Waveguide Of Arbitrary Cross Section Research Articles

High-Precision Calculation Using the Method of Analytical Regularization for the Cut-Off Wave Numbers for Waveguides of Arbitrary Cross Sections with Inner Conductors

A method for the accurate calculation of the cut-off wavenumbers of a waveguide with an arbitrary cross section and a number of inner conductors is demonstrated. Concepts of integral and infinite-matrix (summation) operator-valued functions depending nonlinearly on the frequency spectral parameter provide a secure basis for formulating the spectral problem, and the Method of Analytical Regularization is employed to implement an effective algorithm. The algorithm is based on a mathematically rigorous solution of the homogeneous Dirichlet problem for the Helmholtz equation in the interior of the waveguide, excluding the regions occupied by the inner conductor boundaries. A highly efficient method of calculating the cut-off wavenumbers and the corresponding non-trivial solutions representing the modal distribution is developed. The mathematical correctness of the problem statement, the method, and the ability to calculate the cut-off wavenumbers with any prescribed and proven accuracy provide a secure basis for treating these as “benchmark solutions”. In this paper, we use this new approach to validate previously obtained results against our benchmark solutions. Furthermore, we demonstrate its universality in solving some new problems, which are barely accessible by existing methods.

The role of evanescent modes in global-local analysis of ultrasonic guided waves in plates with varying local zone-scatterer relations

In order to provide a reliable and robust SHM performance, Ultrasonic Guided Waves (UGWs) need to be analyzed and understood. Numerical modeling of UGW propagation and scattering by hybrid methods offers the possibility of simulating UGW interaction with waveguides of arbitrary cross-sections and discontinuities. Maximizing the accuracy of such methods is important to perform quantitative SHM, while maintaining minimum computational cost. This work investigates the role of evanescent modes in the numerical analysis of UGWs in aluminum and composite plates with defects, by the hybrid Global-Local method. The complex solutions to the UGW eigenvalue problem are found and the scattering spectra for A0 and S0 incident modes are calculated. The accuracy of the numerical solution is then studied by computing the error in terms of energy balance. Parametric studies with respect to the local zone size, defect dimensions and shape are conducted including and excluding evanescent modes in the analysis. Considerations are provided to obtain a solution with error no greater than 5%, in terms of varying local zone – scatterer relations within plate waveguides.

Transverse components of the electromagnetic field in a waveguide with modulated in space and in time magnetodielectric filling

The propagation of transverse magnetic (TM) and transverse electric (TE) electromagnetic waves in a regular ideal waveguide of arbitrary cross section is considered. It is assumed that the permittivity and permeability of the magnetodielectric filling of the waveguide are functions that depend on the coordinate and time. Analytical expressions for the transverse components of the magnetic and electric vectors of the TM- and TE-fields in the waveguide are obtained from the system of Maxwell equations. They are expressed in terms of the longitudinal components of the electric and magnetic vectors, which describe the transverse magnetic and transverse electric fields in the waveguide. For the above longitudinal components of the electric and magnetic vectors, the wave equations are given, which are also obtained from the system of Maxwell's equations. Keywords: Maxwell equations, propagation of electromagnetic waves, waveguide with modulated filling, transverse components, Helmholtz equations, Dirichlet and Neumann problems.

Complex TE-modes in Slotted Waveguides of Arbitrary Cross Section

Implementation of the rigorous Analytical Regularization Method is presented for plane wave scattering by arbitrary two-dimensional cavities with longitudinal slit. The general solution of the Neumann boundary value problem for Helmholtz equation is obtained in a form of two coupled infinite systems of linear algebraic equations of the second kind. Compactness of the matrix operator provides efficient numerical solution of the joint system by truncation method. Fast convergence of the truncated system of linear algebraic equations makes this method an effective instrument for accurate analysis of spectral and diffraction problems. Considering the homogeneous version of equations and finding the complex roots of their determinants, we calculate the complex eigenvalues of complex oscillations. Employing spline interpolation and mollifier function the problem geometry is generalized.

