Functions For Multilayered Media Research Articles

The FIT-MoM Method for Analysis of Electromagnetic Scattering by Bodies-of-Revolution Embedded in Multilayered Media

In this article, the previously introduced finite-integration technique/method-of-moments (FIT-MoM) hybrid method, which is suited for the analysis of electromagnetic scattering by inhomogeneous bodies of revolution (BoRs), is generalized to problems involving multilayered environment. Due to the fact that BoR-typical azimuthal mode decomposition is used, appropriate modal Green's functions for multilayered media are given. They are responsible for source-field interactions within the region that is external with regard to the FIT part. Formulas for modal decomposition of incident plane wave fields as well as the approximation enabling computing fields produced by sources associated with individual modes in the far-zone are also provided.

Boundary element method simulation of 3D heat diffusion in defective layered media for IRT building applications

This paper presents a numerical model to simulate heat transfer by conduction in defective layered media, looking to contribute to the interpretation of thermographic results obtained in active Infrared Thermography (IRT) tests performed on building elements. The proposed model is developed to simulate 3D heat diffusion in a multilayered system containing a 3D thin defect (considered to be a null thickness inclusion). The proposed model uses the frequency domain Boundary Element Method (BEM) formulation written in terms of normal derivative integral equation formulation, referred to here as TBEM, in order to handle the null thickness of the defect. 3D Green's functions for multilayered media are used to avoid the discretization of the interfaces between layers. These 3D Green's functions are expressed as Bessel integrals and written as the sum of source terms and terms which are defined by imposing the required boundary conditions at each interface. When using this procedure, only the defect's surface is discretized. The proposed solution is verified against a previously developed 3D TBEM formulation for unbounded media using a mirror image source technique. To illustrate the applicability of the proposed methodology in active IRT, time-domain and phase contrast results are simulated and presented.

Construction of Green's Functions for Multilayered Media Using Signal-Flow Graphs [Education Column

The utilization of signal-flow graphs is demonstrated as a simple and intuitive approach for constructing Green's functions for multilayered media. The branches of the signal-flow graphs represent wave transmission or reflection coefficients in or between the different layers, while their nodes correspond to layer interfaces, the source and the observer points. First, the flow-graph derivation of the Green's function is presented for the one-dimensional case of a plane wave produced by a uniform electric-current-sheet source normally incident on a two-layered medium. The derivation is next generalized to the case of multilayered media. The problem is solved for the case where both the excitation and the observation points are inside the first-layer medium. Finally, the one-dimensional case is then extended to higher dimensions.

Comparison of Two Approaches to Evaluate Nonsymmetrical Components of Green's Functions for Multi-Layered Media in the Near-Field Region

The numerical implementation of Green's functions is a fundamental step for analyzing multi-layered media applications. The computation time and the accuracy of results, which should be maintained for all field regions, are two crucial issues. The discrete complex image method is one of the methods that proved its efficiency in accelerating the computation time and yielding accurate results in the near- and intermediate-field regions. In order to retain this accuracy for the far-field region, the surface-wave contribution should be extracted. However, this procedure results in erroneous results in the near field. This article is concerned with the nonsymmetrical components of the magnetic vector potential. Two different approaches to handle this problem are analyzed. In both approaches, additional artificial poles are extracted in order to eliminate the problem of contaminated results in the near field. The results of both approaches are presented, and the effect of these artificial poles is explored. The results are compared with the numerical integration technique.

An accurate evaluation of the nonsymmetrical components of Green's functions for multilayered media in the near‐field region

AbstractThe discrete complex image method has proved to be one of the most efficient techniques to evaluate Green's functions for multilayered media, particularly in the near‐ and intermediate‐field regions. Although the extraction of surface waves extends its validity to the far field, it suffers from erroneous results that contaminate the computation of the near field. To handle this problem for the nonsymmetrical components of Greens functions, we follow the same approach adopted by the author and others for the symmetrical components where a number of artificial poles are extracted for each physical surface‐wave pole occurrence. This approach has proved its validity and yielded good results in all field regions. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 881–885, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24201

Third and fourth Stokes parameters in polarimetric passive microwave remote sensing of rough surfaces over layered media

