Fiber Propagation Research Articles

Dynamical structures of optical solitons for highly dispersive perturbed NLSE with $$\beta $$-fractional derivatives and a sextic power-law refractive index using a novel approach

Dynamical structures of optical solitons for highly dispersive perturbed NLSE with $$\beta $$-fractional derivatives and a sextic power-law refractive index using a novel approach

Phase Portraits and Abundant Soliton Solutions of a Hirota Equation with Higher-Order Dispersion

The Hirota equation, an advanced variant of the nonlinear Schrödinger equation with cubic nonlinearity, incorporates time-delay adjustments and higher-order dispersion terms, offering an enhanced approximation for wave propagation in optical fibers and oceanic systems. By utilizing the traveling wave transformation generated from Lie point symmetry analysis with the combination of generalized exponential differential rational function and modified Bernoulli sub-ODE techniques, several traveling wave solutions, such as periodic, singular-periodic, and kink solitons, emerge. To examine the solutions visually, parametric values are adjusted to create 3D, contour, and 2D illustrations. Additionally, the dynamic properties of the model are explored through bifurcation analysis. The exact results demonstrate that both techniques are practical and robust.

NIMG-81. PREDICTING TUMOR PROGRESSION WITH FIBER DENSITY-WEIGHTED WHITE MATTER PATHLENGTH MAPS IN PATIENTS WITH GLIOBLASTOMA

Abstract PURPOSE Although histopathological evidence indicates that glioma cells preferentially migrate along large white-matter bundles, standard-of-care (SOC) radiation therapy (RT) planning remains an isotropic expansion of the anatomical lesion. We hypothesize that anisotropic expansion of RT target volumes along white-matter pathways using fiber density-weighted, white-matter pathlength maps (DW-WMPLMs) derived from diffusion tensor imaging (DTI) could improve the prediction of tumor cell migration beyond surgical margins by a deep learning model compared to SOC clinical target volumes (CTVs). METHODS DTI and anatomical MRI from 118 patients newly-diagnosed with glioblastoma were retrospectively analyzed with anatomical imaging from post-surgical resection and latest progression scan before intervention. Parallel-transport tractography seeded from the pre-surgery T2-lesion was used to estimate white-matter fiber propagation. Fibers that intersected with the resection cavity were weighted by their density to control the length of expansion and create a DW-WMPLM that was used together with T2-FLAIR and T1-post-contrast images as inputs to a novel 3D-Swin-UNetR network, trained to predict the recurrence region using 4-fold cross-validation and evaluated in a holdout test-set (95/23 CV/test). New weighted-overlap, coverage, and sparing indices were introduced to evaluate coverage of the progressed lesion and healthy brain excluded. RESULTS 52% of patients had progression outside the standard 2cm-isotropic CTV margin, motivating the need for anisotropic CTVs. Our novel DW-WMPLMs had 87±20% and 83±18% overlap with contrast-enhancing and T2-lesion progression, respectively. The deep-learning model trained with DW-WMPLMs and anatomical images achieved 19% and 56% higher Dice and weighted-overlap indices compared to the isotropic 2cm-CTV(p<0.02), with less normal brain included. CONCLUSION This study demonstrates the feasibility and benefit of incorporating a novel metric of white-matter track characterization into deep learning progression prediction models of glioblastoma for RT-planning. Current work is validating findings in a prospective cohort acquired immediately prior to RT and incorporating other imaging metrics.

Chaotic structures and unveiling novel insights of solutions to the (2+1)-dimensional generalized Kadomtsev–Petviashvili equation with its stability analysis

In current research work, study the (2+1)-dimensional generalized Kadomtsev–Petviashvili equation, which explains wave propagation in optical fibers, mathematical physics and behaviors of solitons. The results and extract using the modified Sardar sub-equation method, the analysis of phase portrait utilizing bifurcation and chaos theory. These methods have been used to extract analytical solutions for the aforementioned equation. Numerous optical solitons, such as singular solitons, solitary waves, periodic solitons, wave collisions, and phase portraits show stable and unstable nodes. The structures of the obtained results are displayed in 3-dimensional, 2-dimensional and contour plots. These solutions have extensive use in various domains, including hydrodynamics, nonlinear optics, plasma physics, fiber optics, and telecommunication systems. The dynamics of chaotic structures are displayed by choosing and appropriate parameter values. These graphs shed light on the properties and behavior of the solutions. The results collected provide evidence of the proposed method’s efficacy, dependability, and simplicity. Such mathematical tools have proved to be very effective in tackling complex challenges generated by nonlinear partial differential equations and have driven immense success in nonlinear sciences, mathematical physics, and soliton theory.

Optically enhanced pump-phase noise in mid-link optical parametric phase conjugation.

