonstrating high-efficiency one-third harmonic generation. Our work opens a new approach to achieving the so far elusive one-third harmonic generation in optical fibers.

Performance analysis of nonlinear crosstalk of WDM systems using modulation schemes criteria

Abstract Nonlinearities in optical fibers are regarded as the most significant barriers that endanger the effectiveness of the optical transmission system and pose a threat to communication quality. Four-wave mixing (FWM) is one of the most important nonlinear effects that greatly reduces the wavelength-division multiplexing (WDM) system performance at high data rates over extended transmission distances. This research examines, and assesses, numerically, the behavior of a 4-channel, 40 Gbps WDM system under the effect of the FWM under various tuning parameters, including dispersion, input power, and wavelength spacing. The system model was built using OptiSystem software, and then three different modulation formats, namely, Non-return-to-zero-frequency shift keying, Return-to-zero frequency shift keying, and differential phase shift keying (DPSK) are used to assess the FWM power penalty. The results demonstrate that the FWM power penalty obtained with 1 nm wavelength separation in the DPSK method is dramatically reduced to −35 dBm. This study also demonstrates that when power variation is taken into consideration, the DPSK modulation scheme delivers a lower bit error rate in comparison to other modulation schemes.

Long-range temperature sensing based on forward Brillouin scattering in highly nonlinear fiber

We propose and experimentally implement a long-range forward Brillouin scattering (FBS) temperature sensor, in which a 25-m highly nonlinear fiber (HNLF) is included in a Sagnac ring and is employed as the main sensing unit, and a 40-km standard single-mode fiber (SMF) is used as the transmission channel to connect the main sensing unit to the data processing center. The approach for quickly acquiring an optimal R0, m mode spectrum is presented. After taking into account the signal-to-noise ratio, sensitivity, and Lorentzian spectral shape, the R0, 17 mode was selected to perform temperature sensing. The frequency shift of the long-range and local FBS sensing demonstrates a linear correlation with the temperature change from 30 ℃ to 60 ℃, with respective frequency shift-temperature coefficients of 73.1 kHz/℃ and 73.4 kHz/℃. Impact of the length of the SMF as the main sensing unit and the SMF as the transmission channel on the FBS gain spectrum has also been discussed, respectively. The proposed long-range FBS scheme is expected to find applications in the investigation of submarine oil and gas pipelines, as well as temperature gradients in underwater and mountainous environments.

Repetition‐Rate and Wavelength Flexible Femtosecond Laser Pulse Generation

AbstractCompared to mode‐locked oscillators, gain‐switched diodes (GSD) have the key advantage of repetition‐rate agility. Yet, large pulse duration and poor coherence of the GSD pulses greatly limit their applications. Here, a GSD‐pumped Raman fiber amplifier is demonstrated, which can effectively generate femtosecond laser pulses with both repetition‐rate and wavelength agility. It is proved that both nonlinear optical gain and single‐frequency seed in the fiber amplifier play critical roles for improving the coherence of the generated laser pulses. In the experimental demonstration, pumped by 1065 nm GSD pulses, the nonlinear fiber amplifier can generate highly coherent 1121 nm femtosecond Raman pulses with up to 80.2% conversion efficiency. The Raman pulses can maintain high performance within the repetition‐rate tuning range from 1 to 150 MHz. The potential for generating 1178 nm femtosecond Raman pulses is also demonstrated with an optical conversion efficiency of 63.8%. This all‐fiber based femtosecond laser with both repetition‐rate and wavelength agility is a promising light source for applications such as nonlinear microscopy and micromachining.

Supercontinuum generation by nonlinear polarization rotation mode-locked fiber laser with pulse type switchable

We report on the generation of a supercontinuum (SC) by nonlinear polarization-rotating (NPR) mode-locked fiber laser, which includes a pulsed switchable NPR mode-locked fiber laser, an Er-doped fiber amplifier, and high nonlinear fiber (HNLF). In the experiment, by adjusting the polarization controller (PC) angle and pump power, we obtained three different pulses. They are traditional soliton bunch pulses, the coexistence of soliton bunch pulses and square pulses, and multi-longitudinal mode noise like square pulses. All three pulses can generate SC with spectrum width be about of 1000 nm. We fixed the pump power in the laser and observed the influence of amplifier power on the spectrum width and output power of SC. The SC width of soliton bunch pulse reaches 950.9 nm, the SC of soliton bunch pulse and square pulse coexisting pulse is 1009.7 nm, and the SC spectrum width of multi-longitudinal mode noise like square pulse is 887.1 nm. Our results demonstrate the generation of SC with three types of switchable pulses, opening up possibilities for various application requirements.