Isotropic Waveguides Research Articles

Damage Quantification Using Mode Converted Guided Wave Based 1D Damage-Spectral Element

Quantifying the sizes of the damages in structures using guided waves is an emerging technology. It needs a suitable mathematical model that represents the behavior of the guided waves as they travel through the structure. Though finite element based theoretical models can provide insight into the behavior, they are computationally very costly. Spectral element is a promising solution in this regard. Quantifying the damage using a mode-converted wave based spectral element has not been reported yet. In this work, a spectral element that represents the characteristics of wave propagation, scattering and mode conversion caused by asymmetric notch-type damage in an isotropic waveguide is presented. This frequency domain damage-spectral element is formulated through a combination of three structural waveguides by enforcing appropriate force equilibrium conditions. The spectral element is able to represent the wave scattering and mode conversion due to the presence of the damage. This spectral element is employed in analyzing the wave propagation in a beam that has damage and the characteristics obtained are in agreement with the results expected based on time-of-flight calculations and those obtained using the finite element method. The relation between the depth of the damage and the magnitude of the mode-converted wave for notch-type damage is established using this spectral element and compared with the experimental result. Usage of the same spectral element in quantifying the length of the damage based on the reflections of the primary propagating wave from the damage ends is also demonstrated.

Determination of dispersion curves of higher order guided ultrasonic waves based on experimental data by a 2D-DFT

Guided ultrasonic wave based structural health monitoring has been subject to research over the last decades. In order to analyze the wave propagation data correctly, knowledge about the fundamental wave propagation properties is indispensable. Due to the multimodal and dispersive nature of guided ultrasonic waves these properties are characterized by dispersion diagrams. In previous work by the authors [1] the dispersion behavior of the guided ultrasonic waves is extracted by an adapted non-uniform 2D-DFT algorithm based on [2]. With this algorithm the dispersion curves can be computed from experimental data in an accurate and highly automated fashion. So far the application is limited to the fundamental wave modes over large frequency ranges. In this work the approach is extended to higher-order wave modes, which are of special interest in particular for the nonlinear wave propagation. To analyze the robustness of the presented data acquisition algorithm the procedure is applied first to isotropic waveguides and second to more complex material systems like fiber metal laminates. The results indicate that the presented approach enables one to derive the dispersion curves over large frequency ranges from experimental data not only for the fundamental A0 and S0 wave modes but also for higher-order modes.

Modelling guided waves in acoustoelastic and complex waveguides: From SAFE theory to an open-source tool

Guided wave (GW)-based techniques have been extensively investigated and applied in material characterization, damage detection, and structural health monitoring. A comprehensive understanding of GW is the cornerstone for the development of such techniques. Based on the semi-analytical finite element (SAFE) method, an open-source dispersion calculator of GW propagating in acoustoelastic and complex waveguides with both isotropic and anisotropic material properties is developed. First, by assuming the simple harmonic motion along the propagation direction and discretizing along the thickness direction, 1D-GLL-SAFE (one-dimensional Gauss-Lobatto-Legendre SAFE) is adopted for the solution of GW in plate waveguide, which is attributed to its superior performance in terms of computational accuracy and efficiency. Different theories on acoustoelasticity are adopted to calculate GWs under loading. Then 2D-Gauss-SAFE (two-dimensional Gauss SAFE) with triangular meshes filling the cross section is adopted for GW in general waveguides considering the ease of convenience in meshing. Finally, based on the 1D-GLL-SAFE and 2D-Gauss-SAFE algorithms, an open-source tool SAFEDC (SAFE-based dispersion calculator) is developed, which not only provides the solution of GW in pre-stressed isotropic waveguide and general cross section, but also extends to GW in laminates with arbitrary layer stacking configurations and hybrid stacking including multiple materials. Most of the GW features, including phase velocity, group velocity, wave number, wave structure in terms of displacement, stress, and strain, and animation of wave propagation are all offered in SAFEDC, which helps the researchers and engineers to understand and utilize GW.

Arbitrarily rotated optical axis waveguide induced by a trimming line.

