Mode Dispersion Research Articles

Optical Solitons for the Dispersive Concatenation Model with Polarization Mode Dispersion by Sardar's Sub-Equation Approach

This paper recovers the spectrum of optical solitons for the dispersive concatenation model with the application of the Sardar sub-equation approach. The single soliton solutions that emerge from this scheme are bright, dark, and of singular type. The parameter constraints for the existence of such solitons are also included.

Optical dromions with polarization–mode dispersion having parabolic law of self–phase modulation with multiplicative white noise

Optical dromions with polarization–mode dispersion having parabolic law of self–phase modulation with multiplicative white noise

M-truncated fractional form of the perturbed Chen–Lee–Liu equation: optical solitons, bifurcation, sensitivity analysis, and chaotic behaviors

This investigation discusses the modified M-truncated form of the perturbed Chen–Lee–Liu (pCLL) dynamical equation. The pCLL equation is a generalization of the original CLL equation, which describes the propagation of optical solitons in optical fibers. The pCLL equation includes additional terms that account for various influences such as chromatic dispersion, nonlinear dispersion, inter-modal dispersion, and self-steepening. A new version of the generalized exponential rational function method is utilized to obtain multifarious types of soliton solutions. Moreover, the planar dynamical system of the concerned equation is created using a Hamiltonian transformation, all probable phase portraits are given, and sensitive inspection is applied to check the sensitivity of the considered equation. Furthermore, after adding a perturbed term, chaotic and quasi-periodic behaviors have been observed for different values of parameters, and multistability is reported at the end. Numerical simulations of the solutions are added to the analytical results to better understand the dynamic behavior of these solutions. The study’s findings could be extremely useful in solving additional nonlinear partial differential equations.

A micro-capillary jetting technology for liquid-liquid microdispersion with narrow size distribution

Liquid-liquid microdispersion is one of the key foundations for chemical process intensification. However, liquid-liquid microdispersion at the conditions of high phase ratio and high volume flow rate remains a problem and new microdispersion technology is highly required. Based on the microscale effect of the liquid jet, we developed the micro-capillary jetting technology. It can produce microdroplets (250–500 μm) with narrow size distribution (CV ≈ 10–20 %) in a wide range of physical properties with large capacity and little cost without the restriction of phase ratio. This paper reports the laws of the micro-capillary jetting technology. The liquid-liquid flow patterns and mechanism are studied, and a precise quantitative model to distinguish different jetting patterns is provided for the first time based on the energy analysis in the microscale. Then important factors including physical properties, dispersion mode and structural parameters are investigated. Accordingly, a mathematical model for the prediction of the average droplet size is established and the energy utilization in the jetting dispersion process is calculated.

Concentric circular stress region-assisted pseudo-elliptical-ring-core polarization-maintaining few-mode fiber

In this paper, a pseudo-elliptical-ring-core polarization-maintaining few-mode fiber structure assisted by concentric circular stress-applying region is proposed. Numerical simulation results show that the structure can stably support 14 transmission modes. By introducing two elliptical stress regions with low refractive index inside the core, and a circular stress region with concentric core between the fiber core and cladding, the effective refractive index difference between higher-order modes is significantly improved. In the C + L band, the minimum refractive index difference between adjacent modes is not less than 2 × 10−4. At 1550 nm, the effective refractive index difference between the two fundamental modes reaches 4.8 × 10−4. The mode dispersions are less than |-33| ps/nm/km, and the maximum bending loss is in the order of 10−7 dB/m (bending radius ≥2.5 cm). This work may pave the way for the development of short-distance large-capacity optical fibers.

