Functions For Layered Media Research Articles

PEEC Formulation Based on Dyadic Green's Functions for Layered Media in the Time and Frequency Domains

This paper presents a novel time- and frequency-domain concept of modeling with the partial element equivalent circuit (PEEC) method, which applies the mixed potential integral equation (MPIE) with dyadic Green's functions for layered media (DGFLM-PEEC). On the one hand, it represents an exact full-wave semianalytical solution for an arbitrary configuration of traces and via holes in multilayered printed circuit boards. On the other hand, the DGFLM-PEEC model is represented in a circuit form, and thus, may be included in general-purpose circuit simulators. The paper derives a general DGFLM-PEEC formulation, which may be applied to all types of the MPIE with dyadic Green's functions. Using this concept, a particular type of layered media, namely a lossy dielectric between two grounds (stripline region), is thoroughly investigated and used to set up a particular DGFLM-PEEC model. The closed-form expressions for partial inductances and potential coefficients have been derived for this case. The time- and frequency-domain DGFLM-PEEC models for the stripline region have been validated using the measurements and the simulation by the method of moments.

Fast evaluation of zero‐offset Green's function for layered media with application to ground‐penetrating radar

We propose an efficient integration path for the fast evaluation of the three‐dimensional spatial‐domain Green's function for electromagnetic wave propagation in layered media for the particular case of zero‐offset, source‐receiver proximal ground‐penetrating radar (GPR) applications. The integration path is deformed in the complex plane of the integration variable kρ so that the oscillations of the dominant exponential term in the spectral Green's function are minimized. The contour does not need to be closed back on the real kρ axis as the complex integrand rapidly damps. The accuracy and efficiency of the technique have been confirmed by comparison with traditional elliptic integration contours. The proposed algorithm appears to be promising development for fast, full‐wave modeling and inversion of GPR data.

An Approximation of the Electromagnetic Green's Function of Layered Media With the Source Point Considered as an Independent Variable

A novel method of approximation of the layered media electromagnetic Green's function is presented. In addition to its closed-form representation, a key attribute of the new approximation is coordinates of the source are kept as independent variables. The mathematical analysis of the accuracy of the approximate Green's function is provided, along with results from its numerical validation.

Neural network model for the efficient calculation of Green's functions in layered media

In this article, neural networks are employed for fast and efficient calculation of Green's functions in a layered medium. Radial basis function networks (RBFNs) are effectively trained to estimate the coefficients and the exponents that represent a Green's function in the discrete complex image method (DCIM). Results show very good agreement with the DCIM, and the trained RBFNs are very fast compared with the corresponding DCIM. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 13: 128–135, 2003.

Calculation of Three-Dimensional Electromagnetic Field of a Nonmagnetic Plate with a Local Inhomogeneity Using the Method of Fundamental Function of Layered Medium

New expressions for calculating Green's magnetic tensor have been obtained. Analytic expressions for the components of Green's electric tensor have been given.

SEM representation of transient scattering from conducting planar objects in layered media

The scattering of a plane wave from conducting planar objects in layered media has been analysed by a frequency-domain method of moments (MoM) with rooftop basis functions and Galerkin's procedure. Green's functions for layered media involved in the computation of the matrix elements are evaluated using the closed-form expressions obtained from the robust approach using the generalised pencil-of-function (GPOF) method. The time-domain scattered field from the scatterer illuminated by an electromagnetic pulse is obtained from its frequency-domain data via the inverse fast Fourier transform (FFT). The poles and residues of the time-domain response are then extracted via the GPOF method. The singularity expansion method (SEM) representation of the time-domain response using the poles and residues is finally obtained. The pole locations in a complex frequency plane as a function of the substrate thickness, relative dielectric permittivity and dielectric loss are also investigated. Complex natural resonances for a microstrip dipole and patch are sufficiently diverse for identification purposes, thus demonstrating that only pole and residue information is required for target characterisation.

