Wave Propagation In Fibers Research Articles

Jetting and Droplet Formation Driven by Interfacial Electrohydrodynamic Effects Mediated by Solitons in Liquid Crystals.

Solitons are highly confined, propagating waves that arise from nonlinear feedback in natural (e.g., shallow and confined waters) and engineered systems (e.g., optical wave propagation in fibers). Solitons have recently been observed in thin films of liquid crystals (LCs) in the presence of ac electric fields, where localized LC director distortions arise and propagate due to flexoelectric polarization. Here we report that collisions between LC solitons and interfaces to isotropic fluids can generate a range of interfacial hydrodynamic phenomena. We find that single solitons can either generate single droplets or, alternatively, form jets of LC that subsequently break up into organized assemblies of droplets. We show that the influence of key parameters, such as electric field strength, LC film thickness, and LC-oil interfacial tension, map onto a universal state diagram that characterizes the transduction of soliton flexoelectric energy into droplet interfacial energy. Overall, we reveal that solitons in LCs can be used to focus the energy of nonlocalized electric fields to generate a new class of nonlinear electrohydrodynamic effects at fluid interfaces, including jetting and emulsification.

Spectral element modeling of ultrasonic guided wave propagation in optical fibers

Recent advancements in fiber optic methods have enabled their use for guided wave sensing. It opens up new possibilities for Structural Health Monitoring. The aim of this paper is to provide insight for the physics related to guided wave propagation and coupling between the optical fiber and solid structure. For this purpose, a new approach for non-matching interface based on Lagrange multipliers and the time domain spectral element method was developed. A parallelized code has been implemented in order to simulate the guided wave propagation in the structure, its coupling into the optical fiber and the propagation in the fiber in a computationally efficient way. The paper presents four studies showing the efficacy of the modeling approach. The paper first shows the improvement in the computation speed through the use of parallelization and a more efficient implementation. Then the results of the simulation of wave propagation in the fiber are compared with results from previous simulation studies using commercially available software. The third study shows that the spectral element method is able to capture the directional sensitivity of optical fiber based sensors. Lastly, the simulation is used for detection of simulated damage using the spectral element method based simulation. The results indicate that indeed the spectral element implementation is able to recreate the wave coupling phenomena, capture the physics of the system including directional sensitivity and reflections from damage.

Circular Airy Beam Shaping by Annular Arrayed-Core Fiber

We propose and theoretically demonstrate a beam shaping method using a novel all-fiber device composed of a single mode fiber, a tapered annular-core fiber, and an annular arrayed-core fiber. By using the proposed device, a circular Airy beam with outward acceleration can be generated using a Gaussian beam shaping and the autodefocusing Airy beam can be converted into an autofocusing Airy beam through a cone-frustum shaped fiber end. The properties of wave propagation in fiber and surrounding media are studied by using coupled-mode theory and angular spectrum method. The calculated results show that the output beam from the proposed device has a circular Airy-like pattern, which experiences autodefocusing (or autofocusing) during propagation, and forms a Bessel-like beam after the focal point. The tolerances of the beam generation device are discussed and we show that the focused output beam from the cone-frustum shaped fiber end can be used for multi-point trap to form an optical trap array.

Dynamic Wave Propagation in Fiber Reinforced Piezoelectric Composites with Cracks

This paper presents the transient dynamic analysis of micro-cracks of arbitrary shape in two-dimensional, linear piezoelectric fiber reinforced composite materials. Interface cracks between fiber and matrix as well as cracks inside the matrix and fibers are investigated. For this purpose, a symmetric Galerkin time-domain boundary element method in conjunction with a multi-domain technique is developed. The time-domain fundamental solutions for linear piezoelectric materials are applied. The time discretization is performed by a collocation method. An explicit time-stepping scheme is obtained to compute the discrete boundary data including the generalized crack-opening-displacements (CODs). Iterative solution algorithms are implemented to solve the nonlinear semi-permeable electrical crack-face boundary conditions and for a crack-face contact analysis at time-steps when a physically unacceptable crack-face intersection occurs. Several numerical examples are presented to reveal the influences of the micro-cracks, the material combinations and the transient dynamic loading on the intensity factors and the scattered wave fields.