Evaluation of Bolt Corrosion Degree Based on Non-Destructive Testing and Neural Network

Anchor bolt corrosion is a complex and dynamic system, and the prediction and identification of its corrosion degree are of significant importance for engineering safety. Currently, non-destructive testing using ultrasonic guided waves can be employed for its detection. Building upon the analysis of anchor bolt corrosion mechanisms, this paper proposes a method for evaluating the corrosion degree of anchor bolts based on multi-scale convolutional neural networks (MS-CNNs) that address the multi-mode propagation and dispersion effects of ultrasonic guided wave signals in non-destructive testing. Electrochemical experiments were conducted to simulate anchor bolt corrosion, and ultrasonic guided wave non-destructive testing was performed every 12 h to obtain waveform data. An MS-CNN was then utilized to accurately diagnose the corrosion degree of the anchor bolts. The test results demonstrate that this method effectively detects and diagnoses the extent of anchor bolt corrosion, facilitating timely troubleshooting and preventing potential safety accidents.

Highly dispersive optical solitons with differential group delay and multiplicative white noise for Fokas–Lenells equation

AbstractThe current article addresses highly dispersive optical solitons with polarization mode dispersion, modeled by the Fokas–Lenells equation in presence of white noise. The corresponding soliton solutions are retrieved with the usage of two integration algorithms. They are the enhanced Kudryashov’s method and the enhanced direct algebraic method. The intermediary solutions are in terms of Jacobi’s elliptic functions and Weierstrass’ elliptic functions. The existence criteria of soliton solutions, by virtue of parameter constraints, are also presented.

Study on optical properties of hexagonal lattice photonic crystal fibers infiltrated with heavy water

In this paper, we analyzed a PCF made from fused silica glass, with a core filled with heavy water. The guiding properties of proposed fibers in terms of effective refractive index, attenuation, and dispersion of the fundamental mode were studied and optimized setups were selected and analyzed in detail. After 25 simulations, we determined two structures possessing optimal dispersion with the lattice constant (Ʌ) and the filling factor as follows: Ʌ = 1.1 µm, d/Ʌ = 0.92 for #F1 and Ʌ = 1.4 µm, d/Ʌ = 0.92 for #F2. Besides, high nonlinearity and low confinement loss are also outstanding points in our model. Thanks to these advantages, the proposed fibers have been targeted for flat and smooth broadband supercontinuum (SC) generation for near-infrared applications.

The Dispersion Calculator - a free software for calculating dispersion curves of guided waves

The nondestructive inspection of components by means of guided waves is an emerging technology in fields like aerospace or pipeline construction and maintenance. The guided waves' capability of propagating many meters in a structure is utilized for swift inspection tasks as well as structural health monitoring. The German Aerospace Center uses Lamb waves for the quality assurance of large-scale aerospace vehicle components made from carbon composites. However, the use of guided waves in NDT requires knowledge of the dispersion curves. DISPERSE is the most renown software for the calculation of dispersion curves. This paper presents the open source Dispersion Calculator (DC). The MATLAB® -based DC is an interactive and fully validated software for the computation of dispersion curves and mode shapes of guided waves in isotropic plates and multilayered anisotropic composites. Damping caused by viscoelasticity and fluid-loading can be considered. DC features the capability of calculating laminates consisting of several hundreds of layers so that even the largest specimens, like rocket booster pressure vessels, can be calculated. This is made possible through the implementation of the stiffness matrix method. DC is also able to distinguish the different mode families, like symmetric, antisymmetric, and nonsymmetric Lamb, shear horizontal, and Scholte waves, depending on the symmetry and coupling properties of a given layup. Lastly, DC features a highly efficient and robust dispersion curve tracing algorithm. DC is available at GitHub, and it has gained many users world-wide since its initial release in 2018.

