Arbitrary Number Of Layers Research Articles

Analysis of Uniaxial Multilayer Cylinders Used for Invisible Cloak Realization

Uniaxial multilayer cylinder cloaks have recently been proposed to prevent scattering of electromagnetic waves. These cloaks are based on spatial variation of constitutive parameters within the structure by means of metamaterials. A mathematical description of invisibility in such cloaks is provided. The analysis approach is based on modal analysis of cylindrical multilayer structures. In order to analyze structures with arbitrary number of layers, an algorithm to calculate spectral-domain Green's functions of uniaxial multilayer structures has been developed. The results show that the recently introduced metamaterial cloaks with reduced variation of constitutive parameters can decrease the total scattering width up to a factor of three, but only in a narrow frequency band due to dispersion in the filling material. Furthermore, it is shown that in the analyzed structures already 6 layers of constant permittivity and permeability approximate well the continuous dependence of constitutive parameters.

Multimodal Solution for a Waveguide Radiating Into Multilayered Structures—Dielectric Property and Thickness Evaluation

Open-ended rectangular waveguides are widely used for microwave and millimeter-wave nondestructive testing (NDT) applications, such as detecting disbond and delamination in multilayered composite structures, thickness evaluation of dielectric sheets and coatings on metal substrates, etc. When inspecting a complex multilayered composite structure that is made of generally lossy dielectric layers with arbitrary thicknesses and backing, the dielectric properties of a particular layer may be of particular interest (e.g., radome inspection). The same is also true when one is interested in the thickness, or, more importantly, thickness variation, of a particular layer within such complex structures. An essential tool for closely estimating the complex permittivity and/or thickness is an accurate forward electromagnetic model for simulating the reflection coefficient at the aperture of the probing open-ended waveguide. To this end, this paper provides a full-wave accurate forward model for calculating the reflection coefficient from a generally lossy multilayered composite structure possessing an arbitrary number of layers and respective thicknesses while accounting for the influence of higher order modes. This model is subsequently validated through comparisons with a commercial numerical tool and actual measurements. Furthermore, a measurement model is provided, which results in an iterative inverse technique for estimating the complex permittivity and thickness of a dielectric layer. Subsequently, this technique is applied to the measured reflection coefficients of several structures. To evaluate the accuracy of this technique, an analysis on its sensitivity to various sources of errors, and, most importantly, the effect of a finite flange size, is also demonstrated by using the simulated data. Finally, the potential of this model to accurately estimate the thickness of an individual layer, which represents a thin disbond, in a multilayered composite structure is presented.

Analyses of steady-state interface fracture of elastic multilayered beams under four-point bending

The closed-form solution for the steady-state interface energy release rate of elastic multilayered beams subjected to four-point bending is presented. The beam can have an arbitrary number of layers and fracture can occur at any interface. Specific results are calculated for alternate layered systems to elucidate the essential trends of the dependences of the normalized steady-state interface energy release rate on the thickness ratio and the modulus ratio for each interface.

Acoustical scattering by radially stratified scatterers

A recursive solution procedure is developed to analyze the acoustical scattering by multilayer concentric circular cylindrical scatterers. The procedure is based on multiple scattering in the single-scatterer methodology originally proposed by one of the authors. The solution for a scatterer having an arbitrary number of layers is solved by recursively using the solution for a dual-layer scatterer. The solution procedure and its implementation are extensively validated. Computational characteristics, including potential pitfalls and their avoidance, are explored. The solution procedure can be used to analyze scatterers with continuously varying properties in the radial direction by approximating such a scatterer as a multilayer system. A comprehensive numerical example shows an interesting phenomenon: when a planar wave impinges onto a cooling tube in air, instead of forming a shadow zone, a strongly collimated beam is formed behind the cooling tube. This phenomenon can be explained as due to the gradient-index acoustical lens that is created around the cooling tube, which bends the sound and collimates it in the forward direction.

Coulomb scattering in high-κ gate stack silicon-on-insulator metal-oxide-semiconductor field effect transistors

A new model for calculating Coulomb perturbation potentials in bidimensional semiconductor structures is proposed. The main advantage of this model is that it can be applied for an arbitrary number of layers with different permittivities. As an example of how it could be used, we studied the influence on Coulomb scattering of high-κ materials used as gate insulators in silicon-on-insulator structures. This study was carried out with insulators of different physical and effective oxide thicknesses. The results show that when a silicon dioxide is replaced by a high-κ dielectric with the same thickness, Coulomb scattering is reduced. However, the strength of this beneficial effect might be diminished in actual devices for two reasons. The first is that an interfacial layer of silicon dioxide is usually placed between the silicon slab and the high-κ dielectric, lessening its influence. Second, a gate high-κ dielectric is normally wider than its silicon dioxide counterpart. As a consequence, the metal or polysilicon gate is further from the silicon channel, and its beneficial screening effect on the perturbation charges is then reduced. Both these effects on Coulomb scattering were examined in this study.