Rotated optical axis waveguides can facilitate on-chip arbitrary wave-plate operations, which are crucial tools for developing integrated universal quantum computing algorithms. In this paper, we propose a unique technique based on femtosecond laser direct writing technology to fabricate arbitrarily rotated optical axis waveguides. First, a circular isotropic main waveguide with a non-optical axis was fabricated using a beam shaping method. Thereafter, a trimming line was used to create an artificial stress field near the main waveguide to induce a rotated optical axis. Using this technique, we fabricated high-performance half- and quarter-wave plates. Subsequently, high-fidelity (97.1%) Pauli-X gate operation was demonstrated via quantum process tomography, which constitutes the basis for the full manipulation of on-chip polarization-encoded qubits. In the future, this work is expected to lead to new prospects for polarization-encoded information in photonic integrated circuits.

Applicability of the Effective Index Method for the Simulation of X-Cut LiNbO3 Waveguides

Photonic integrated circuits (PIC) find applications in the fields of microwaves, telecoms and sensing. Generally, PICs are fabricated on a base of isotropic materials such as SOI, Si3N4, etc. However, for some applications, anisotropic substrates such as LiNbO3 are used. A thin film of LiNbO3 on an insulator (LNOI) is a promising material platform for complex high-speed PICs. The design and simulation of PICs on anisotropic materials should be performed using rigorous numerical methods based on Maxwell’s equations. These methods are characterized by long calculation times for one simulation iteration. Since a large number of simulation iterations are performed during the PIC design, simulation methods based on approximations should be used. The effective index method (EIM) is an approximation-based method and is widely applied for simulations of isotropic waveguides. In this study, the applicability of EIM for simulations of anisotropic waveguides is analyzed. The results obtained by EIM are compared with the calculation results of a rigorous finite-difference frequency-domain (FDFD) method for evaluation of the EIM’s applicability limits. In addition, radiation losses in waveguides with rough sidewalls are estimated using the Payne–Lacey model and EIM. The results demonstrate the applicability of EIM for the simulation of anisotropic LNOI-based waveguides with cross-section parameters specified in this paper.

Consistent transmitting boundaries for time‐domain analyses of wave propagation in layered anisotropic waveguides

AbstractConsistent transmitting boundaries for time‐domain analyses of scalar‐ and elastic‐wave propagation in horizontally layered anisotropic or transversely isotropic waveguides are developed. Governing equations and corresponding consistent nodal forces are derived for scalar and elastic waves in layered waveguides for which finite‐element discretization is considered in the vertical layering direction. Auxiliary variables for the horizontal derivatives and integrals of displacements are introduced to modify the governing equations and the nodal forces. The desired consistent transmitting boundaries applicable to time‐domain analyses of scalar‐ and elastic‐wave propagation in isotropic and anisotropic waveguides are then derived. The transmitting boundary for a scalar wave satisfies the criteria for an accurate and well‐posed boundary condition and shows convergent, accurate, and stable behaviors for a variety of scalar‐wave propagation problems in waveguides. Although the boundary for an elastic wave is demonstrated as convergent and stable for elastic‐wave propagation problems in waveguides, limited accuracy is observed in the numerical examples. Nevertheless, the newly proposed approach is expected to provide another way to solve elastic‐wave propagation problems.

Abnormal Transmission of Elastic Waves through a Thin Ligament Connecting Two Planar Isotropic Waveguides

Abnormal Transmission of Elastic Waves through a Thin Ligament Connecting Two Planar Isotropic Waveguides

3D-Printable Piezoelectric Composite Sensors for Acoustically Adapted Guided Ultrasonic Wave Detection.

Commercially available photopolymer resins can be combined with lead zirconate titanate (PZT) micrometer size piezoelectric particles to form 3D-printable suspensions that solidify under UV light. This in turn makes it possible to realize various non-standard sensor geometries which might bring benefits, such as increased piezoelectric output in specific conditions and less interference with incoming waves due to better acoustical adaptation compared to solid PZT ceramics. However, it is unclear whether piezoelectric composite materials are suitable for guided ultrasonic wave (GUW) detection, which is crucial for structural health monitoring (SHM) in different applications. In this study, thin piezoelectric composite sensors are tape casted, solidified under UV light, covered with electrodes, polarized in a high electric field and adhesively bonded onto an isotropic aluminum waveguide. This approach helps to demonstrate the capabilities of tape casting’s freedom to manufacture geometrically differently shaped, thin piezoelectric composite sensors for GUW detection. In an experimental study, thin two-dimensional piezoelectric composite sensors demonstrate successful detection of GUW for frequency-thickness products of up to 0.5 MHz mm. An analytical calculation of the maximum and minimum amplitudes for the ratio of the wavelength and the sensor length in wave propagation direction shows good agreement with the sensor-recorded signals. The output of the piezoelectric composite sensors and occurring reflections as measure for wave interactions are compared to commercial piezoelectric discs to evaluate their performance.