Statistical Analysis of Modal Dispersion in Field-Installed Coupled-Core Fiber Link

Statistical Analysis of Modal Dispersion in Field-Installed Coupled-Core Fiber Link

Full Dispersion‐Spectrum Inversion of Surface Waves

AbstractNowadays, the most successful applications of full‐waveform inversion (FWI) involve marine seismic data under acoustic approximations. Elastic FWI of land seismic data is still challenging in theory and practice. Here, we propose a full dispersion spectrum inversion method and apply it to seismic data acquired in West Antarctica. Inspired by the conventional surface wave dispersion curve inversion method, we propose to invert the surface wave dispersion spectrum instead of the complicated waveforms. We compare the frequency‐velocity, frequency‐slowness, and frequency‐wavenumber spectra in terms of their ability to resolve dispersion modes and the feasibility of their adjoint updates and conclude that the frequency‐slowness spectrum is the best for our inversion objectives. We test four objective functions, subtraction, zero‐lag crosscorrelation, optimal transport, and the local‐crosscorrelation to quantify the spectrum mismatch and provide the corresponding adjoint source. We then theoretically analyze the convexity of the proposed objective functions and examine their convergence behavior using numerical examples. We also compare the proposed method with the classic FWI method and the traditional surface wave dispersion curve inversion method and discuss the strengths and weaknesses of each method. This technique is employed to evaluate the shallow velocity structures beneath a seismic array stationed in West Antarctica. Our proposed inversion scheme is also useful for more general applications such as imaging the shallow subsurface of the critical zones, like geothermal reservoirs, and CO2 storage sites.

Dynamics of switching optical soliton in fiber with sixth order dispersion and inter modal dispersion

This work pertains to the study of switching soliton in fiber for nonlinear Schrödinger (NLS) equation with the presence of higher order dispersion and inter modal dispersion (IMD). The nonlinear wave in the optical fiber are described by the NLS equation which having the second order, fourth order, fifth order, sixth order dispersion, higher order nonlinearity and IMD. The main goal of the paper is to examine the sixth order dispersion on nonlinear wave in the fiber with the conditions of IMD. Hence, we employ the Bäcklund transformation of the Riccati equation (BTRE) approach to NLS equation and obtain the soliton solution. By the use of soliton solution along with graphical snapshots, we provide the conditions for forming switching solition in optical fiber and also analyze the effect of sixth order dispersion in fiber. The stability of the solution of NLS equation is also addressed.

Spectral Characteristics and Displacement Sensing of U-Shaped Single-Mode-Multimode-Single-Mode Fiber Structure.

The U-shaped fiber configuration represents the elementary form of micro-displacement sensing, characterized by its exceptional freedom and flexibility. The study proposes the U-shaped bent single-mode-multimode-single-mode (SMS) fiber structure that integrates the multimode interference (MMI) effect for enhanced mode dispersion and the Mach-Zönder interference (MZI) effect for spectral sensitivity improvement. The transmission spectral properties of the U-shaped SMS fiber structure with a bent radius over 1 cm are experimentally measured as the change in displacement varied within the range of 5 mm in this work. As the radius decreases, the spectrum shows redshift, which is related to the central wavelength of the peak or dips-a smaller wavelength results in a stronger redshift for the same displacement change. The average sensitivity of micro-displacement measurement within a range of 5 mm is 5.41 pm/μm, and the linearity is 99.62%. The maximum sensitivity of U-shaped SMS fiber structure is 34.46 pm/μm, with the minimum displacement change of approximately 5.804 nm. The transmission spectral properties of the U-shaped SMS fiber structure within the ranges of 50 μm, 500 μm, and 5 mm are experimentally measured in this work. This experiment observed a relatively uniform spectral drift pattern in a large range of micro-displacement sensing. The measurement range is limited by the limited spectral range of the light source and the discontinuous variation in the effective refractive index. This provides an experimental reference for further understanding the characteristics of U-shaped fiber structures and applying its application in micro-displacement sensing.

