Randomness enhancement of noise-like pulses in nonlinear polarization rotation fiber cavity

Mode division multiplexing (MDM) is an emerging optical communication solution for high-capacity wired–wireless applications. Due to the presence of modal crosstalk and link impairments in MDM, this work aims to design a system that provides low complexity, an improved Shannon Capacity limit, and high spectral efficiency. In this work, a quad modal MDM system using an integrated parabolic index multimode fiber and free-space optics (PIMMF-FSO) link is presented. Four linearly polarized (LP) modes, LP01, LP22, LP03, and LP13 based on a 16 × 10 Gbps MDM system offering different sixteen channels, are realized. Results show that the system can sustain a 7.5 dB insertion loss over 100 m FSO and a 100 m fiber range for different LP modes under the impact of clear air, moderate haze, heavy rain and wet snow climates with weak turbulence. A faithful fiber range of 3000 m can be obtained successfully in the proposed system with a −10 dB link loss, −7.62 dBm received power and 10 dB noise. Compared to existing designs, the proposed design offers optimum performance in terms of high channel capacity and a high traffic rate with low complexity and high spectral efficiency. Additionally, high received power, with acceptable noise, link loss, FSO misalignments and fiber nonlinearities, is successfully obtained.

A comprehensive analytical and numerical investigation is presented for a perturbed M-fractional Kairat-X equation with variable coefficients and dissipative effects. The model is motivated by fractional nonlinear wave phenomena arising in inhomogeneous optical, plasma, and ferromagnetic media, where spatial variability and weak perturbations play a crucial role in wave propagation and stability. In contrast to existing studies that primarily focus on constant-coefficient formulations and exact solution construction, the present work develops a rigorous analytical framework for a variable-coefficient fractional model, thereby addressing an important gap in the literature. By extending the classical fractional Kairat–X equation to include variable-coefficient potentials and perturbation terms, a more realistic and physically relevant framework is obtained. A rigorous mathematical analysis is carried out by employing a traveling-wave reduction under clearly stated assumptions on the variable coefficients, followed by the application of fixed-point theory to establish the existence and uniqueness of traveling-wave solutions. Furthermore, Lyapunov-type energy estimates are developed to derive explicit stability conditions, providing deeper insight into the influence of coefficient structure and fractional-order effects on solution behavior. In addition, a convergent numerical scheme is constructed to support the analytical results, and its stability and accuracy are demonstrated through discrete error analysis. The numerical results are presented in a systematic tabulated form, highlighting convergence properties, stability regimes, and the sensitivity of solutions with respect to the fractional order and perturbation parameters. The results demonstrate that the introduction of variable coefficients and perturbations significantly affects solution stability and parameter sensitivity, thereby extending and strengthening existing constant-coefficient fractional Kairat–X models. Overall, this study provides a unified analytical and computational framework for investigating nonlinear fractional wave equations with spatial heterogeneity, offering new insights into their long-time dynamics and stability mechanisms, with potential applications in nonlinear optics, ferromagnetic materials, and optical fiber systems.

Circular braiding is an advanced manufacturing process for forming fiber-reinforced composite preforms, featuring excellent design flexibility and superior near-net-shape forming capability. However, this high-speed and flexible manufacturing method also introduces the problem of nonlinear fiber bundle distribution at the edges of the mandrel. The influencing mechanisms and control strategies regarding fiber bundle distribution remain unclear. This paper establishes a high-fidelity finite element model for radial circular braiding under the 176-carrier process based on the digital element method. It systematically compares the effects of circular and elliptical guide rings with different aspect ratios on the braiding process of rectangular cross-section mandrels, and proposes an effective method for extracting braiding angles. It has been found that the guide ring increases the difference in yarn convergence distance on adjacent sides of the rectangular cross-section mandrel by regulating the spatial position of the yarn guide points. This compensates for the inherent non-axisymmetric geometry of the rectangular cross-section mandrel, thereby effectively suppressing in-plane yarn bending, reducing variations in braiding angles between adjacent surfaces, and improving the overall uniformity of the braiding angle. This study provides a theoretical foundation and process guidance for the shape optimization of guide rings for mandrels with complex cross-sections, contributing to the precise braiding of high-performance composite preforms.