A Numerical Scheme to Model Current and Voltage Excitation of Organic Light-Emitting Diodes

We present a method to model organic light-emitting devices driven by a current source in the context of drift-diffusion models. The method is extended to the case of voltage excitation, and calculations with current and voltage excitation are compared. An advantage over the application of Poisson's equation is that standard numerical solvers can be used for the ordinary differential equations that result from the spatial discretization of the model equations. We employ the model to calculate I- V characteristics and to examine the transient response of an organic light-emitting diode under pulsed current operation. The approach is generalized to the case of an arbitrary number of layers.

Transmission of Magnetic Fields in Three-Dimensional Multilayered Structures

We have extended an earlier two-dimensional (2-D) analysis to provide a relatively simple approach to calculating the transmission of magnetic fields in three-dimensional (3-D) multilayered structures. The approach accommodates complex structures composed of an arbitrary number of layers, each of which may have an arbitrary magnetization direction and anisotropic permeability. The procedure relies on an initial transformation into the 2-D spatial frequency domain and then the use of transmission matrices to relate the fields in the different layers. The approach is general in that it provides a method for finding the field configuration for any set of 3-D magnetic sources embedded in a layered magnetic structure with a linear B-H relationship. In this paper, we concentrate on the analytical formulation and we illustrate the method by using it to determine both the external and internal fields of some relatively simple finite 3-D geometric shapes. We also derive new 3-D expressions for the flux density at the surface of a multilayered magnetic recording medium. In a companion paper, the procedure is applied to examine readback responses for a variety of 3-D magnetic recording configurations.

Readback Responses in Three Dimensions for Multilayered Recording Media Configurations

We have applied a technique for modeling the transmission of three-dimensional (3D) magnetic fields through an arbitrary number of layers of a layered structure to the specific case of a recording medium in order to study and explain the readback response for a variety of perpendicular recording configurations. We examine in particular the low-frequency response associated with flux-flow in the soft underlayer and the behavior of the main response for finite read and write widths. Our work leads to a useful analytic approximation for the 3D on-track readback response.

Fast Computation of Layered Medium Green's Functions of Multilayers and Lossy Media Using Fast All-Modes Method and Numerical Modified Steepest Descent Path Method

A fast and accurate approach, based on the fast all-modes method (FAM) and the numerical modified steepest descent path method (NMSP), was previously used to calculate the spatial Green's function for a single-layer lossless dielectric medium over a perfect electric conductor. This paper successfully extends that approach to two new cases. The first is the multilayer case where the medium has an arbitrary number of layers. The second is lossy media over an imperfect conductor. The FAM locates all modes accurately on the complex plane. The modes include surface wave modes, leaky wave modes, and improper modes. For a typical six-layer case over a ground plane, the FAM requires only 2.265 s of pre-processing that includes computing 200 mode locations by using a P4 3.2-GHz PC with Matlab. The NMSP is then used to evaluate the steepest descent path integral. Accuracy within 0.2% is achieved in comparison with the benchmark calculations. Within this context of accuracy, the total CPU per distance point is less than 7.6 ms for distances larger than 0.02 free-space wavelength and is less than 2.7 ms for distances larger than two free-space wavelengths. This method is shown to be fast and accurate, even for large-distance interactions in the multilayer and lossy media.

On the Resonance and Radiation Characteristics of Multi-Layered Spherical Microstrip Antennas

The resonance and radiation characteristics of a spherical microstrip with its circular metallic patch located inside a coating, possessing an arbitrary number of layers, are investigated. The developed methodology combines the Legendre transform with a T-matrix method. The appropriate basis functions for the surface current on the patch are chosen according to the cavity model. The complex resonant frequencies are the singular points of a homogeneous linear system, resulting by following a Galerkin's technique. The numerical results of this article propose novel multi-layered spherical microstrip configurations. More precisely, a new type of excitation that concerns an amplifying layer located between core and patch is proposed. The control mechanism of the amplifying capability via the layer's thickness and dielectric constant is reported. Moreover, the behavior of a microstrip with two airgaps that are surrounded by a zero-index material is analyzed. Finally, a coating's continuous distribution, following a “shifted” Luneburg law, is treated by a step approximation of the radial function of its dielectric constant, and the achieved high quality factor of such a microstrip is discussed.