Study on joint effects of modal dispersion, mode-dependent loss and noise by unified density-matrix formalism

We generalize the density-matrix formalism to provide a simple and unified framework for the study of modal dispersion (MD), mode-dependent loss (MDL) and noise in mode-division-multiplexing communication systems. Fundamental concepts and formulas in the original formalism are generalized, while new elements and associated equations are introduced and/or derived. Due to the ability of the density operator to characterize partially-coherent fields, the generalized density-matrix formalism is particularly useful for analyzing the field propagation in presence of noise. Combining the unified density-matrix formalism and the stochastic-process theory, we conduct detailed numerical simulation and analysis on the modal properties of a randomly-perturbed 6-mode fiber with loss and noise. We find that although the MDL only slightly affects the statistics of the group delays, it can cause significant non-orthogonality among the principal modes, which might induce extra crosstalk and temporal spreading in the signal pulses. Furthermore, with the coherency of fields in the fiber being reduced by the noise, the MDL can induce substantial fluctuation in the field coherency even though it does not significantly affect the averaged field coherency.

Differential Configurational Entropy Measurement of Optical Dark Simlaritons

The nonlinear Schrödinger equation (NLSE) describes various types of physical systems such as water waves, nonlinear optics, plasma Physics. In optics, NLSE describes a wide range of non-linearity effects in fiber optics. The solution to the above equation might be examined in order to investigate these consequences. Differential configurational entropy (DCE) is used to analyze the dark similariton solution in this specific situation of NLSE with bright and dark similariton solutions. DCE provides us with the measure of information required to examine stability for various physical systems and to characterize a systems spatial profile using the Fourier transform. It is show that even for the same solitonic solution of the NLS equation, the variations in the spatial shape is induced by different choices of the relevant parameter α. The global minima of the DCE correspond to the saturation of the breadth of dark solitons. While dark similariton waves propagate through waveguides, such low entropic values result in minimum dispersion of momentum modes, and this should be taken into consideration while designing the waveguides.

Illuminating Urban Near-Surface with Distributed Acoustic Sensing Multimodal Noise Surface-Wave Imaging

Abstract Urban subsurface exploration requires high spatial and temporal resolution, cost-effective operation, and minimal interference with urban activities. Distributed acoustic sensing (DAS)—an innovative seismic observation tool—emerges as a promising solution for urban surveys. In this study, we repurposed a 7.9 km telecommunication cable traversing Hefei into a seismic observation array with 3850 channels spaced at 2 m intervals. Noise cross-correlation functions (NCFs) were constructed from recordings by iDAS2 and ZD-DAS interrogators along the entire cable. Spatial variation in the NCFs was observed and attributed to different traffic conditions. Employing the recently developed modified frequency–Bessel transform method to NCFs from the 2 km southern subsection of the optic cable, we extracted broadband, high-resolution multimodal dispersion curves. The inverted near-surface structure beneath the cable unveiled a sediment thinning trend from the center to the periphery of the Hefei basin, consistent with borehole inspections. The three-station interferometry (C3) method and beamforming with the Bessel kernel function are applied to mitigate challenges arising from the weak coupling between the cable and the Earth, as well as persistent localized noise sources. These techniques facilitated the acquisition of broadband surface waves. Distinct secondary scatters are observed in NCFs near channels 2090 and 2287, accompanied by a substantial velocity contrast of 30%–40%, suggesting the existence of a blind fault. The study reaffirms the significant potential of DAS arrays for high-resolution imaging of subsurface structures in challenging urban environments, emphasizing the importance of advanced processing techniques to enhance imaging accuracy and robustness.

Frequency diversity of modal dispersion in mode-division multiplexing systems from strong to weak coupling regimes

Based on a statistical model applicable to all mode-coupling regimes and a trace covariance function of the group-delay matrix for characterizing the modal-dispersion correlation, we study the frequency diversity of modal dispersion in randomly-perturbed mode-division multiplexing optical communication systems. Particularly, we conduct detailed numerical simulation and analysis on the statistical properties of the modal dispersion in a 6-mode fiber under random perturbation. The results show that, at two frequencies of sufficiently large difference, while the modal dispersion eventually gets uncorrelated in the strong coupling regime, there remains a significant amount of “residual” correlation in the weak coupling regime. Also, we find that, although the typically-assumed frequency-domain ergodicity is reasonably valid in the strong coupling regime, it clearly fails in the weak coupling regime. The crossover from the strong to weak coupling regimes is also quantitatively investigated.

