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In this paper, the stabilized biconjugate gradient fast Fourier transform (BCGS-FFT) method is used to solve the electromagnetic scattering problem for 3-D inhomogeneous uniaxial anisotropic objects embedded in a layered uniaxial medium. The optical axis of the background medium is perpendicular to the layer boundaries. However, the optical axis of the scatterer can be rotated through any angles. The electric field integral equation (EFIE) is formulated in the layered uniaxial anisotropic background medium. The volumetric roof-top function is used for the basis function as well as the testing function. The dyadic Green’s functions (DGFs) for both the electric field and the magnetic vector potential are used to solve the EFIE, and the results as well as the performance are compared. Several numerical simulations are carried out to validate the accuracy and efficiency of the proposed method. The major new contribution of this paper is to extend the BCGS-FFT method to accommodate the uniaxial anisotropy of the layered background medium. Therefore, the DGFs for the layered uniaxial medium are evaluated before solving the EFIE. In addition, the DGF for the electric field is also used to solve the 3-D scattering problem through BCGS-FFT iterations, which is different from the previous work. [ABSTRACT FROM AUTHOR]

The faithful modelling of the propagation of linear waves in a layered, periodic structure is of paramount importance in many branches of the applied sciences. In this paper, we present a novel numerical algorithm for the simulation of such problems which is free of the artificial singularities present in related approaches. We advocate for a surface integral formulation which is phrased in terms of impedance-impedance operators that are immune to the Dirichlet eigenvalues which plague the Dirichlet-Neumann operators that appear in classical formulations. We demonstrate a high-order spectral algorithm to simulate these latter operators based upon a high-order perturbation of surfaces methodology which is rapid, robust and highly accurate. We demonstrate the validity and utility of our approach with a sequence of numerical simulations. [ABSTRACT FROM AUTHOR]

The stress wave scattering off of any finite slab may be used as a physical approach to determining some or all of the overall dynamic constitutive parameters of such a specimen. In this paper, this approach is applied to normal incidence of symmetric and asymmetric layered structures with elastic or viscoelastic layers. The method determines all of the overall constitutive constants of a Willis-type material (including zero and non-zero coupling parameters) for all frequencies, even in stop bands of elastic structures, exactly. The ambiguity in phase velocity calculation is overcome using continuity considerations. Symmetries in coupling constants and the restrictions due to energy conservation and dissipation are presented. Integrating the wave equations directly leads to a proposed micro-structural scheme for determination of the overall constitutive parameters. The results of this method are identical to those derived based on the scattering response for all frequencies, including stop bands, and beyond the long wavelength limit of traditional homogenization techniques. The proposed approach has the potential to be applied to 3D-structured unit cells, oblique incidences, and simultaneous scattering of multiple waves. [ABSTRACT FROM AUTHOR]

The fast scattering and inverse scattering algorithms for acoustic wave propagation and scattering in a layered medium with buried objects are an important research topic, especially for large-scale geophysical applications and for target detection. There have been increasing efforts in the development of practical, accurate, and efficient means of imaging subsurface target anomalies. In this work, the acoustic scattering problem in layered media is formulated as a volume integral equation and is solved by the stabilized bi-conjugate gradient fast Fourier transform (BCGS-FFT) method. By splitting the layered medium Green's function interacting with the induced source into a convolution and a correlation, the acoustic fields can be calculated efficiently by the FFT algorithm. This allows both the forward solution and inverse solution to be computed with only computation time per iteration, where is the number of degrees of freedom. The inverse scattering is solved using a simultaneous multiple frequency contrast source inversion (CSI). The stable convergence of this inversion process makes the multiple frequency simultaneous CSI reconstruction practical for large acoustic problems. Some representative examples are shown to demonstrate the effectiveness of the forward and inverse solvers for acoustic applications. [ABSTRACT FROM AUTHOR]