Design and optimization of highly nonlinear polarization-maintaining Ge23Sb7S70 chalcogenide photonic crystal fiber for mid-infrared supercontinuum generation

Physics-informed neural networks for predicting ultrashort optical pulse dynamics in nonlinear fiber systems

Abstract Wavelength division multiplexing (WDM) has become a fundamental technology for meeting the rapidly increasing demand for high-capacity optical communication networks. While significant advancements have been achieved through improved modulation formats and optical amplification, the ultimate performance of WDM systems is fundamentally constrained by physical-layer impairments and information-theoretic limits. This paper presents a comprehensive information-theoretic analysis of the capacity limits of WDM optical communication systems. Starting from Shannon’s channel capacity theorem, analytical expressions for channel capacity are derived by incorporating key optical impairments, including amplified spontaneous emission (ASE) noise, optical signal-to-noise ratio (OSNR), chromatic dispersion, and fiber nonlinearities. The relationship between modulation formats, OSNR, and achievable spectral efficiency is investigated. Numerical evaluations demonstrate how system parameters such as launch power, channel spacing, and amplifier noise figure influence the achievable capacity per channel and total WDM system capacity. The presented analysis provides valuable theoretical insight into the fundamental performance limits of WDM systems and serves as a guideline for the optimal design of high-capacity optical networks.

Deep Learning-Assisted Characterization of Ultrafast Optical Pulses Using Nonlinear Fiber Optics

The nonnegligible fiber nonlinearity and the relentless growth in transmission rates in modern optical systems has brought unprecedented challenges to the existing optical signal-to-noise ratio (OSNR) monitoring techniques. In this work, a novel phase-aware, nonlinear-tolerant, and interpretable physics-informed neural network (PINN) OSNR estimator based on the nonlinear Schrödinger equation (NLSE) and the fractional Fourier transform (FrFT) is proposed and experimentally validated for the first time. The proposed PINN OSNR estimator reveals the impact of phase-related information on OSNR estimation via an indirect phase-aware strategy based on NLSE. The FrFT is applied to achieve joint time-frequency and amplitude-phase features and further enhance OSNR estimation performance. Integration of the NLSE into the loss function allows the model to be closely aligned with the intrinsic physical characteristics of optical transmission systems, endowing it with improved interpretability and enhancing its robustness under unseen conditions. Experimental results yield consistently favorable results across high-nonlinearity, higher-order modulation coherent systems, and out-of-distribution data. The proposed model achieves average OSNR monitoring errors of 0.13, 0.26, and 0.19 dB for quadrature phase shift keying (QPSK), 16 quadrature amplitude modulation (16QAM), and 64QAM systems, respectively, and achieves an average estimation error of 1.12 dB with a maximum error of 2.6 dB on out-of-distribution data.

This study applies the generalized exponential rational function technique to construct new optical soliton solutions of the nonlinear conformable Schrödinger equation with Kudryashov’s nonlinear refractive index governed by the quadrupled-power law and dual nonlocal nonlinearity. Various analytical solutions, including bright, dark, and wave solitons, are derived within the conformable fractional framework. The effects of the fractional-order parameter and temporal parameter on the obtained solutions are illustrated through contour, two-dimensional, and three-dimensional plots. The results reveal how fractional dynamics influence soliton structure, amplitude, and propagation behaviour. These findings contribute to a deeper understanding of pulse evolution and stability in nonlinear optical fibres and related photonic systems.

Characterization of anisotropic nonlinear material properties along with fiber directions for soft tissues based on known deformations (strains) and external loads is a significant clinical goal. A gradient-based inverse solver is developed to retrieve anisotropic nonlinear tissue properties. By directly minimizing nodal force residuals using known deformed and reference configurations, the method avoids repeated forward simulations. To represent complex, non-trivial spatial distributions, the material properties are parameterized using a multilayer perceptron (MLP) that maps spatial location to material behavior, in contrast to methods that use such networks to approximate the displacement field itself. For faster convergence, residual smoothing is performed, and the Jacobian computation is parallelized. The framework supports general constitutive laws as demonstrated by Neo-Hookean and Fung-type models. The inverse solver is verified for a variety of cases, including spatially varying elasticity and anisotropic fiber distributions, and its applicability to complex 3D geometries is demonstrated on a bioprosthetic heart valve. The residual-only formulation leads to faster optimization iterations compared to Physics-Informed Neural Network (PINN) approaches, which involve computationally expensive updates to a displacement-approximating network. Unlike the Neo-Hookean constitutive model, the Fung model, especially with element-wise recovery of parameters, exhibits nonuniqueness, where different spatial distributions of parameters can yield similar residual levels; in contrast, fiber direction recovery remains robust across all cases. The inverse solver is capable of recovering nonlinear material properties and fiber directions even for complex 3D problems with large deformations such as heart valves.

