Mode Conversion Phenomena Research Articles

Simulations of multi-functional optical devices based on a sharp 90° bending graphene parallel pair

We theoretically demonstrate the properties of surface plasmon polaritons (SPPs) propagating along a 90° sharp bending graphene parallel pair and the mode conversion phenomenon around the corner. They are illustrated numerically using the finite-difference time-domain (FDTD) method. As applications, a couple of bending graphene sheets are employed to construct Mach–Zehnder interferometers, T-shaped splitters and switches, and two-Y-shaped splitters and switches. By means of a gate voltage, these devices present novel optical properties and yield a new way to obtain tightly confined and low loss SPPs for nanophotonic networks. Undoubtedly, the proposed devices will have significant application prospects in ultra-compact integrated circuits for optical communications and switching.

The effect of frequency on secondary wave mode generation for ultrasonic health monitoring of fatigue damaged plate structures

ABSTRACTA computational frequency analysis of secondary wave mode generation is considered in this paper. Secondary wave mode conversion at the tip of a through‐thickness slit in a circular isotropic plate is analysed similar to a classical Sommerfeld's diffraction problem. The analysis is useful for quantitative non‐destructive evaluation of fatigue cracked plate structures that involve propagation of a single wave mode (a vertically polarised symmetric Lamb mode) and measurement of the amplitude of a new mode (a horizontally polarised shear mode). A two‐dimensional finite element model is first introduced as a baseline reference for the non‐dispersive scenario. This model is used to study the effect that P‐wave angle of incidence has on the mode converted S‐wave from the tip of the slit. A dispersive three‐dimensional finite element model of the circular plate is then introduced at a number of frequency‐thickness products within the range 0.5–3 MHz.mm−1. Within this frequency–thickness range, significant changes to the through‐thickness displacement profiles of the incident S0 Lamb mode occur. The secondary SH0 plate wave mode generated by mode conversion from the 45o incident S0 Lamb mode at the tip of a slit is analysed to establish the efficiency of the mode conversion. Visualisations of the wave fields demonstrate that at frequency–thickness products higher than the first symmetric Lamé mode (where there is no in‐plane surface displacement), the in‐plane through‐thickness displacement profile of the incident S0 Lamb mode becomes incompatible with that of the SH0 plate mode, and the mode conversion phenomenon is thus severely compromised.

Mode transformation using graded photonic crystals with axial asymmetry

We propose a mode conversion method that enables transformation of the propagating mode from fundamental to higher-order modes by utilizing asymmetric graded index (A-GRIN) structures. Refractive index variations of two different asymmetric gradient profiles, i.e., exponential and Luneburg lens profiles, have been approximated by two-dimensional photonic crystals (PCs). The basic structure is composed of constant radii with different lattice sizes. The designed GRIN mode converters provide relatively high transmission efficiency in the spectral region of interest and achieve the transformation in compact configuration. Numerical approaches utilizing the finite-difference time-domain and plane wave expansion methods are used to analyze the mode conversion phenomenon of proposed GRIN PC media. Analytical formulation based on ray theory is outlined to explore both ray trajectories and the physical concept of a wavefront retardation mechanism.

Numerical Investigation of Influence of Temperature on Propagation of Ultrasonic Waves in Waveguides with Mode Conversion

In the case of the objects with a high temperature the measurements are often performed using waveguides in order to protect the ultrasonic piezoelectric transducers from a high temperature. In some cases, for measurement of specific properties of materials, shear waves are used. Shear waves can be generated exploiting mode conversion phenomenon using a longitudinal wave transducer and a waveguide with deflected front surface. However, the deflection angle has to be carefully selected, when it is required that the shear waves would propagate parallel to the waveguide axis. The proper deflection angle depends on material used for the waveguide properties. When the temperature changes, the properties of the material (as ultrasonic velocity) change as well, causing the change of the reflection angle and the propagation path. A numerical investigation was performed in order to evaluate how the change of the temperature will influence the reflection angle of the ultrasonic waves and the propagation path. It is shown that the change of the temperature influences the reflection angle and propagation path of ultrasonic waves and should be taken into account.DOI: http://dx.doi.org/10.5755/j01.eee.18.10.2537

Spectral and perturbation analysis for ultrasonic guided waves

The influence of damage on waves propagating in complex geometry waveguides is investigated through a numerical model formulated by combining the Spectral Finite Element Method and Perturbation Techniques. The resulting numerical tool allows efficient computation of the wave propagation response and the analysis of the effects of damages of various extent and location. The dynamic behavior of the damaged waveguides is described through a general higher order model which couples different waves thus allowing the prediction of mode conversion phenomena. Arbitrary cross-section can be considered through Finite Element (FE) discretization according to well-established Semi-Analytical Finite Element (SAFE) procedures. Two types of damages which allow the application of perturbation theory are considered: a small localized reduction of the thickness and a reduction of material stiffness and density. A validation by comparison with a Finite Element Model as well as numerical examples are presented to illustrate the model capabilities.