Damage Imaging of Lamb Wave in Isotropic Plate Using Phased Array Delay and Sum Based on Frequency-domain Inverse Scattering Model

ABSTRACT Among many damage imaging methods based on Lamb wave, phased array Delay and Sum (DAS) has attracted much attention because of its high efficiency. However, inherent dispersion effect leads to the inaccurate acquisition of time-domain features, which affects imaging accuracy. The imaging index based on the amplitude of scattering wave ignores the interaction between Lamb wave and damage, which is difficult to reflect the physical characteristics of damage scattering, and further affects imaging accuracy. We use the physical characteristic parameter-reflectivity of the damage surface as the imaging index and establish an inverse scattering model of damage in frequency domain with dispersion relationship. The simulation and experiment results show that the DAS method combined with the frequency-domain inverse scattering model can realise the high-quality imaging of the damage in the isotropic waveguide structure.

Imaging damage in plate waveguides using frequency-domain multiple signal classification (F-MUSIC)

Earlier, an ameliorated MUSIC (Am-MUSIC) algorithm is developed by the authors [1], aimed at expanding conventional MUSIC algorithm from linear array-facilitated nondestructive evaluation to in situ health monitoring with a sparse sensor network. Yet, Am-MUSIC leaves a twofold issue to be improved: i) the signal representation equation is constructed at each pixel across the inspection region, incurring high computational cost; and ii) the algorithm is applicable to monochromatic excitation only, ignoring signal features scattered out of the excitation frequency band which also carry information on structural integrity. With this motivation, a multiple-damage-scattered wavefield model is developed, with which the signal representation equation is constructed in the frequency domain, avoiding computationally expensive pixel-based calculation - referred to as frequency-domain MUSIC (F-MUSIC). F-MUSIC quantifies the orthogonal attributes between the signal subspace and noise subspace inherent in signal representation equation, and generates a full spatial spectrum of the inspected sample to visualize damage. Modeling in the frequency domain endows F-MUSIC with the capacity to fuse rich information scattered in a broad band and therefore enhance imaging precision. Both simulation and experiment are performed to validate F-MUSIC when used for imaging single and multiple sites of damage in an isotropic plate waveguide with a sparse sensor network. Results accentuate that effectiveness of F-MUSIC is not limited by the quantity of damage, and imaging precision is not downgraded due to the use of a highly sparse sensor network - a challenging task for conventional MUSIC algorithm to fulfil.

Slab cholesteric waveguide with randomly fluctuating propagation constant

In this work, we present a stochastic theoretical analysis of an electromagnetic wave propagating inside a planar slab waveguide filled with a cholesteric material. In this system, the propagation constant of the wave is assumed to be a randomly fluctuating parameter. By means of the van Kampen systematic expansion method, Maxwell’s electromagnetic equations with random coefficients, and appropriate boundary conditions, are obtained. Numerical examples of the effects of the randomness on the propagating constant, on the ratio between magnetic and electric modes, on the field profiles, and on the energy flow are given. The results show that the stochastic waveguide can support multiple Transverse Magnetic (TM) or Transverse Electric (TE) modes with the same cutoff frequency, and furthermore, they support a distribution of electric and magnetic fields with phase shift. Our results are consistent with those of an isotropic waveguide.

Partial Energy Transfer Model of Lamb Waves Scattering in Materially Isotropic Waveguides

The scattering phenomena of the fundamental antisymmetric Lamb wave mode with a horizontal notch enabling the partial energy transfer (PET) option is addressed in this paper. The PET functionality for a given waveguide is realized using the material interface. The energy scattering coefficients are identified using two methods, namely, a hybrid approach, which utilizes the finite element method (FEM) and the general orthogonality relation, and the semi-analytical approach, which combines the modal expansion technique with the orthogonal property of Lamb waves. Using the stress and displacement continuity conditions on the present (sub)waveguide interfaces, one can explicitly derive the global scattering matrix, which allows detailed analysis of the scattering process across the considered interfaces. Both methods are then adopted on a simple representation of a surface breaking crack in the form of a vertical notch, of which a certain section enables not only the reflection of the incident energy, but also its nonzero transfer. The presented results show very good conformity between both utilized approaches, thus leading to further development of an alternative technique.