A computer model to study the properties of guided waves

The author's research group has a specialist interest in developing guided wave techniques for the Non Destructive Testing (NDT) of structures. Guided waves travel along the structure and so can be used to inspect large lengths or areas very much faster then the traditional point‐by‐point ultrasonic methods. The development of these inspection methods requires careful study and understanding of the properties of the guided waves. To address this need, the author's team has created a general purpose modelling tool. This can model waves in waveguides consiting of an arbitrary number of layers which can be flat or cylindrical, elastic or damped, isotropic or anisotropic solids, or perfect or viscous fluids, and can be immersed in a fluid or embedded in a solid. The primary output of the program is the dispersion curves, that is the frequency‐velocity relationships of any modes which could travel in the structure. The program also predicts the attenuation of the modes, caused by leakage into surrounding materials or by material damping, and the mode shapes The presentation will explain the basis of the modelling tool and illustrate the way in which it can be used to understand the guided waves.

On energy levels of a particle in a comblike structure

Previously, two similar one-dimensional problems have been considered [1‐4] concerning the eigenvalues of the effective refractive index of a multilayer waveguide and the energy eigenvalues of a quantum particle in a piecewise constant potential field. In these problems, the main attention is focused on an equation that determines the eigenvalues of the indicated parameters for an arbitrary number of layers (in the first problem) and of the segments of constant potential (which are also considered as layers) in the second case. The form of this equation was guessed by the author during the calculation of multilayer waveguides, which was performed under the guidance of A.A. Ma œ er. This equation is referred to as the “multilayer” equation, since it is obtained by equating to zero the so-called multilayer function, which depends on the energy E of a particle. The outer layers of the layered structures under consideration are assumed to be infinite. If the total number of layers (including the unbounded outer layers) is n , the multilayer function F j ( E ) and, consequently, the multilayer equation for the same layered structure can be written in n ‐ 2 ways. Each of these ways corresponds to the choice of a distinguished j th layer of a finite width. For certainty, let us concentrate below on the second problem, that is, the problem of energy eigenvalues of a particle in a multilayer structure. In the case of three layers, the multilayer equation reduces to the well-known equation [5] for energy eigenvalues of a particle in a square potential well. In the case of a greater number of layers, the results obtained with the use of the multilayer equation are in complete agreement with the data obtained using numerical methods. Note also that the multilayer equation can be used not only in the problem under consideration, but also in other problems and situations as was done, for example, in [6]. Our method of determining the number of eigenvalues can also be extended to these

Comment on ‘Electronic minibands in complex basis superlattices: a numerically stablecalculation’

Hsueh, Lin and Chen (HLC) (2007 J. Phys.: Condens. Matter 19 266007) present a graphtheory-based derivation of a stable method for determining the energy minibands ofsuperlattices with an arbitrary number of layers per unit cell. Here it is shown that theabove result is immediately derivable from the transfer matrix formalism by factoring out asingle cosine function per layer.

Reflection and transmission of weakly inhomogeneous anisotropic and bianisotropic layers calculated by perturbation method

With the use of perturbation theory the zero- and higher-order approximations are obtained for characteristic matrices, reflection and transmission operators, scalar reflectance and transmittance of monochromatic electromagnetic waves impinging on a transparent weakly inhomogeneous stratified bianisotropic medium. The proposed procedure of perturbation series formation enables finding the corrections to the reflection and transmission factors in closed form for specified coordinate dependencies for the material tensors of the bianisotropic layers. The general expressions obtained are applied to calculate the first-order corrections for normal incident light on (i) a twisted uniaxial slab, (ii) an isotropic medium with arbitrary inhomogeneity profile and (iii) a one-dimensional photonic crystal with arbitrary number of layers. Exact and approximate solutions of the wave equations are numerically compared.

Pattern instability of functionally graded and layered elastic films under van der Waals forces

This paper investigates surface instability of a functionally graded and layered elastic film interacting with another flat rigid body [or interacting with another functionally graded and layered elastic film (or simply-supported elastic plate)] through surface van der Waals forces under plane strain conditions. The shear modulus in each functionally graded layer is assumed to be exponentially varied in the thickness direction. A homogeneous elastic layer, which is the focus of this research, can be considered as a special case of the functionally graded layer by taking the magnitude of the gradient parameter to be very small. The solution for any functionally graded layer is obtained in terms of the pseudo-Stroh formalism; then the solution for the multilayered system is derived based on the transfer-matrix method. As a result the displacement and traction vectors at the top surface of the layered film (or plate) can be expressed in terms of those at the bottom surface of the layered film (or plate). We can thus obtain simple relationships between the surface normal traction and surface deflection. Expressions for the interaction coefficient as a function of the wave number of the instability mode are therefore obtained. The critical value of the interaction coefficient for surface instability and the associated instability mode can be determined easily by identifying the minimum of the interaction coefficient. An advantage of the present method lies in that it is very convenient to address a film (or a plate) with an arbitrary number of layers. The correctness of the present approach is verified by comparison with known results. The results show that it is possible to find N distinct surface instability modes for an N-layered elastic film interacting with another flat rigid body; and that it is also possible to find that there are at most N1+N2 distinct surface instability modes for an N1-layered elastic film interacting with another N2-layered elastic film. When a multilayered elastic film interacts with a simply-supported multilayered elastic plate, the film-plate system will exhibit the instability mode of the film or that of the plate depending on the stability strength of the plate versus that of the film.