The Phenomenon of Continuous Mode Conversion of Lamb Waves in CFRP Plates

The effect of mode conversion of Lamb waves is a well known phenomenon. Lamb waves occur in multiple modes, which can transform into each other under special conditions. Typically mode conversion takes place at discrete positions inside a structure, e.g. damages and edges. However, we observed a continuous mode conversion in a multi-layer composite plate. The symmetric S0-mode converts continuously into the A0-mode without passing a macroscopic discontinuity. In the paper this phenomenon of continuous mode conversion is investigated experimentally as well as numerically.

Modal solutions for SH guided waves radiated by an EMAT in a ferromagnetic plate

Electromagnetic acoustic transducers (EMAT) generate forces which are sources of elastic waves in a part without contact with it. Depending on the EMAT design, normal or tangential forces can be generated. Thanks to these capabilities, EMATs constitute an interesting alternative to piezoelectric devices in many configurations of non-destructive examination. In this paper, only shear horizontal (SH) guided waves radiated by an EMAT in a plate made of ferromagnetic material are modelled. These waves are particularly interesting to use for testing welded structures: SH waves may propagate in a weld without scattering and mode conversion phenomena. All the forces generated by an EMAT (Lorentz's, magnetosctrictive and magnetic forces) being exponentially decreasing with depth, they are rewritten as series of moments, then, approximated as equivalent surface stresses. Surface stresses are then taken into account as terms of source of elastic waves. Specific features of EMAT can eventually be exploited to derive simple analytic expressions of the applied stress, leading to closed-form solutions for the modal amplitude of SH guided waves. Using these solutions, which are calculated at no computing cost, it becomes easy to study the influence of typical EMAT parameters on the modal amplitude of waves generated in the plate.

TWO DIMENSIONAL MULTI-PORT METHOD FOR ANALYSIS OF PROPAGATION CHARACTERISTICS OF SUBSTRATE INTEGRATED WAVEGUIDE

In this paper, two dimensional multi-port method is used to analyze substrate integrated waveguide by using Green's function approach to obtain the impedance matrix of equivalent planar structure. Modes propagation constant of substrate integrated waveguide, as a periodic structure, is calculated by applying Floquet's theorem on the impedance matrix of a unit cell. Field distribution of the propagating mode is obtained by this method. Results obtained by this method are verifled, in a broad range of dimensions, by comparing with published results and also those calculated by commercial electromagnetic simulator, HFSS. Electromagnetic band gaps and mode conversion phenomenon as properties of periodic structures are also observed and investigated. Mode conversion in SIW is reported for the flrst time by our proposed method.

Sizing of impact damages in composite materials using ultrasonic guided waves

A parametric 2D finite-element inversion scheme is used for sizing cracked zone type strip defect caused by a linear and uniform impact on a composite material plate. The reflection and transmission coefficients produced by mode conversion phenomenon when a pure incident S 0 Lamb wave mode is sent towards the defect are used as input data for the inversion process. The inversion process consists in quantifying two unknown parameters, i.e., width and depth representing the assumed triangular geometry of cracked zone like defect. The inversion scheme consists of a finite element based model, which is used to simulate the Lamb wave scattering for various values of the aimed parameters, and specific post-processing based on Shkerdin's orthogonality relation is applied to predict the needed reflection and transmission coefficients. A laboratory experiment is performed for creating a linear and uniform impact on a carbon epoxy composite plate sample. Then another ultrasonic experiment is performed in laboratory for measuring reflection and transmission coefficients by sending a pure S 0 mode towards the defect. The measured coefficients are then used for the inversion purpose. The two principles used in inversion process give almost similar optimised values for these parameters, showing the usefulness of this technique.

Numerical simulation of ultrasonic wave propagation for the evaluation of dental implant biomechanical stability

Osseointegration of dental implants remains poorly understood. The objective of this numerical study is to understand the propagation phenomena of ultrasonic waves in prototypes cylindrically shaped implants and to investigate the sensitivity of their ultrasonic response to the surrounding bone biomechanical properties. The 10 MHz ultrasonic response of the implant was calculated using a finite difference numerical simulation tool and was compared to rf signals taken from a recent experimental study by Mathieu et al. [Ultrasound Med. Biol. 37, 262-270 (2011a)]. Reflection and mode conversion phenomena were analyzed to understand the origin of the different echoes and the importance of lateral wave propagation was evidenced. The sensitivity of the ultrasonic response of the implant to changes of (i) amount of bone in contact with the implant, (ii) cortical bone thickness, and (iii) surrounding bone material properties, was compared to the reproducibility of the measurements. The results show that, either a change of 1 mm of bone in contact with the implant, or 1.1 mm of cortical thickness or 12% of trabecular bone mass density should be detectable. This study paves the way for the investigation of the use of quantitative ultrasound techniques for the evaluation of bone-implant interface properties and implant stability.