This paper discusses the impact of pump-phase noise in the χ(2)-based optical parametric amplification process on the phase-conjugated idler. We show that the dispersive fiber propagation of the phase-conjugated idler causes the optically enhanced pump-phase noise (OEPN) effect including a group-velocity jitter. The signal penalty caused by the OEPN in the mid-link optical phase conjugation systems was quantified analytically and proved by numerical simulations. We also experimentally evaluated the OEPN with an optical parametric phase conjugator using periodically poled LiNbO3 waveguides. With a 96-Gbaud probabilistically constellation-shaped 64QAM signal, the experimental results were in good agreement with the analytically derived penalty in a standard single-mode fiber link up to 800 km.

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.

AE based crack size estimates from delamination propagation in fiber reinforced thermoset composites

In previous research it has been shown that micro-crack sizes estimated from acoustic emission (AE) data recorded during Mode I interlaminar delamination propagation in a carbon fiber reinforced PEEK and micro-crack sizes seen in video recordings from simultaneously performed X-ray projection radiography with a contrast agent indicate reasonable agreement. Now the approach of estimating crack sizes from AE data is extended to a carbon and a glass fiber reinforced epoxy laminate, using the same matrix. In a first step sensitivity of the AE measurement is estimated based on recorded AE data and estimated delamination area. Different signal filtering approaches are applied to AE data resulting in different estimated sensitivities. Furthermore, assumed delamination area affects sensitivity. Optical microscopy is used to account for roughness of the delamination area. Depending on the assumed sensitivity, average crack size diameters are either slightly below or above 100 µm in both investigated laminates.

Progressive damage and stiffness degradation assessments of double‐lap CFRP/Ti interference fit bolted joints under quasi‐static tensile load

AbstractMatrix crack propagation and stiffness degradation behaviors of the carbon fiber reinforced polymer/titanium alloy (CFRP/Ti) bolted joint were characterized by a synergistic damage mechanics approach. The parametric study including pre‐tightening torques and interference fit sizes was conducted. The results showed that the joint stiffness degradation exhibited characteristics of local stiffness degradation due to local stress concentration. Stiffness degradation in different plies was caused by matrix crack damage occurring in different directions. The pre‐tightening torque significantly increased the joint stiffness and restrain matrix crack progression, effectively inhibiting the stiffness degradation of the joint. Moreover, the low interference fit level delayed the crack initiation in −45° ply and 45° ply and the crack propagation of the laminate, while promoted the crack initiation in 90° ply. The stiffness degradation of the laminate could be significantly reduced by interference fit.Highlights Matrix crack propagation and stiffness degradation behaviors of the CFRP laminate were characterized by a synergistic damage mechanics method. A FE model of the CFRP/Ti double‐lap interference fit bolted joint was established. Influences of pre‐tightening torques on both matrix crack initiation and propagation were investigated. The optimum interference fit size of the matrix damage strengthening was 0.20%–0.60%.

A tunable spatial coherence imaging with ultrasonic array for defects in composites

ABSTRACT Ultrasonic phased array detection technology is a promising non-destructive testing (NDT) method that has been widely used for defect detection. Due to the high attenuation characteristics of ultrasonic wave propagation in carbon fibre reinforced polymer (CFRP) and the directivity of the array elements, the possibility of false or missed detection for defects that are far from the array elements or located very close together will increase. In addition, the total focusing method (TFM) employs only the defect information contained in the full matrix capture (FMC) dataset while ignoring the spatial information of the array signals, leading to image mixed with artefact and noise. An improved method called p-weighted-TFM (p-WTFM) is proposed. First, this method scales the magnitude of time-delayed channel signal by p-th root while maintaining the phase unchanged. Second, channel summation with energy compensation and directional correction will be realised. Finally, the signal dimensionality is restored by p-th power. Experimental results show that the p-WTFM can use any rational p-value to flexibly adjust image quality. Specially, this method can accurately distinguish adjacent defects spaced 1 mm apart with p value of 2.5, and it can also detect two defects located 10 mm deep with p value of 3.0.

Soliton solutions of derivative nonlinear Schrödinger equations: Conservative schemes and numerical simulation

In this paper, we numerically study soliton solutions of derivative nonlinear Schrödinger equations based on several conservative finite difference methods. All schemes own second-order accuracy with the convergence order O(τ2+h2) in the discrete L∞-norm, where h denotes the spatial step size and τ denotes the temporal step size. We show that difference schemes preserve some discrete counterparts of continuous conservation laws, and all these schemes are solvable. Extensive numerical examples with soliton solutions are carried out to verify the theoretical results. These results manifest that our schemes have potential application to soliton propagation in optical fibers.