Mathematical Theory of Surface Waves in a Lossy Inhomogeneous Dielectric Waveguide of Arbitrary Cross Section

Mathematical Theory of Surface Waves in a Lossy Inhomogeneous Dielectric Waveguide of Arbitrary Cross Section

Normal Waves in an Open Anisotropic Regular Waveguide of Arbitrary Cross Section

Normal Waves in an Open Anisotropic Regular Waveguide of Arbitrary Cross Section

Метод операторных пучков и оператор-функций в задаче о нормальных волнах закрытого регулярного неоднородного диэлектрического волновода произвольного сечения

Метод операторных пучков и оператор-функций в задаче о нормальных волнах закрытого регулярного неоднородного диэлектрического волновода произвольного сечения

Wave propagation in waveguides with graded plasmonic obstacles

In this paper, wave propagation in a hollow waveguide with a graded dielectric layer is studied. Analytic formulas are derived for the electric field components as well as general analytical results for the reflection and transmission coefficients for propagating waves. These results are all valid for waveguides of arbitrary cross sections, and the derived reflection and transmission coefficients are in exact asymptotic agreement with those obtained for a very thin homogeneous dielectric layer using cascading and mode-matching techniques. Furthermore, the power transmission, reflection, and absorption coefficients, as functions of frequency and layer width, are studied, showing the expected behavior of these parameters. The method proposed in this paper gives directly applicable results that do not require cascading and mode matching, while at the same time having the ability to model smooth transitions that are more realistic in several applications.

Numerical‐analytical method for determining the dielectric constant of 1D inhomogeneous plate in a waveguide

The inverse diffraction problem is considered for a layered dielectric plate in a metal waveguide of arbitrary cross-section. The proposed solution is based on the Cauchy problem for the Riccati equation. Based on this solution, algorithm and code are developed for the dielectric permittivity profile reconstruction. The measured and mathematically simulated values of the complex reflection coefficient at finite number of frequencies are used as input data. Reconstructed dielectric permittivity profiles for layered plates are in good agreement with measured ones.

The Effects of Stress on Second Harmonics in Plate-Like Structures

Cumulative second harmonic of ultrasonic guided waves is considered to have great application potential in evaluating internal stress of structures. One difficulty with the application is the diversity and complexity of modal response to the stress change in waveguide. At present, there is a lack of relevant theoretical studies and experimental results to guide the applications. In this article, a method is proposed to characterize the amplitude change of cumulative second harmonic mode in a plate under stress through calculating the amplitude coefficient, which can be acquired based on mode shape analysis. The steel plate is taken as an example to demonstrate the analysis method. Experimental studies are presented with results consistent with the theoretical predictions. The results of this study indicate that the amplitudes of different cumulative second harmonic modes may increase or decrease monotonically with the change of stress. Therefore, when the phenomenon of modes mixing occurs in the waveguide, it is necessary to analyze and predict the amplitude of selected cumulative second harmonic mode with the change of stress in advance; otherwise, wrong results may be obtained. The method and conclusions proposed in this paper can also be applicable to waveguide of arbitrary cross-section and have universality.

MATHEMATICAL THEORY OF NORMAL WAVES IN AN OPEN METAL-DIELECTRIC REGULAR WAVEGUIDE OF ARBITRARY CROSS SECTION

The problem of normal waves in an open metal-dielectric regular waveguide of arbitrary cross-section is considered. This problem is reduced to the boundary eigenvalue problem for longitudinal components of electromagnetic field in Sobolev spaces. To find the solution, we use the variational formulation of the problem. The variational problem is reduced to study of an operator-function. Discreteness of the spectrum is proved and distribution of the characteristic numbers of the operatorfunction on the complex plane is found.