Sizing strip-like defects in plates using guided waves

This paper deals with developing a parametric 2D finite-element technique, which can size strip-like defects in elastic or viscoelastic, isotropic or anisotropic material plates. A pure incident Lamb wave mode is sent towards the defect and reflection and transmission coefficients produced by mode conversion phenomenon are used as input data for the inversion process, which consists in quantifying two unknown parameters representing the geometry of the defect. A finite-element-based model is used to simulate the Lamb wave scattering for various values of the aimed parameters, and specific post-processing based on Shkerdin’s orthogonality relation is applied to predict the needed reflection and transmission coefficients. The target is known reflection and transmission coefficients initially obtained from an experiment, which can be either a numerical experiment for validation purposes, or proper measurements on a sample for NDE application purposes. The inversion process is stopped when the predicted reflection and transmission coefficients fit at best those obtained from initial experiment. In this paper, we have quantified two geometrical parameters for three types of defects in different waveguides: the through-thickness depth (or position) and width (or radius) of (1) a circular hole inside an aluminium plate, (2) a rectangular notch at the surface of a Perspex plate, (3) a cracked zone inside a composite plate, representing an impact damage.

Mode-selective excitation and detection of ultrasonic guided waves for delamination detection in laminated aluminum plates

Selective modes of guided Lamb waves are generated in a laminated aluminum plate for damage detection using a broadband piezoelectric transducer structured with a rigid electrode. Appropriate excitation frequencies and modes for inspection are selected from theoretical and experimental dispersion curves. Dispersion curves are obtained experimentally by short time Fourier transform of the transient signals. Sensitivity of antisymmetric and symmetric modes for delamination detection are investigated. The antisymmetric mode is found to be more reliable for delamination detection. Unlike other studies, in which the attenuation of the propagating waves is related to the extent of the internal damage, in this investigation, the changes in the time-of-flight (TOF) of guided Lamb waves are related to the damage progression. The mode conversion phenomenon of Lamb waves during progressive delamination is investigated. Close matching between the theoretical and experimentally derived dispersion curves and TOF assures the reliability of the results presented here.

Frequency–wavenumber domain analysis of guided wavefields

Full wavefield measurements obtained with either an air-coupled transducer mounted on a scanning stage or a scanning laser vibrometer can be combined with effective signal and imaging processing algorithms to support characterization of guided waves as well as detection, localization and quantification of structural damage. These wavefield images contain a wealth of information that clearly shows details of guided waves as they propagate outward from the source, reflect from specimen boundaries, and scatter from discontinuities within the structure. The analysis of weaker scattered waves is facilitated by the removal of source waves and the separation of wave modes, which is effectively achieved via frequency–wavenumber domain filtering in conjunction with the subsequent analysis of the resulting residual signals. Incident wave removal highlights the presence and the location of weak scatterers, while the separation of individual guided wave modes allows the characterization of their separate contribution to the scattered field and the evaluation of mode conversion phenomena. The effectiveness of these methods is demonstrated through their application to detection of a delamination in a composite plate and detection of a crack emanating from a hole.

The choice of torsional or longitudinal excitation in guided wave pipe inspection

Long-range screening of pipework using guided waves is now in routine industrial use. The T(0,1) mode is generally preferable to the L(0,2) mode as the transduction system required is simpler and lighter. The L(0,2) mode may be useful in a small number of cases but tests reported here demonstrate that it is unlikely to be useful in liquid-filled pipes. It also tends to give poorer signal-to-noise ratio, and a double mode conversion phenomenon can give extra echoes that could be incorrectly called as defects. In principle it is possible to test each length of pipe using both modes, though at a considerable penalty in equipment complexity, weight and cost. It is argued that if increased confidence is required, a better strategy generally is to test each section of pipe from both directions using the torsional mode.