Abstract This study introduces a novel investigation into the propagation dynamics of diverse pulse profiles—Gaussian, super-Gaussian, and hyper-Gaussian within AlGaAs photonic crystal fibers (PCFs) under the governance of a cubic-quintic nonlinear Schrödinger equation (CQNLSE). The novelty lies in the comprehensive application of a variational approach to derive explicit evolution equations for crucial pulse parameters, including temporal width, chirp, and frequency shift, while rigorously accounting for higher-order effects such as third-order dispersion, self-steepening, and intrapulse Raman scattering. A key result is the demonstration of quintic nonlinearity's stabilizing influence, effectively saturating the nonlinear response and counteracting dispersion-induced broadening, thereby enabling soliton-like propagation even in supercritical energy regimes. Notably, our findings reveal that hyper-Gaussian pulses exhibit superior temporal and spectral stability compared to Gaussian and super-Gaussian counterparts due to their flattened intensity profiles. These results offer new insights into the manipulation of ultrafast optical pulses in PCFs and hold significant potential for advancements in high-performance photonic devices.

This research addresses the pure-cubic nonlinear Schrödinger equation augmented by third-order dispersion, characterized by quadratic–cubic nonlinearities and explicitly excluding the group-velocity dispersion term. Such an equation is well suited for representing the behavior of ultrashort optical pulses in nonlinear fibers, in which higher-order effects strongly influence the dynamics. By applying the new Kudryashov method and the Jacobi elliptic function method, we systematically derive a wide family of soliton solutions, including bright solitons, W-shaped solitons and kink solitons, each exhibiting distinct amplitude profiles and propagation characteristics. The role of essential system parameters, including quadratic and cubic nonlinear coefficients along with third-order dispersion strength, is systematically explored, revealing the physical conditions under which these nonlinear waveforms emerge. The results highlight the rich diversity of soliton structures possible in this system and underscore the potential applications in the control of high-speed optical pulses. In the absence of the group-velocity dispersion term, this version of the equation has not been previously explored; here, we present the first modulation instability analysis, incorporating the effects of quadratic and cubic nonlinearities, with results expected to offer valuable input to the field.

In this study, accurate solitary wave solutions of the generalized (3+1)-dimensional Sasa-Satsuma equation are investigated using the modified F-expansion approach and the extended hyperbolic function method. The model under consideration describes the propagation of ultrashort optical pulses in nonlinear optical fibers, where nonlinear derivative terms, self-steepening, and third-order dispersion are important higher-order effects. A wide range of analytical solutions, including solitonic, trigonometric, rational, and exponential wave shapes, are derived using the modified F-expansion method. Additionally, the extended hyperbolic function method is used to generate bright, dark, and singular soliton solutions as well as periodic wave solutions under appropriate parametric restrictions. Furthermore, modulation instability is examined using linear stability theory, and the parameter regimes in which the solutions become unstable are determined using the associated dispersion relation. The acquired solutions are unique and have not been documented in the current literature, as far as we are aware. The suggested techniques are useful tools for the analysis of a broad class of nonlinear evolution equations because they are simple, effective, and widely applicable. Graphical representations are used to help clarify the physical properties of the generated solutions.

This work studies the exact solutions of the integrable (3+1)-dimensional combined potential Kadomtsev-Petviashvili (pKP) equation with the B-type Kadomtsev-Petviashvili (BKP) equation, which is used to characterize several nonlinear oscillations occurring in hydrodynamics, plasma physics, and nonlinear optics. A bilinear representation of the pKP-BKP model is used to study the properties of different wave solutions. A variety of ansatzes are utilized to derive lump cross-kink waves, lump cross-periodic waves, rogue waves, as well as two, three, and multi-wave solutions pertinent to the model. In addition, a traveling wave transformation is applied to transform the problem into an ordinary differential equation. The new auxiliary equation methodology yields solutions including rational, exponential, hyperbolic, and trigonometric functions. Graphical visualizations using 2D plots, contour plots, and 3D plots show the dynamics of the obtained solutions. These solutions are of great importance in nonlinear fiber optics and telecommunications, which contribute to our understanding of the fundamental physical models.