Calculation of wave dispersion curves in multilayered composites using semi-analytical finite element method

The enormous potential of Guided waves have a significant use for non-destructive evaluation(NDE) and structural health monitoring(SHM). It is common to use different solution approaches to predict dispersion curves depending on the material type, isotropic, transversely isotropic, or orthotropic, of the medium in which the wave propagates, shape of the waveguide, etc. Inability to model waveguides of arbitrary cross-section by existing matrix methods has led to development of Semi-Analytical Finite Element(SAFE) Method. In this study, rapid and accurate prediction of the propagation characteristics for guided waves in a wide range of structures has been performed by implementation of SAFE method. Damped and undamped waveguides of different shapes can be modelled. Wave propagation characteristics in both isotropic and anisotropic composite structures can also be studied. To benchmark the solution, a case study using Transfer Matrix Method (TMM) for composite plate has been evaluated. It was found that the element discretizaton plays an important role in accurate prediction of modes in SAFE method, neglecting which leads to loss of higher order modes.

Finite Element Analysis of Stimulated Brillouin Scattering in Integrated Photonic Waveguides

We describe a finite element algorithm for modeling stimulated Brillouin scattering in optical waveguides of arbitrary cross-section. The method allows rapid calculation of optical and elastic dispersion relations, field profiles, and gain. Additionally, we provide an open and extensible set of standard problems and reference materials to facilitate the bench-marking of our solver against subsequent tools. Such a resource is needed to help settle discrepancies between existing formulations and implementations, and to facilitate comparison between results in the literature. The resulting standardized testing framework will allow the community to gain confidence in new algorithms and will provide a common tool for the comparison of experimental designs of opto-acoustic waveguides.

Eigenwaves in a lossy metal-dielectric waveguide

ABSTRACTThe problem of normal waves in a closed (shielded) regular waveguide of arbitrary cross-section is considered. This problem is reduced to the boundary eigenvalue problem for longitudinal components of electromagnetic field in Sobolev spaces. To find the solution, we use the variational formulation of the problem. The variational problem is reduced to study an operator-function. Discreteness of the spectrum is proved and distribution of the characteristic numbers of the operator-function on the complex plane is found. We also consider properties of system of eigenvectors and associated vectors of the operator-function. Double completeness of system of eigenvectors and associated vectors with a finite defect is established.

Investigation of the Spectrum of the Problem of Normal Waves in a Closed Regular Inhomogeneous Dielectric Waveguide of Arbitrary Cross Section

The problem of normal waves in a closed (screened) regular waveguide of arbitrary cross section is considered. It is reduced to a boundary value problem for the longitudinal components of the electromagnetic field in Sobolev spaces. The solutions are defined using the variational formulation of the problem. The problem is reduced to the study of an operator function. The properties of the operators involved in the operator function (which are necessary for analyzing its spectral properties) are examined. Theorems are proved concerning the discrete character of the spectrum and the distribution of characteristic numbers of the operator function on the complex plane. The completeness of the system of eigen- and associated vectors of the operator function is investigated. It is proved that the system of eigen- and associated vectors of the operator function is doubly complete with a finite defect.

Semi-analytical discontinuous Galerkin finite element method for the calculation of dispersion properties of guided waves in plates.

The development of reliable guided waves inspection systems is conditioned by an accurate knowledge of their dispersive properties. The semi-analytical finite element method has been proven to be very practical for modeling wave propagation in arbitrary cross-section waveguides. However, when it comes to computations on complex geometries to a given accuracy, it still has a major drawback: the high consumption of resources. Recently, discontinuous Galerkin finite element method (DG-FEM) has been found advantageous over the standard finite element method when applied as well in the frequency domain. In this work, a high-order method for the computation of Lamb mode characteristics in plates is proposed. The problem is discretised using a class of DG-FEM, namely, the interior penalty methods family. The analytical validation is performed through the homogeneous isotropic case with traction-free boundary conditions. Afterwards, functionally graded material plates are analysed and a numerical example is presented. It was found that the obtained results are in good agreement with those found in the literature.