A wave-based damage index for the analysis of the filtered response of damaged beams

This paper introduces a wave propagation-based damage index which relies on the evaluation of the strain energy distribution associated with propagating waves. The presence of localized damages typically distorts the wavefield by causing reflections and diffractions. The evaluation of such distortions, in reference to the wavefield corresponding to the undamaged structure, can be used as an indicator which potentially locates, quantifies and classifies the damage. The damage index formulation is first illustrated through a numerical model of a beam with a small notch, modeled as a localized thickness reduction. The beam's wave propagation response is simulated through the combined application of perturbation techniques and the spectral finite element method. The perturbation approach and a first order model for the beam capture the coupling between bending and axial behavior caused by the damage, and allow the prediction of mode conversion phenomena. The perturbation solution allows direct comparison between undamaged and damaged strain energy contributions, which are directly associated with perturbation solutions of different orders. The resulting damage index locates the damage along the beam length and estimates its severity. Experimentally, the damage index is implemented by considering full wavefield measurements obtained through a scanning laser vibrometer. The undamaged reference response is derived directly from measurements on the damaged component, through the application of a filtering procedure operating in the wavenumber/frequency domain.

Resonant absorption and mode conversion in a transition layer between positive-index and negative-index media

We study the propagation of electromagnetic waves through a transition layer between positive-index and negative-index media theoretically. We consider three models where both the dielectric permittivity epsilon and the magnetic permeability micro change linearly from positive values to negative values. At the positions where epsilon or micro vanishes, the mode conversion of the incident electromagnetic waves into longitudinal plasma oscillations can occur. Using the invariant imbedding theory of mode conversion in inhomogeneous media, we calculate the mode conversion coefficient and the electromagnetic field profile in a numerically exact manner. We find that strong mode conversion can occur for both s- and p-polarized incident waves. The dependence of mode conversion on polarization is influenced very sensitively by the spatial profiles of epsilon and micro. We also discuss the interaction effects between mode conversion phenomena occurring at two resonance points located nearby.

Spectral and Perturbation Analysis of First-Order Beams With Notch Damage

The influence of damage on waves propagating in beam structures is investigated through a numerical model formulated by combining spectral finite elements and perturbation techniques. The resulting numerical tool allows for an efficient computation of the wave propagation response and the analysis of the effects of localized damages of various extents and locations. The dynamic behavior of damaged beams is described through a first-order model, which couples bending and axial behavior, thus allowing the prediction of mode conversion phenomena. Damage is modeled as a small, localized reduction of the beam thickness which, allows for an application of perturbation theory. Numerical examples in the time and frequency domains are presented to illustrate the model capabilities.

Propagation of electromagnetic waves in stratified media with nonlinearity in both dielectric and magnetic responses

We develop a generalized version of the invariant imbedding method, which allows us to solve the electromagnetic wave equations in arbitrarily inhomogeneous stratified media where both the dielectric permittivity and magnetic permeability depend on the strengths of the electric and magnetic fields, in a numerically accurate and efficient manner. We apply our method to a uniform nonlinear slab and find that in the presence of strong external radiation, an initially uniform medium of positive refractive index can spontaneously change into a highly inhomogeneous medium where regions of positive or negative refractive index as well as metallic regions appear. We also study the wave transmission properties of periodic nonlinear media and the influence of nonlinearity on the mode conversion phenomena in inhomogeneous plasmas. We argue that our theory is very useful in the study of the optical properties of a variety of nonlinear media including nonlinear negative index media fabricated using wires and split-ring resonators.

Modal analysis of multilayer planar lossy anisotropic optical waveguides

A systematic rigorous matrix method based on generalized transmission line (TL) modelling for the full-vectorial analysis of the guided modes of multilayer planar lossy anisotropic optical waveguides is developed. By means of the proposed method, complex propagation constants and mode field distributions of the propagating modes of planar waveguides with an arbitrary finite number of layers made of arbitrarily oriented anisotropic media are determined. The mode coupling and conversion phenomenon in a biaxial slab waveguide is demonstrated and a mode labelling scheme based on the polarization of the allowable plane waves in anisotropic media is proposed.

Invariant imbedding theory of mode conversion in inhomogeneous plasmas. II. Mode conversion in cold, magnetized plasmas with perpendicular inhomogeneity

A new version of the invariant imbedding theory for the propagation of coupled waves in inhomogeneous media is applied to the mode conversion of high frequency electromagnetic waves into electrostatic modes in cold, magnetized, and stratified plasmas. The cases where the external magnetic field is applied perpendicularly to the direction of inhomogeneity and the electron density profile is linear are considered. Extensive and numerically exact results for the mode conversion coefficients, the reflectances, and the wave electric and magnetic field profiles inside the inhomogeneous plasma are obtained. The dependencies of mode conversion phenomena on the magnitude of the external magnetic field, the incident angle, and the wave frequency are explored in detail.