We investigate the nonlinear propagation of light in graded-index multimode fiber, utilizing it as an optical computing unit, and quantify how it employs waveguide modes to process information. Using a time-dependent spatiotemporal propagation model with modal decomposition, we evaluate several benchmark regression and classification tasks and study the modal content of the generated speckles, which couples with a simple digital layer to perform optical computing. Analysis of modal entropy and energy-based mode counts reveals that effective computation is confined to a low-dimensional modal subspace, whose identity depends on the task and propagation regime. This also sets a trade-off between modal richness and nonlinear beam self-cleaning. These results establish modal statistics as practical design metrics for fiber-based optical computers.

Nonlinear fiber amplifiers allow for scaling the pulse energy, while the pulse properties can be tailored by the interplay of dispersion and Kerr-nonlinearity, aiming to significantly shorten the input pulses. Here, we describe a monolithic polarization-maintaining nonlinear fiber amplifier based on thulium, relying solely on single-mode step-index fused silica fibers. During the amplification of up-chirped pulses with an initial transform-limited pulse duration of 2.3 ps in an anomalous dispersive gain fiber, monotonic spectral broadening occurs and is subsequently extended in a normal dispersive fiber. The setup generates pulses with ultra-broadband spectra of up to 119 nm at pulse energies of up to 74 nJ. The pulses can be well compressed to sub-100 fs duration, equivalent to a compression factor of 24. Even though massive nonlinear spectral broadening is observed, the noise performance characterized by the relative intensity noise remains almost unaffected. Fundamentals for design and limitations of the output parameters are discussed by a numerical model.

We demonstrate a high-energy 2 µm femtosecond mode-locked oscillator utilizing a double-clad thulium-doped fluoride fiber. The active fiber was pumped by a multi-mode semiconductor laser, and stable mode-locked operation was achieved via nonlinear polarization rotation. The maximum pulse energy reached 7.8 nJ, representing one of the highest energies reported for a stable femtosecond mode-locked fiber laser oscillator at 2 µm. While the direct output pulse duration was 1.3 ps, we obtained 72 fs pulses through nonlinear self-compression in a 48 cm single-mode silica fiber. Furthermore, we demonstrate the generation of an octave-spanning supercontinuum by launching the pulse into a highly nonlinear fiber.

ABSTRACT Ultrafast laser sources are the cornerstone of advancements in diverse fields such as precision metrology, biomedical imaging, and attosecond science. However, the development of compact, multifunctional platforms that combine high performance with robust integration remains a key challenge. Here, we demonstrate an all‐fiber‐integrated platform capable of generating either an octave‐spanning coherent supercontinuum or few‐cycle pulses by simply controlling the length of spliced highly nonlinear fiber (HNLF). Seeded by a home‐made femtosecond fiber laser, the system utilizing a 0.12 m HNLF generates a highly coherent supercontinuum spanning 400–2400 nm. To the best of our knowledge, this represents the first femtosecond‐pumped, visible coherent supercontinuum generated within an all‐fiber structure. Alternatively, employing a 0.02 m HNLF enables nonlinear compression to high‐fidelity 22.4 fs pulses. This duration constitutes the shortest pulse achieved to date from a fully fiber‐integrated system. The source exhibits excellent stability (0.12% RMS power fluctuation) and near‐diffraction‐limited beam quality (M 2 < 1.15). This work provides a robust and flexible architecture, delivering record‐level performance for applications requiring either ultra‐broadband coherence or few‐cycle pulses in a single, fully integrated format.

In this Letter, we experimentally demonstrate a 16.7 Tb/s co-frequency co-time full-duplex 10 km mobile fronthaul on C band by harnessing the ultralow loss, nonlinearity, dispersion, and Rayleigh backscattering of anti-resonant hollow-core fiber. 112 GBaud four-level pulse amplitude modulation signals are adopted with direct detection. Bit error rates of all the channels are below 6.7% hard-decision forward error correction threshold of 3.8 × 10-3. Few sensitivity penalties of inter-channel nonlinear interference and backward crosstalk are observed as 0.2 dB and 0.5 dB, respectively. This work shows that anti-resonant hollow-core fiber is a promising medium for implementing a high-capacity 6 G fronthaul architecture.