In this paper, the formulation of reverse time migration (RTM) is improved for impulse borehole radar imaging in the subsurface scenarios with layered media. By fully adopting the prior information of surrounding media, the time gating function is designed and applied to the incident wave field and scattering wave field for each imaging point, which strengthens the correlation between the wave fields in the time domain. The clutters partly caused by the multiple reflections between different media layers are suppressed due to the gating function. A normalized zero-offset cross correlation with gated samples is conducted and used to weight the result of RTM. The improved approach is compared with the conventional RTM, the back-projection method, and the Stolt migration algorithm with synthetic data and is then validated by a single-borehole radar experiment in a layered media scenario. The results demonstrate that the developed approach is superior to the conventional methods in locating targets and robust in complex subsurface environments. [ABSTRACT FROM AUTHOR]

Scattering particles find application in organic light emitting diodes (OLEDs) for an enhanced outcoupling of the generated light. This paper presents a computational scheme to exactly model the electromagnetic fields and the power outcoupling efficiency of a typical OLED geometry, comprising a thin film system with spherical scattering particles inside. The model is based on the expansion of the fields in plane and spherical vector wave functions, as well as the scattering matrix formalism for the layer system reflections. In a numerical application example, the effect of 1000 spherical high index scattering particles on the internal outcoupling from a realistic OLED structure is discussed. [ABSTRACT FROM AUTHOR]

Predictions of the fourth-order small perturbation method (SPM) are examined for scattering from two rough surfaces in a layered geometry. Cross-polarized backscatter, in particular, is emphasized because use of the fourth-order SPM is required to obtain this quantity. The formulation of the SPM fields and incoherent ensemble-averaged normalized radar cross sections (NRCSs) up to the third and the fourth order in surface rms heights, respectively, are reviewed. It is shown that the fourth-order NRCS includes distinct contributions from upper and lower interface roughnesses, as well as an “interaction” term that couples the upper and lower interface roughnesses. A comparison with NRCS values computed using the “numerically exact” method of moments in the full bistatic scattering pattern is shown for verification, and NRCS values at the second and the fourth order are compared in order to assess the convergence of the SPM series. Although the number of parameters inherent in the two-layer rough surface scattering problem makes an exhaustive study of scattering effects difficult, several illustrative examples are presented to capture a range of scattering behaviors. The results emphasize the importance of interactions between the rough surfaces in producing cross-polarized backscattering and also indicate an increased significance of fourth-order contributions in the two-layer geometry as compared to the single-layer case. [ABSTRACT FROM PUBLISHER]

Two different perturbative approaches have been recently presented for the evaluation of scattering from layered media characterized by rough interfaces: the Boundary Perturbation Theory (BPT) and the Volumetric-Perturbative Reciprocal Theory (VPRT). These two approaches are conceptually different: They employ different strategies to provide closed-form solutions to the scattering problem, and, at first sight, they rely on different basic assumptions, so that different regimes of validity seem to be expected. In spite of that, both approaches lead to the same expression of the first-order scattered field. To solve this (seeming) incongruence, in this paper a careful theoretical analysis of basic assumptions of VPRT is carried out. This requires also considering the procedure to obtain the VPRT solution that, in this paper, is reformulated relying on a more physically sound way. The performed analysis demonstrates that, actually, basic assumptions of VPRT are equivalent to those of BPT, so that their ranges of validity are, consistently, also the same. Thus, the seeming incongruence is solved: The two theoretical constructs can be now regarded in a conceptually coherent frame. [ABSTRACT FROM AUTHOR]

An efficient finite-element method is presented to analyze the scattering from complex bodies of revolution buried or partly buried in layered lossy media. In the proposed method, high-order edge-based vector basis functions are used to expand the transverse field components and high-order node-based scalar basis functions are used to expand the angular component. A locally conformal perfectly matched layer (PML) by complex coordinate stretching for inhomogeneous medium is presented and used to truncate the computational domain. Such a kind of PML is very easy to implement in the numerical process and is able to enclose an arbitrarily shaped convex object in the spatial domain. Numerical examples are presented to demonstrate the accuracy and efficiency of the presented method. [ABSTRACT FROM AUTHOR]