A Fast Prediction Framework for Multi-Variable Nonlinear Dynamic Modeling of Fiber Pulse Propagation Using DeepONet

Traditional femtosecond laser modeling relies on the iterative solution of the Nonlinear Schrödinger Equation (NLSE) using the Split-Step Fourier Method (SSFM). However, SSFM’s high computational complexity leads to significant time consumption, particularly in automatic control and system optimization, thus limiting control model responsiveness. Recent studies have suggested using neural networks to simulate fiber dynamics, offering faster computation and lower costs. In this study, we introduce a novel fiber propagation method utilizing the DeepONet architecture for the first time. By separately managing fiber parameters and input–output pulses in the branch and trunk networks, this method can simulate various fiber configurations with high accuracy and without altering the architecture. Additionally, while SSFM generation time increases linearly with fiber length, the GPU-accelerated AI generation time remains consistent at around 0.0014 s, regardless of length. Notably, in high-order soliton (HOS) compression over a 12 m distance, the AI method is approximately 56,865 times faster than SSFM.

The multi-positon and breather positon solutions for the higher-order nonlinear Schrödinger equation in optical fibers

Under investigation in this paper is the higher-order nonlinear Schrödinger equation, which can imitate the ultrashort pulses propagation in optical fibers. The modulation instability is analyzed based on the plane-wave solution. With the help of the generalized Darboux transformation, the second-, third- and fourth-order positon solutions are constructed. Furthermore, the second-, third- and fourth-order breather positon solutions are obtained, and the influences of parameters for the characteristics of solutions are analyzed.

M-shaped, W-shaped and dark soliton propagation in optical fiber for nonlocal fourth order dispersive nonlinear Schrödinger equation under distinct conditions

The formation of soliton in optical fiber governed by nonlocal nonlinear Schrödinger (NLS) equation with fourth order dispersion is studied. The model of nonlocal NLS equation with fourth order dispersion is solved using the new extended auxiliary method and the solutions are obtained. The solutions are in the form of hyperbolic and trigonometric functions which are based on Jacobi elliptic function m. Shape changing soliton in optical fiber for nonlocal fourth order dispersive NLS equation is discussed by suitably choosing the values of kerr and quintic nonlinearities and by varying fourth order dispersion term. The effect of fourth order dispersion on soliton in fiber for different conditions of kerr and quintic nonlinearity is also discussed. In addition, the phase portraits of the system have been investigated and the stability of wave in optical fiber for nonlocal NLS equation is discussed using fourth order Runge-Kutta algorithm. This paper addresses a significant gap in the current literature by examining the impact of fourth order dispersion on the nonlocal NLS equation in optical fiber.

TW-scale few-cycle short-wave infrared laser based on nonlinear compression in a large-core gas-filled hollow core fiber

In this Letter, we present the generation of terawatt-scale few-cycle short-wave infrared (SWIR) lasers using nonlinear compression in a large-core gas-filled hollow core fiber. Through the experimental verification, we investigate the energy scaling properties and nonlinear pulse propagation in the argon-filled hollow core fiber. At static pressure, the system delivers pulses with 5.55 mJ/9.04 fs at a central wavelength of 1.45 μm, resulting in a peak power of about 0.5 TW. Subsequently, based on the chirped input pulses and pressure gradient, the system delivers terawatt-scale two-cycle SWIR pulses with 9.52 mJ/10.65 fs, resulting in a record peak power of about 0.7 TW. This study marks a crucial advancement in the field of SWIR ultra-intense, ultrashort pulse nonlinear interaction platforms. This high-energy, few-cycle SWIR source has significant applications in high-intensity THz radiation, x-ray generation, and other fields of strong-field physics.

Resonant optical soliton solutions for time-fractional nonlinear Schrödinger equation in optical fibers

In this paper, several new optical soliton solutions of the time-fractional generalized resonant nonlinear Schrödinger equation, relevant to pulse propagation in optical fibers, are constructed using the extended simplest equation approach. The new exact solutions are expressed in terms of hyperbolic functions, trigonometric functions, and rational functions. Further, two-dimensional, three-dimensional, and contour graphs of king-type, wave, dark–bright, bright, and bell-shaped optical soliton solutions are plotted to elucidate the significance of the time-fractional generalized resonant nonlinear Schrödinger equation using appropriate values of physical parameters. The dynamic behavior of the present solutions, incorporating the effect of the conformable fractional derivative, is depicted through two-dimensional graphs. The derived optical solutions are considered novel and have presumably not been previously reported in the literature.