Electromagnetic Wave Interaction of Conducting Object With Rough Surface By Hybrid Spm/Mom Technique - Abstract

An electromagnetic wave scattering model based on a hybrid SPM/MoM technique has been developed for the study of the EM wave interaction of a conducting object above a rough surface. In this hybrid technique, the Green's function and surface variables are expanded in terms of the surface height function on the mean surface, so that the integral equations based on the extinction theorem and boundary conditions can be decomposed into different orders. Each order represents the problem of EM wave scattering from an object on a flat interface excited by a wave from an equivalent source. With the introduction of the dyadic Green's function for layered media, the integral equations are reformulated and solved without involving the surface variables on the interface. Since the returned fields using the hybrid technique are expressed term by term, the EM wave interaction of the object with the rough surface can be clearly identified and characterized. The total returned fields calculated by the hybrid technique, which are the sum of individual interaction terms, are compared with simulation results computed with the standard MoM, and good agreement is obtained.

Continuous wavelet representation of Green functions in layered media

A continuous wavelet analysis technique is applied in the spectral domain to efficiently represent the multiscale features of the spectral-domain Green functions in layered media. Numerical examples for a microstrip and a shielded microstrip are presented.

Microwave Imaging of Dielectric Cylinder in Layered Media

Microwave imaging of a lossless two-dimensional dielectric object buried in layered media using time domain scattering data is considered in this paper. The method is based on volume equivalence principle and moment method. Born type approximation is adopted. It is an iterative method. In each iteration, both the direct and inverse problems are solved once. The direct problem is solved by finite-difference time domain method. To overcome the ill-posedness of the inverse problem, the pseudoinverse technique is adopted. The Green function in layered media excited by a unit line current source is derived by plane wave expansion method. Several examples are given to show the ability of this method to invert arbitrarily shaped permittivity profiles. Good imaging solutions are obtained.

Electromagnetic scattering solution of conducting strips in layered media using the fast multipole method

The fast multipole method (FMM) is applied to the solution of the electromagnetic scattering problems in layered media for the first time. This is achieved by using closed-form expressions for the spatial-domain Green's functions for layered media. Until now, the FMM has been limited to the homogeneous-medium problems. An integral equation based on the twodimensional scalar Helmholtz equation is solved to compute the electromagnetic scattering from sample geometries of conducting strips in layered media in order to demonstrate the accuracy and the efficiency of the new method.

Comparative evaluation of absorbing boundary conditions using Green's functions for layered media

Absorbing boundary conditions are comparatively studied using the Green's functions of the vector and scalar potentials for multilayer geometries and general sources. Since the absorbing boundaries are introduced as additional layers with predefined reflection coefficients into the calculation of the Green's functions, this approach provides an absolute measure of the effectiveness of different absorbing boundaries. The Green's functions are calculated using different reflection coefficients corresponding to different absorbing boundaries and compared to those obtained with no absorbing boundary. It is observed that the perfectly matched layer (PML) is by far the best among the other absorbing boundary conditions whose reflection coefficients are available.

Effective reflection coefficients for the mean acoustic field between two rough interfaces

A formalism is presented that demonstrates that the mean Green’s function for the acoustic field between two rough interfaces can be expressed as a Green’s function associated with two flat interfaces with effective reflection coefficients. This result incorporates all orders of the fluctuations in the half-space scattering amplitudes associated with each interface considered separately. From the mean Green’s function modal attenuations can be found. To lowest order in the surface height fluctuations it is shown that it is not sufficient to use mean half-space scattering amplitudes as effective reflection coefficients. The formalism is designed to provide approximations for the Green’s function in layered media which are based on previously developed approximations for half-space scattering amplitudes.