In this paper, the model parameters of a two-layer dielectric structure with random slightly rough boundaries are retrieved from data that consist of the backscattering coefficients for multiple polarizations, angles, and frequencies. We use the small perturbation method to solve the forward problem. The inversion problem is then formulated as a least square problem and is solved using a global optimization method known as simulated annealing, which is shown to be a robust retrieval algorithm for our purpose. The algorithm performance depends on several parameters. We make recommendations on these parameters and propose a technique for exiting local minima when encountered. We test the sensitivity of the inversion scheme to measurement noise and present the noise analysis results. [ABSTRACT FROM AUTHOR]

An analytical-numerical technique for the solution of the plane-wave scattering problem by a set of perfectly conducting circular cylinders, buried in a dielectric slab, is presented. The problem is solved for both TM and TE polarizations, and for near- and far-field regions. The proposed method expresses the scattered fields in terms of cylindrical waves, and exploits the plane-wave spectrum of a cylindrical function to take into account the refiection and transmission through the planar interfaces. Numerical results are reported and the validity of the approach is confirmed by comparison with results given in the literature, showing a good agreement. [ABSTRACT FROM AUTHOR]

A closed-form first-order perturbative solution to the problem of electromagnetic scattering from a layered structure with an arbitrary number of rough interfaces is presented in this paper. Following the classical scheme employed to deal with a rough surface, a perturbative expansion of the fields in the rough-interface layered structure is performed, assuming that roughness heights and slopes are small enough. In this manner, in the first-order approximation, the geometric randomness of the corrugated interfaces is translated into random current sheets imposed on the unperturbed (flat) interfaces and radiating in the unperturbed (flat boundaries) layered media. The scattered field is then represented as the sum of up- and down-going waves, and a systematic approach that involves the use of matrix formalism and generalized reflection/transmission coefficients is employed. This approach permits us to avoid the necessity of the cumbersome Green function formalism. The demonstration of the consistency of the presented solution is analytically provided, showing that the proposed solution reduces to the corresponding existing ones when the stratification geometry reduces to the simplified ones considered by the other authors. [ABSTRACT FROM AUTHOR]

• A novel High-Order Spectral method for Hyperbolic Materials. • A demonstration of the fidelity and accuracy of this novel algorithm. • Comparison of highly accurate solutions with simulations produced by engineers. Electromagnetic metamaterials are artificial media assembled from components which have dimensions much smaller than the wavelength of the illuminating radiation. It has been demonstrated that these media can have properties beyond those found in conventional materials with important applications to many areas of science and engineering. Among the collection of such materials currently garnering significant attention are the Hyperbolic Metamaterials. These are highly anisotropic structures which have a hyperbolic dispersion relation due to the fact that one principal component of the relative permittivity or permeability tensor has the opposite sign of the other two. For such materials scattered wave information at all scales is transmitted far away which suggests a number of important applications, the most immediate of which is imaging objects below the diffraction limit (superlensing). Clearly it is of great current interest to have numerical simulation capabilities for these fascinating materials. As the hyperbolic response is quite strong and its nature is very sensitive, numerical simulations of these configurations should be robust and highly accurate. For this reason we focus on High–Order Spectral algorithms which efficiently produce high fidelity solutions. More specifically, we describe a High–Order Perturbation of Surfaces approach which enjoys the greatly reduced operation counts and memory savings of interfacial methods while avoiding the complexities and indefinite linear systems faced by Integral Equation algorithms. We give a full discussion of our formulation in terms of Impedance–Impedance Operators (which avoids spurious singularities of other formulations) and implementation details, followed by numerical validation and simulation of results which appear in the engineering literature. [ABSTRACT FROM AUTHOR]

An efficient inverse scattering method is developed for imaging near-surface heterogeneities using scattered surface waves. Three dimensional elastodynamic wave propagation and scattering in a laterally invariant embedding medium is considered. The Born Approximation is used and the scattered wavefield is expressed as a domain type integral representation. The computation time of Green's tensor elements is reduced by considering the radial symmetry of the medium. The method is validated by numerical tests. Ultrasonic laboratory data obtained from a scale model experiment are used for imaging the near-surface inhomogeneities caused by an epoxy-filled hole in the surface of an aluminum block. Both synthetic and the scale model tests show that the location, the actual density contrast and the depth of the inhomogeneities are reasonably well estimated. [ABSTRACT FROM AUTHOR]