The role of adiabatic and non-adiabatic phenomena in passing waves from a semi-bounded loss-free waveguide to semi-bounded plasma waveguide

Thermal effects have been studied in phenomena of wave transportation from a loss-free isotropic cylindrical metallic waveguide to a semi-bounded warm plasma waveguide. The considered configuration consists of two semi-bounded waveguides which connected to each other. The first part is a dielectric waveguide with loss-free metallic wall and the second part is a cylindrical dielectric waveguide where a warm plasma column is placed on its symmetric axis. An incident wave in a single mode will be inserted from first part toward to second part via transversely anisotropic boundary surface. The incident wave is reflected and transmitted via interface surface of two waveguides. Taking into account the suitable boundary conditions on the interface surface of two waveguides and using warm approximation for the plasma column, the reflection and transmission coefficients of each new modes have been calculated. The reflection and transmission coefficients are function of the geometrical dimensions, the incident wave frequency and the temperature of the plasma. The diagrams of the reflection and transmission coefficients of the reflected and transmitted waves and phase difference of the reflected and transmitted waves respect to the incident wave, in term of the plasma temperature have been investigated.

Highly Sensitive Permittivity Sensor Using an Inhomogeneous Metamaterial Cylindrical Waveguide

Cylindrical waveguides filled with anisotropic metamaterials enable novel wave propagation phenomena. A nanoporous alumina microtube is a manifestation of such an anisotropic waveguide with an effective permittivity tensor (ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ≠ ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">φ</sub> = ε <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</sub> ). The metamaterial would be considered to be filled homogeneously or inhomogeneously depending on the variation of the size of the nanopores and density of the nanopores. The electromagnetic fields in such metamaterial waveguide are highly sensitive to the refractive index of the material embedded in the nanopores and the variation of the density of the inclusion in the radial direction due to the modal field distributions. We show that there is a large variation in the reflection coefficient (S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> ) of the inhomogeneously filled nanoporous waveguide with an embedded liquid with small variations in the material properties of the liquid. This variation in the S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> parameter can use to determine the purity of liquid. Our results show that the permittivity variations of the inclusion material can be monitored up to the sixth decimal places theoretically. The analysis also indicates that the inhomogeneous metamaterial waveguide is more sensitive compared to both the homogeneously filled metamaterial waveguide and an isotropic waveguide covered with metamaterial clad. This waveguide has potential applications in biomedical and chemical sensing applications.

Color‐ and Dimension‐Tunable Light‐Harvesting Organic Charge‐Transfer Alloys for Controllable Photon‐Transport Photonics

AbstractAn electron donor/acceptor pair comprising perylene (Pe) and 9,10‐dicyanoanthracene (DCA) was specifically designed to construct organic charge‐transfer (CT) alloys via weak CT interaction through a solution co‐assembly route. By adjusting the molar ratio between Pe and DCA, we achieve color‐ and dimension‐tunable CT alloy assemblies involving one‐dimensional (1D) (DCA)1−x(Pe)x (0 ≤ x ≤10 %) microribbons and two‐dimensional (2D) (Pe)1−y(DCA)y (0 ≤ y ≤5 %) nanosheets as a consequence of energy transfer from DCA or α‐Pe to Pe‐DCA CT complex. Importantly, dimension‐related optical waveguiding performances are also revealed: continuously adjustable optical loss in 1D (DCA)1−x(Pe)x microribbons and successive conversion from isotropic waveguide to anisotropic waveguide in 2D (Pe)1−y(DCA)y nanosheets. The present work provides a desired platform for in‐depth investigation of light‐harvesting organic CT alloy assemblies, which show promising applications in miniaturized optoelectronic devices.

Color- and Dimension-Tunable Light-Harvesting Organic Charge-Transfer Alloys for Controllable Photon-Transport Photonics.

An electron donor/acceptor pair comprising perylene (Pe) and 9,10-dicyanoanthracene (DCA) was specifically designed to construct organic charge-transfer (CT) alloys via weak CT interaction through a solution co-assembly route. By adjusting the molar ratio between Pe and DCA, we achieve color- and dimension-tunable CT alloy assemblies involving one-dimensional (1D) (DCA)1-x (Pe)x (0 ≤ x ≤10 %) microribbons and two-dimensional (2D) (Pe)1-y (DCA)y (0 ≤ y ≤5 %) nanosheets as a consequence of energy transfer from DCA or α-Pe to Pe-DCA CT complex. Importantly, dimension-related optical waveguiding performances are also revealed: continuously adjustable optical loss in 1D (DCA)1-x (Pe)x microribbons and successive conversion from isotropic waveguide to anisotropic waveguide in 2D (Pe)1-y (DCA)y nanosheets. The present work provides a desired platform for in-depth investigation of light-harvesting organic CT alloy assemblies, which show promising applications in miniaturized optoelectronic devices.