Broadband dispersion compensation and high birefringence photonic crystal fiber for CWDM/DWDM networks

In this study, we propose a new design based on photonic crystal fibers (PCFs) for broadband dispersion compensation in telecommunication networks. The proposed design has a hexagonal structure arrangement of air-holes rings of different diameters between the silica core and the cladding. The PCF properties like effective area, nonlinearity, dispersion slope, confinement loss, and birefringence are reported and discussed. For the best performance we present three designs A, B and C. Simulation results show that the three designs cover the six-telecommunication optical bands O-, E-, S-, C-, L- and U- bands (wavelengths ranging from 1260 to 1675 nm). Design A achieves a large negative dispersion value of about − 1716 ps/(nm.km) with relative dispersion slope equals to that of conventional single-mode optical fibers (SMFs) of about 0.0036 nm−1, which makes it very suitable for long-haul DWDM transmission systems. With a little modification in the core, designs B and C achieve much higher confinement ability and achieve a very large birefringence value for polarization mode dispersion and sensing applications. Design C is engineered to have exact opposite dispersion of SMF with zero dispersion at the wavelength 1310 nm, which makes it a promising design in CWDM transmission system. The numerical values have been investigated using the full vector finite element method.

Sound attenuation at low to mid frequencies in low velocity seabottoms.

Attenuation is the most difficult seafloor acoustic property to get, particularly at low to mid frequencies. For low velocity bottoms (LVB), it becomes even more challenging, due to its small attenuation and lower velocity (relative to the velocity of the adjacent water). The latter one causes a fatal "seafloor velocity-attenuation couplings" in geo-acoustic inversions. Thus, attenuation inversions for the LVB require an accurate seafloor velocity profile, especially the velocity in the LVB layer. The propagation of explosive sound in the Yellow Sea with a strong thermocline and a top LVB layer exhibits many prominent characteristics: modal dispersion (the ground wave, water wave, Airy phase), two groups of water waves at high frequencies, and the siphon effect which causes abnormally large sound transmission loss at selected frequencies, etc. These observations are used to precisely measure the critical frequency, the Airy frequency, Airy wave velocity, 1st mode group velocity, and to derive the velocities in the LVB layer and in the basement. Using inverted seafloor parameters, the source level-normalized transmission loss and the first mode decay rate in ranges up to 27.66 km, the sound attenuations in the LVB are derived for a frequency range of 13-5000 Hz.

Octupolar Cyclotriphosphazene-Cored Self-Standing Covalent Organic Framework Membranes as Nonlinear Optical Materials: Impact of Linkage Types and Material Forms.

Conjugated and processable self-standing vinylene-linked covalent organic framework membranes (COFMs) are highly demanding for photonics and optoelectronics. In this work, we have fabricated the first cyclotriphosphazene (CTP) cored vinylene-linked self-standing COFM (CTP-PDAN). For comparison purposes, we have successfully fabricated the imine-linked congener (CTP-PDA). Leveraging the inherent nonlinear optical (NLO) response of the CTP core, both membranes were directly mounted to evaluate NLO parameters using the open-aperture (OA) Z-scan technique. Direct measurement of NLO responses on membranes is advantageous and free from solvent and scattering effects, making it a more practical approach compared to the conventional dispersion mode. The OA Z-scan transmission yields a reverse saturable absorption signature exhibiting a higher NLO absorption coefficient (β) of 58.37 cm/GW for CTP-PDAN, compared to that of the imine-linked CTP-PDA COFM (β = 8.5 cm/GW). These results can be correlated to the efficient conjugation through the vinylene linkage in CTP-PDAN compared to the imine linked congener.