Abstract: The radiation characteristics of relativistic electrons, traversing stacks as 1D-layered media, have been found by a new, semi-numerical method. The analytical part of an algorithm based on Maxwell equations was used as a basis for a numerical code. As the calculations show, all known kinds of radiation induced in stacks are properly accounted for. Special calculations were made for transition radiation in random stacks. No effect of a new type of radiation, resonant diffusive radiation (RDR), predicted recently by Gevorkian et al., is found. An analysis is given showing that this negative result is not unexpected. [Copyright &y& Elsevier]

Electromagnetic scattering from rough surfaces has been investigated extensively for the past decades. There exist analytical solutions to rough surface scattering such as small perturbation method (SPM) or Kirchhoff approximation (KA). These solutions, however, are limited to either small or large roughness regimes. Recent efforts have been put forth to study electromagnetic scattering of multilayer rough surface in the application of deep soil moisture and ice property estimation. In this paper, multilayer rough surface scattering is analyzed based on the extended boundary condition method (EBCM) and truncated singular value decomposition. The method of extended boundary condition can accurately handle scattering from a slightly rough surface. For mild and large roughness regime, ill-conditioned matrices can arise from EBCM. In this paper, we present a regularization scheme to mitigate this ill-conditioning effect via truncated singular value decomposition (TSVD).The truncation parameters are set to enforce power conservation relations across all rough interfaces. Bistatic scattering coefficients are then obtained by incoherently averaging the power computed from the resulting Floquet modes in the scattering directions. Therefore, the electromagnetic wave interactions in multilayer rough surfaces are analyzed in a systematic way. Finally, the results are validated against the analytical SPM solution to two-rough-interface rough surface scattering. In addition, the formulation is extended to solve scattering from three-rough-interface rough surfaces. Several results are reported. [ABSTRACT FROM AUTHOR]

An analytical method to calculate the bistatic-scattering coefficients of a three-dimensional layered dielectric structure with slightly rough interfaces is presented. The interfaces are allowed to be statistically distinct, but possibly dependent. The waves in each region are represented as a superposition of an infinite number of up- and down-going spectral components whose amplitudes are found by simultaneously matching the boundary conditions at both interfaces. A small-perturbation formulation is used up to the first order, and the scattered fields are derived. The calculation intrinsically takes into account multiple scattering processes between the boundaries. The formulation is then validated against known solutions to special cases. New results are generated for several cases of two- and three-layer media, which will be directly applicable for modeling of the signals from radar systems and subsequent estimation of a layered medium subsurface properties, such as moisture content and layer depths. [ABSTRACT FROM AUTHOR]

The stabilized biconjugate gradient fast Fourier transform (BCGS-FFT) method is applied to simulate electromagnetic and acoustic scattering from inhomogeneous objects embedded in a layered medium in two dimensions. Two-dimensional layered-media Green's functions are computed adaptively by using Gaussian quadratures after singularity subtraction. The Green's function is split into convolutional and correlational components in order to apply the FFT so as to solve the scattering problem efficiently. The CPU time and memory cost of this BCGS-FFT method is O(N log N) and O(N), respectively, where N is the number of unknowns, which is significantly more efficient than using the method of moments (MoM). As a result, this method is capable of solving large-scale electromagnetic and acoustic scattering problems for inhomogeneous objects embedded in a layered medium with an arbitrary number of layers. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 47: 128–134, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21101 [ABSTRACT FROM AUTHOR]

Abstract: This paper gives an overview of computational electromagnetics for simulating complex structures with a large number of unknowns using integral equation method. First, it discusses the pros and cons of differential equation solvers versus integral equation solvers. Then it gives an overview of different fast algorithms for solving integral equations. It also discusses the difficulty of solving electromagnetic problems in the “twilight zone” between static and full-wave electromagnetics. Finally, it discusses various methods for fast solutions of scattering and coupling problems involving layered media both for statics and dynamic problems, and presents some numerical results. To cite this article: W.C. Chew et al., C. R. Physique 6 (2005). [Copyright &y& Elsevier]