Some Basic Ideas for the Simulation of Wave Propagation in Microstructures using Proper Orthogonal Decomposition

AbstractFor the modeling of micro‐heterogeneous materials, models are required that take into account the microstructure. More and more, computational homogenization is used to quantify the effective macroscopic response. The large number of resulting microscopic boundary value problems need to be solved efficiently. To reduce the computational effort and simulation time, model reduction methods may be applied. In this contribution the performance of the proper orthogonal decomposition is analyzed for the wave propagation in fiber reinforced materials. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

PROPAGATION OF LOVE WAVE IN FIBER-REINFORCED MEDIUM OVER A NONHOMOGENEOUS HALF-SPACE

The present paper is devoted to study the Love wave propagation in a fiber-reinforced medium laying over a nonhomogeneous half-space. The upper layer is assumed as reinforced medium and we have taken exponential variation in both rigidity and density of lower half-space. As Mathematical tools the techniques of separation of variables and Whittaker function are applied to obtain the dispersion equation of Love wave in the assumed media. The dispersion equation has been investigated for three different cases. In a special case when both the media are homogeneous our computed equation coincides with the classical equation of Love wave. For graphical representation, we used MATLAB software to study the effects of reinforced parameters and inhomogeneity parameters. It has been observed that the phase velocity increases with the decreases of nondimensional wave number. We have also seen that the phase velocity decreases with the increase of reinforced parameters and inhomogeneity parameters. The results may be useful to understand the nature of seismic wave propagation in fiber reinforced medium.

Semi-implicit operator splitting Padé method for higher-order nonlinear Schrödinger equations

We propose a semi-implicit finite difference operator splitting Padé (OSPD) method for solving the higher-order nonlinear Schrödinger equation which describes the optical soliton wave propagation in fibers. The method achieves fourth order of accuracy in space and has been proven to be stable by linear stability analysis. Numerical experiments and comparisons are investigated to show the advantages and effectivity of the OSPD method. And some interesting collision behaviors are also observed.

Nonlinear transmission problems in bounded domains of Rn

We study a semilinear elliptic problem in a bounded domain of Rn(n2) with nonlinear transmission conditions on a submanifold of the domain. This problem is related to electromagnetic wave propagation in fibers, where such conditions appear at the interface between the core and the cladding of the fiber. We present a variational formulation of this problem and obtain a weak solution by means of the mountain pass lemma. By constructing suitable trace spaces, we show that this solution satisfies the required interface conditions in a generalized sense.

Dynamic self-consistent analysis for elastic wave propagation in fiber reinforced composites

A dynamic self-consistent method previously proposed and validated for composites containing spherical inclusions is applied to the simplest two-dimensional problem: SH wave propagation in unidirectional fiber reinforced composites. The self-consistent conditions for SH waves are derived and the effective wave speed and coherent attenuation are calculated numerically for five different composites. For two composites showing very different dynamic behaviors, the results of the present theory are compared with those of multiple scattering theories and another self-consistent theory. At low volume fractions the present theoretical results coincide with those of the multiple scattering theory using exact pair-correlation functions, whereas the results based on another self-consistent theory deviate markedly from the others. As the volume fraction increases, the three theories give different results although they have qualitatively similar trends. The present theoretical results for composites considered in this article exhibit less dispersion and physically realizable attenuation. An important observation is that the multiple scattering theory predicts vanishingly small attenuation at low frequency when volume fraction is high. Experiments over wide ranges of frequency and volume fraction are needed in order to assess the accuracy and validity of the present theory.

Wave Propagation in Fiber Reinforced Composites for Oblique Incidence

Wave Propagation in Fiber Reinforced Composites for Oblique Incidence

Recursive numerical solution for nonlinear wave propagation in fibers and cylindrically symmetric systems

An efficient and compact recursive numerical solution of the wave equation is developed and applied to cylindrically symmetric optical systems. Numerical results are given for wave propagation through an aperture and in linear and nonlinear optical fibers. This code is most useful for multiwave mixing and wave propagation in nonlinear media.

Load transfer and surface wave propagation in fiber reinforced composite materials

A system of linear elastic equations recently obtained for fiber reinforced composite materials is applied to some simple problems concerning the transfer of load from the reinforcement to the matrix. The same equations are applied to surface waves propagating in the direction of the fiber reinforcement. Since the defined constants occurring in the above-mentioned linear equations for a two-constituent composite material have never been measured, calculations cannot be performed. When the model is simplified sufficiently, the effective constants in the description can be partially estimated from the known elastic constants of the individual constituents in the composite. With the reduced equations calculations are performed for surface waves propagating both in and normal to the direction of the fiber reinforcement. The calculations indicate the existence of a high (optical type) as well as a low (acoustic type) surface wave mode, both of which are dispersive. We believe the optical type mode is an analytical consequence of the simplified model and does not actually exist. The dispersion of the acoustic type surface wave mode could provide a means of non-destructively evaluating the integrity of a fiber reinforced composite material.