Role of radial nonuniformities in the interaction of an intense laser with atomic clusters

A model for the interaction of an intense laser with atomic clusters is presented. The model takes into account the spatial nonuniformities of the cluster as it evolves in time. The cluster is treated as a stratified sphere having an arbitrary number of layers. Electric and magnetic fields are obtained by solving the vector Helmholtz equation coupled with one-dimensional Lagrangian hydrodynamics. Results are compared with the uniform density nanoplasma model. Enhancement in the amount of energy absorbed is seen over the uniform density model. In some cases the absorbed energy increases by as much as a factor of 40.

Recursive algorithm and accurate computation of dyadic Green’s functions for stratified uniaxial anisotropic media

A recursive algorithm is adopted for the computation of dyadic Green’s functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing the coefficients of the Sommerfeld integrals are obtained according to the continuity condition of electric and magnetic fields across the interface between different layers, which are in correspondence with the TM wave produced by a vertical unit electric dipole and the TE or TM wave produced by a horizontal unit electric dipole, respectively. All the linear equation groups can be solved via the recursive algorithm. The dyadic Green’s functions with source point and field point being in any layer can be conveniently obtained by merely changing the position of the elements within the source term of the linear equation groups. The problem of singularities occurring in the Sommerfeld integrals is efficiently solved by deforming the integration path in the complex plane. The expression of the dyadic Green’s functions provided by this paper is terse in form and is easy to be programmed, and it does not overflow. Theoretical analysis and numerical examples show the accuracy and effectivity of the algorithm.

Balancing waveform relaxation for age-structured populations in a multilayer environment

In this paper we present a balancing domain decomposition method of Neumann–Neumann type for the numerical approximation of an age-structured population diffusing in a multilayer environment. We give a quasi optimal convergence result for the algorithm via Fourier analysis in a two-layers case, and we address the variational generalization to an arbitrary number of layers as well as its finite dimensional formulation. We illustrate our approach with some numerical results.

Hybrid-Mode Analysis of High-Tc Thick Superconducting Microwave Circuits on Multilayered Anisotropic Layers

An efficient full-wave algorithm based on spectral domain approach (SDA) is developed for high temperature superconductors (HTS) microwave circuits on multilayered anisotropic substrates. The substrate may consist of arbitrary number of layers whose permittivity and permeability are tensors. The effects of the superconducting material, of finite complex conductivity and finite thickness, are taken into account. Good agreement is shown with regard to published data particularly for circuits having high film-to-substrate thickness ratio.

Influence of Alpha Radiolysis of Water on UO2 Matrix Alteration: Chemical/Transport Model

A combined transport and radiolysis model is proposed in this paper to predict the oxidation/dissolution of UO2 under alpha radiolysis of water. The UO2-water interface is divided into an arbitrary number of layers. The Chemsimul kinetic code is used for radiolysis calculations in each layer, and the modeling of transport between the layers is based on Fick’s law. The calculation proceeds in an iterative way, and an alpha dose rate profile is taken into account as input data. To limit the calculation time, which depends on the computer capacity and the duration of the leaching experiment described, a compromise between the thickness and the number of cells has to be found. At present, simulations of leaching experiments lasting several days cannot be carried out because of the very long calculation time. However, the calculation has been compared with experimental results obtained under irradiation at high flux levels of a UO2-water interface subjected to a beam of He2+ particles generated by a cyclotron. Owing to computer time limitation, calculations are carried out by considering 200 layers, each 10 μm thick, to simulate 1-h experiments. In the experimental geometry (monoenergetic linear alpha beam), the alpha dose rate profile is well described by a summation of Bragg curves. The comparison relates to experiments performed in aerated and deaerated media at a high flux of 3.3 × 1010 α·cm-2·s-1 and 3.3 × 1011 α·cm-2·s-1. The calculated uranium content in solution is three times lower than the experimental value, and the hydrogen peroxide concentration is ten times lower in aerated media. In deaerated media, however, the comparison is quite good. Finally, a calculation was carried out with a large imposed dissolved hydrogen concentration in solution to check the inhibition of matrix dissolution. The release of uranium in solution is relatively high despite the hydrogen concentration in solution because of the primary formation of hydrogen peroxide. This is probably because of a lack of knowledge concerning the inhibitor mechanism under alpha radiolysis (influence of the surface under alpha irradiation, hydrogen activation, validity of primary radiolytic yield in presence of H2, etc.), which is not taken into account in our calculations.