Wave transmission characteristics in elastic media that have periodic microstructure over a finite spatial length are examined theoretically as well as numerically. Two classes of such media are demonstrated, namely, one-dimensional multilayered media with finite-length periodicity and two-dimensional composite media with square arrays of aligned fibers within a finite length. From these one-dimensional and two-dimensional analyses, the influence of the finite-length periodicity on the wave transmission characteristics is discussed. In these media, there are frequency bands (stop bands) where the energy transmission coefficient appears to vanish or takes very low values, while in pass bands it oscillates with the frequency due to the finite-length periodicity. It is theoretically demonstrated in the one-dimensional case of multilayers how the frequency intervals of the oscillation in the transmission spectrum depend on the repeating number of the periodic cells as well as other acoustic and geometrical parameters. The results of the two-dimensional fiber arrays, which are obtained numerically by solving the equations of the SH wave multiple scattering, are shown to fit well in the one-dimensional framework of multilayered structures up to a certain frequency encompassing the first stop band. This similarity between two classes of problems is demonstrated by appropriately identifying the one-dimensional reduced transfer matrix for a single cell that is representative of the periodic fiber array. [Copyright &y& Elsevier]

Summary: In this paper, by applying a non linear model for the electromagnetic inverse scattering, a technique for the dielectric profiling of a planarly layered medium is investigated and applied to void localization and diagnostics inside a homogeneous lossless slab (one-dimensional geometry). Data are collected under plane wave multifrequency normal incidence. Suitable finite dimensional representations for the unknown functions are introduced and their influence on the model is discussed. The resulting functional equation is solved by the method of weighted residuals and the solution algorithm amounts to minimizing a non quadratic function, where particular attention is devoted to reduce the occurrence of local minima. Finally, the inversion algorithm is validated by applications to both simulated and experimental data. [Copyright &y& Elsevier]

This paper is concerned with the numerical modeling of elastic wave propagation in layered media. It considers two isotropic homogeneous elastic solids in perfect contact. The interface is parallel to the free surface. Two finite difference methods are developed. The usefulness of the methods are investigated for long time simulations and the accuracy of the results are compared with the response from an approximate model. [ABSTRACT FROM AUTHOR]

This paper presents an efficient technique for the analysis of electromagnetic scattering by arbitrarily shaped perfectly conducting objects in layered media. The technique is based on a higher order method of moments (MoM) solution of the electric field, magnetic field, or combined-field integral equation. This higher order MoM solution comprises higher order curved patches for the geometry modeling and higher order hierarchical basis functions for expansion of the electric surface current density. Due to the hierarchical property of the basis functions, the order of the expansion can be selected separately on each patch depending on the wavelength in the layer in which the patch is located and the size of the patch. In this way, a significant reduction of the number of unknowns is achieved and the same surface mesh can be reused in a wide frequency band. It is shown that even for fairly large problems, the higher order hierarchical MoM requires less memory than existing fast multipole method (FMM) or multilevel FMM implementations. [ABSTRACT FROM AUTHOR]

• A software for the simulation of light scattering by multiple particles near planar interfaces is presented. • The usage of the software is illustrated by several application examples. • The accuracy of the results is verified by comparison to FEM and FDTD results. • Simulations with several thousand wavelength-scale particles are feasible. SMUTHI is a python package for the efficient and accurate simulation of electromagnetic scattering by one or multiple wavelength-scale objects in a planarly layered medium. The software combines the T-matrix method for individual particle scattering with the scattering matrix formalism for the propagation of the electromagnetic field through the planar interfaces. In this article, we briefly introduce the relevant theoretical concepts and present the main features of SMUTHI. Simulation results obtained for several benchmark configurations are validated against commercial software solutions. Owing to the generality of planarly layered geometries and the availability of different particle shapes and light sources, possible applications of SMUTHI include the study of discrete random media, meta-surfaces, photonic crystals and glasses, perforated membranes and plasmonic systems, to name a few relevant examples at visible and near-visible wavelengths. [ABSTRACT FROM AUTHOR]