Complex image method for sources in bounded regions of multilayer structures

Other researchers have employed complex image theory to rapidly evaluate spatial-domain Green's functions in layered media. While workable in instances where the source lies within or at the interface of an unbounded region, the more general methodology given for a source embedded in a dielectric layer is incorrect. This paper explains the nature of the error and how it can be corrected.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A numerically efficient technique for the method of moments solution for planar periodic structures in layered media

A numerically efficient technique for the calculation of the method of moments (MoM) impedance matrix is presented for planar periodic structures rendered in arbitrary triangular discretizations and embedded in layer media. The technique is based on the MoM applied to a mixed potential integral equation (MPIE) in conjunction with triangular-domain basis functions. Rapid convergence of the matrix elements is achieved with a hybrid spectral/spatial decomposition of Green's functions. Transformations of the spectral to spatial Green's functions for layered media are performed by using complex images. Examples demonstrating the numerical efficiency and accuracy of the method are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A model with ellipsoidal scatterers for polarimetric remote sensing of anisotropic layered media

This paper presents a model with ellipsoidal scatterers for applications to polarimetric remote sensing of anisotropic layered media at microwave frequencies. The physical configuration includes an isotropic layer covering an anisotropic layer above a homogeneous half space. The isotropic layer consists of randomly oriented spheroids. The anisotropic layer contains ellipsoidal scatterers with a preferential vertical alignment and random azimuthal orientations. Effective permittivities of the scattering media are calculated with the strong flucutation theory extended to account for the nonspherical shapes and the scatterer orientation distributions. On the basis of the analytic wave theory, dyadic Green's functions for layered media are used to derive polarimetric backscattering coefficients under the distorted Born approximation. The ellipsoidal shape of the scatterers gives rise to nonzero cross‐polarized returns from the untilted anisotropic medium in the first‐order approximation. Effects of rough interfaces are estimated by an incoherent addition method. Theoretical results and experimental data are matched at 9 GHz for thick first‐year sea ice with a bare surface and with a snow cover at Point Barrow, Alaska. The model is then used to study the sensitivity of polarimetric backscattering coefficients with respect to correlation lengths representing the geometry of brine inclusions. Polarimetric signatures of bare and snow‐covered sea ice are also simulated based on the model to investigate effects of different scattering mechanisms.

Dynamics of piles and pile groups in layered soil media

A general formulation is presented for the dynamic response analysis of piles and pile groups in a layered halfspace. Green's functions for layered media, evaluated numerically by the application of Integral transform techniques, along with analytical solutions for the dynamic response of piles are the ingedients of this formulation. The analytical derivations are presented in this paper and the extension of the formulation to seismic analyses is described. In addition, a limited number of representative results on the dynamic stiffnesses and seismic response of pile groups are presented.

A note on the mixed potential representation of electric fields in layered media

A mixed potential formulation is given for electrical fields in layered environments. Contributions to the field from charges are identified explicitly through a scalar Green's function for layered media. The outcome is a computationally expedient Sommerfeld integral representation. >

An observation on the Sommerfeld-integral representation of the electric dyadic Green's function for layered media

The authors discuss the electric dyadic Green's function for layered dielectrics. It is known that for the free-space electric dyadic Green's function, evaluation of the electric field at observation points within the source region requires specification of a principal volume along with the corresponding depolarizing dyad. Special considerations are invoked for layered background media which are appropriate for the electromagnetics of integrated electronics. It is shown that use of the Sommerfeld-integral representation of the electric dyadic Green's function leads to an innate choice for the depolarizing dyad. A corresponding principal volume is subsequently identified; it is demonstrated that there exists an alternative choice for this excluding region which leads to the same depolarizing dyad.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Calculation of the elasto-dynamic Green's function in layered media by means of a modified propagator matrix method

Summary. The calculation of the two-dimensional elasto-dynamic Green’s function for a stratified medium is investigated. The solution is represented in the form of an inverse Fourier integral which is to be integrated along a properly chosen path in the complex wavenumber plane. The integrand is computed using a modified propagator matrix method. This method is based on a mixed formulation using the propagator matrix and the matrix of minors of the propagator matrix (compound matrix). The major advantages of this approach are the elimination of the numerical loss of precision problems associated with the Thomson-Haskell formulation, without losing the attractive tractability and compactness of the propagator matrix method. This modified method is first mathematically derived, and theoretical seismograms are then presented for two examples.