Extraction of newly soliton wave structure of generalized stochastic NLSE with standard Brownian motion, quintuple power law of nonlinearity and nonlinear chromatic dispersion

Stochastic optical solitons are a fascinating phenomenon in nonlinear optics where soliton-like behavior emerges in systems affected by stochastic noise. This study investigates the influence of Brownian motion on wave propagation in optical fibers. The propagation is modeled using a stochastic nonlinear Schrödinger equation incorporating quintuple power-law nonlinearity and nonlinear chromatic dispersion. To explore this, the improved modified extended tanh (IMET) scheme, leveraging the extended Riccati equation, is employed. This technique facilitates the extraction of various stochastic solutions, including bright, dark, and singular solitons. Furthermore, solutions in the shapes of exponential, singular periodic, and Weierstrass elliptic forms are investigated. The study looks at how the strength of noise impacts various solutions, and Matlab software is used to create 2D and 3D graphs that show the results. It has been noted that when noise intensity rises, signal level falls and surface flattens.

Exploring the impact of multiplicative white noise on novel soliton solutions with the perturbed Triki–Biswas equation

This study examines the effects of multiplicative white noise on soliton perturbations governed by the Triki–Biswas equation for the first time. Triki–Biswas equation advances research on ultrashort pulse propagation in optical fibers. It modifies the nonlinear Schrödinger equation to describe the behavior of femtosecond pulses more accurately in optical media, becoming a critical tool in the field. The paper employs two innovative methods, the enhanced direct algebraic method and the new projective Riccati equations method to uncover a broad range of soliton solutions, including bright, dark, and singular solitons. The solutions are expressed in terms of Jacobi elliptic functions and exhibit a transition to soliton-type solutions as the elliptic modulus approaches unity. This investigation is the first of its kind to explore the effects of multiplicative white noise within this context, providing new perspectives and methodologies for future research in the field. The study sheds light on previously unexplored aspects of multiplicative white noise and contributes significantly to the body of knowledge in soliton theory and its application to optical fiber technology.

Automating physical intuition in nonlinear fiber optics with unsupervised dominant balance search.

Identifying the underlying processes that locally dominate physical interactions is the key to understanding nonlinear dynamics. Machine-learning techniques have recently been shown to be highly promising in automating the search for dominant physics, adding important insights that complement analytical methods and empirical intuition. Here we apply a fully unsupervised approach to the search for dominant balance during nonlinear and dispersive propagation in an optical fiber and show that we can algorithmically identify dominant interactions in cases of optical wavebreaking, soliton fission, dispersive wave generation, and Raman soliton emergence. We discuss how dominant balance manifests both in the temporal and spectral domains.

Optical soliton solution of the perturbed Biswas-Milovic equation having cubic-quintic-septic law nonlinearity in the presence of spatio-temporal and chromatic dispersion

In this manuscript, we investigate the analytical and soliton solutions of the cubic-quintic-septic law for the perturbed Biswas-Milovic equation, considering spatio-temporal and chromatic dispersions. The perturbed Biswas-Milovic equation with the spatio-temporal and chromatic dispersion terms provides a comprehensive study for describing nonlinear optical wave propagation in optical fiber. We use the wave transformation to reduce the main equation to a nonlinear ordinary differential equation. The transformation of the original equation into a more simplified form aims to attain a more profound comprehension of the fundamental dynamics of the system. We retrieve the analytical solutions of the presented model by implementing the new Kudryashov technique and a subversion of the new extended auxiliary equation approach. Besides, bright, singular, and V-shape soliton structures are represented. By employing powerful analytical techniques, we systematically derive a wide range of soliton solutions. This approach successfully captures diverse soliton types highlighting the novelty of applying the new Kudryashov technique and a subversion of the new extended auxiliary equation method to this complex model. Moreover, we analyze the soliton behavior influenced by various parameters. The analysis of the parameter influences reveals the complicated relationship governing the dynamics of the perturbed Biswas-Milovic model. Furthermore, this manuscript includes the modulation instability analysis for the presented model. Conducting modulation instability analysis for the presented equation enhances our understanding of the system’s stability and dynamics.

Deep Learning-Based Simultaneous Temperature- and Curvature-Sensitive Scatterplot Recognition.

Since light propagation in a multimode fiber (MMF) exhibits visually random and complex scattering patterns due to external interference, this study numerically models temperature and curvature through the finite element method in order to understand the complex interactions between the inputs and outputs of an optical fiber under conditions of temperature and curvature interference. The systematic analysis of the fiber's refractive index and bending loss characteristics determined its critical bending radius to be 15 mm. The temperature speckle atlas is plotted to reflect varying bending radii. An optimal end-to-end residual neural network model capable of automatically extracting highly similar scattering features is proposed and validated for the purpose of identifying temperature and curvature scattering maps of MMFs. The viability of the proposed scheme is tested through numerical simulations and experiments, the results of which demonstrate the effectiveness and robustness of the optimized network model.