Acoustic Waveguide Eigenmode Solver Based on a Staggered-Grid Finite-Difference Method

A numerical method of solving for the elastic wave eigenmodes in acoustic waveguides of arbitrary cross-section is presented. Operating under the assumptions of linear, isotropic materials, it utilizes a finite-difference method on a staggered grid to solve for the acoustic eigenmodes (field and frequency) of the vector-field elastic wave equation with a given propagation constant. Free, fixed, symmetry, and anti-symmetry boundary conditions are implemented, enabling efficient simulation of acoustic structures with geometrical symmetries and terminations. Perfectly matched layers are also implemented, allowing for the simulation of radiative (leaky) modes. The method is analogous to that in eigenmode solvers ubiquitously employed in electromagnetics to find waveguide modes, and enables design of acoustic waveguides as well as seamless integration with electromagnetic solvers for optomechanical device design. The accuracy of the solver is demonstrated by calculating eigenfrequencies and mode shapes for common acoustic modes across four orders of magnitude in frequency in several simple geometries and comparing the results to analytical solutions where available or to numerical solvers based on more computationally expensive methods. The solver is utilized to demonstrate a novel type of leaky-guided acoustic wave that couples simultaneously to two independent radiation channels (directions) with different polarizations – a ‘bi-leaky’ mode.

New method of calculating the wakefields of a point charge in a waveguide of arbitrary cross section

Recently, a new method for calculating the Cherenkov field acting on a point-like electron bunch passing through longitudinally homogeneous structures lined with arbitrary slowdown layers was proposed, where the formalism was obtained though consideration of a general integral relation that allows calculation of the fields at the vicinity of a point-like bunch. It demonstrates that the Cherenkov field at the point of the short relativistic bunch does not depend on the waveguide system material and is a constant for any given transverse dimensions and cross-section shapes of waveguides. With this paper we present a strict derivation of the fields formulas valid at the cross-section of a bunch on the basis of a conformal mapping method. We generalize the results of the previous paper to the case of transversely distributed bunch by deriving a two-dimensional Green function at the cross-section of a bunch. Comparison of the results proving validity of the method is given in the appendix.

Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perfectly matched layer methods

Among the numerous techniques of non-destructive evaluation, elastic guided waves are of particular interest to evaluate defects inside industrial and civil elongated structures owing to their ability to propagate over long distances. However for guiding structures buried in large solid media, waves can be strongly attenuated along the guide axis due to the energy radiation into the surrounding medium, usually considered as unbounded. Hence, searching the less attenuated modes becomes necessary in order to maximize the inspection distance. In the numerical modeling of embedded waveguides, the main difficulty is to account for the unbounded section. This paper presents a numerical approach combining a semi-analytical finite element method and a perfectly matched layer (PML) technique to compute the so-called trapped and leaky modes in three-dimensional embedded elastic waveguides of arbitrary cross-section. Two kinds of PML, namely the Cartesian PML and the radial PML, are considered. In order to understand the various spectral objects obtained by the method, the PML parameters effects upon the eigenvalue spectrum are highlighted through analytical studies and numerical experiments. Then, dispersion curves are computed for test cases taken from the literature in order to validate the approach.

Semi-analytical FEM Analysis and Experimental Measurement for Propagating Guided Waves Modes in Rail

Acoustical guided waves modal analysis in rail is the basis of long distance guided wave inspection and rail vibration and noises control. In particular the various propagating guided waves in the rail are identified in terms of their propagation wavenumber coefficients and their corresponding deformed shapes. The semi-analytical finite element method is used to formulate the governing equation for guided waves propagating in elastic waveguides of arbitrary cross-section on the basis of the virtual work principle, wavenumber dispersion curves and deformed shapes are extracted by solving governing equation, which provide the basis for selecting mode and frequency during application. The propagating guided waves wavenumber dispersion curves and deformed shaped under 0-8 k Hz frequency range for CHN60 type free rail are obtained using semi-analytical finite element method, and the characteristics of the eight based guided waves mode in rail are discussed. Instrumented hammer experimental study and modal analysis using sever vibration accelerometers mounted on rail are carried out to verify the vertically vibrating mode and horizontally vibrating mode guided waves wavenumber dispersion coefficient. Modeling and experimental investigations of lateral and vertical excitation in railhead shows that good agreement between numerical calculation and experiment.