In-plane backward and zero group velocity guided modes in rigid and soft strips.

Elastic waves guided along bars of rectangular cross sections exhibit complex dispersion. This paper studies in-plane modes propagating at low frequencies in thin isotropic rectangular waveguides through experiments and numerical simulations. These modes result from the coupling at the edge between the first order shear horizontal mode SH0 of phase velocity equal to the shear velocity VT and the first order symmetrical Lamb mode S0 of phase velocity equal to the plate velocity VP. In the low frequency domain, the dispersion curves of these modes are close to those of Lamb modes propagating in plates of bulk wave velocities VP and VT. The dispersion curves of backward modes and the associated zero group velocity (ZGV) resonances are measured in a metal tape using noncontact laser ultrasonic techniques. Numerical calculations of in-plane modes in a soft ribbon of Poisson's ratio ν≈0.5 confirm that, due to very low shear velocity, backward waves and ZGV modes exist at frequencies that are hundreds of times lower than ZGV resonances in metal tapes of the same geometry. The results are compared to theoretical dispersion curves calculated using the method provided in Krushynska and Meleshko [J. Acoust. Soc. Am. 129, 1324-1335 (2011)].

Electromagnetic energy rotation along plasma-dielectric interface caused by azimuthal surface waves in isotropic cylindrical metallic waveguide

Electromagnetic energy rotation around the axis of cylindrical metallic waveguides partially filled by isotropic plasma is studied. Angular phase velocity and angular velocity of energy transfer are analyzed as functions of the plasma waveguide parameters: plasma column radius, plasma particle density, azimuthal wavenumber, dielectric layer width and dielectric constant, and collision frequency. This study generalizes the results obtained earlier in the case of the wave propagation in two-component plasma-metal structures (cylindrical metallic waveguides entirely filled by magnetoactive plasma) to the case of three-component plasma-dielectric-metal structures.

The mode generation due to the wave transmission phenomena from a loss free isotropic cylindrical metallic waveguide to the semi-bounded plasma waveguide

ABSTRACT Using the suitable boundary conditions, the problem of wave transmission from a loss free isotropic cylindrical metallic waveguide to a semi-bounded plasma waveguide has been analyzed. The considered configuration consists of two semi-bounded waveguides with different configurations. The first part of the waveguide system is a semi-bounded cylindrical waveguide with metallic wall, which is filled with a dielectric. The second part of the waveguide system is a semi-bounded dielectric waveguide with a plasma rod. An electromagnetic wave in a single mode has been considered to arrive from part one to part two of the waveguide system. Taking into account the boundary conditions on the interface surface of two regions, the reflection and the transmission coefficients have been calculated for each new modes of the reflected and the transmitted waves. Since the plasma is time dispersive, the reflection and transmission coefficients depend on the wave frequency. Therefore, the reflected and transmitted waves in each mode have a phase difference with respect to the incident wave.

Waves in a Plane Rectangular Lattice of Thin Elastic Waveguides

We study the spectrum of a thin (with the relative width h ≪ 1) rectangular lattice of elastic isotropic (with the Lame constants ⋋ ≥ 0 and μ > 0) plane waveguides simulating joining seams of a doubly periodic system of identical absolutely rigid tiles. We establish that the low-frequency range of the essential spectrum contains two spectral bands (passing ones for waves) of length O(e−δ/(2h)), δ > 0. Above these bands there is a gap of width O(h−2) (stopping zones for waves) and then, in the mid-frequency range, above the cut-off value μπ2h−2 of the continuous spectrum of the infinite cross-shaped waveguide, there is a family of spectral bands of length O(h); moreover, between some of these bands there are opened up gaps of width O(1). The character of the wave propagation depends on whether the frequencies are below or above the cut-off value. In the first case, the oscillations are strictly concentrated near the lattice nodes and the edges are practically immovable. In the second case, the oscillations are localized on the lattice edges, i.e., the nodes are left at relative rest. We show that single perturbations of nodes or edges can cause the appearance of points of the discrete spectrum under the essential spectrum or inside the gaps; moreover, an infinite collection of identical perturbations of nodes can also change the essential spectrum. Bibliography: 78 titles. Illustrations: 5 figures.