AbstractWe consider the four Stokes parameters in microwave emission from a layered medium with the top interface being a rough surface. The rough surface varies in one horizontal direction so that azimuthal asymmetry exists in the 3‐D problem. Dyadic Green's functions of multilayered media are used to formulate the surface integral equations. Periodic boundary conditions are used. The numerical results show that the presence of the layered media below the rough surface reduces the vertical and horizontal brightness temperatures. The interaction between the rough surface and the layered media also enhance the third and fourth Stokes parameters. In particular, the fourth Stokes parameter can be large for such geometrical configurations. Results show that the nonzero third and fourth Stokes parameters exist for all frequencies and are particularly large when the rough surface has large slope. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 3063–3069, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23892

Closed-Form Expressions of Multilayered Planar Green's Functions That Account for the Continuous Spectrum in the Far Field

The rational function fitting method has been found useful in the derivation of closed-form expressions of spatial-domain Green's functions for multilayered media. However, former implementations of the rational function fitting method lead to Green's functions expressions that are not accurate in the far field when this far field is dominated by the continuous spectrum instead of being dominated by surface waves (as it happens, for instance, in the case of lossy multilayered media). In this paper, the authors introduce a novel implementation of the rational function fitting method, which leads to Green's functions expressions that are accurate in the far field when this is dominated either by the continuous spectrum or by surface waves. In the new approach, the far-field contribution of the continuous spectrum to the Green's functions is numerically fitted in terms of functions with closed-form Hankel transforms, and this far-field contribution is explicitly added to the total least squares approximations of the Green's functions. The numerical results obtained for the Green's functions with the new approach have been compared with numerical results obtained via direct numerical integration of Sommerfeld integrals, and excellent agreement has been found despite the contribution - continuous spectrum or surface waves - dominating the far field.

Application of Total Least Squares to the Derivation of Closed-Form Green's Functions for Planar Layered Media

A new technique is presented for the numerical derivation of closed-form expressions of spatial-domain Green's functions for multilayered media. In the new technique, the spectral-domain Green's functions are approximated by an asymptotic term plus a ratio of two polynomials, the coefficients of these two polynomials being determined via the method of total least squares. The approximation makes it possible to obtain closed-form expressions of the spatial-domain Green's functions consisting of a term containing the near-field singularities plus a finite sum of Hankel functions. A judicious choice of the coefficients of the spectral-domain polynomials prevents the Hankel functions from introducing nonphysical singularities as the horizontal separation between source and field points goes to zero. The new numerical technique requires very few computational resources, and it has the merit of providing single closed-form approximations for the Green's functions that are accurate both in the near and far fields. A very good agreement has been found when comparing the results obtained with the new technique with those obtained via a numerically intensive computation of Sommerfeld integrals

AN EFFICIENT HYBRID SWARM INTELLIGENCE-GRADIENT OPTIMIZATION METHOD FOR COMPLEX TIME GREEN'S FUNCTIONS OF MULTILAYER MEDIA

A new hybrid technique for optimization of a multivariable function is proposed. This method is applied to the problem of complex time Green's function of multilayer media. This technique combines Particle Swarm search algorithm with the gradient based quasi-Newton method. Superiority of the method is demonstrated by comparing its results with other optimization techniques.

A direct discrete complex image method from the closed-form Green's functions in multilayered media

Sommerfeld integration is introduced to calculate the spatial-domain Green's functions (GF) for the method of moments in multilayered media. To avoid time-consuming numerical integration, the discrete complex image method (DCIM) was introduced by approximating the spectral-domain GF by a sum of exponentials. However, traditional DCIM is not accurate in the far- and/or near-field region. Quasi-static and surface-wave terms need to be extracted before the approximation and it is complicated to extract the surface-wave terms. In this paper, some features of the matrix pencil method (MPM) are clarified. A new direct DCIM without any quasi-static and surface-wave extraction is introduced. Instead of avoiding large variations of the spectral kernel, we introduce a novel path to include more variation before we apply the MPM. The spatial-domain GF obtained by the new DCIM is accurate both in the near- and far-field regions. The CPU time used to perform the new DCIM is less than 1 s for computing the fields with a horizontal source-field separation from 1.6/spl times/10/sup -4//spl lambda/ to 16/spl lambda/. The new DCIM can be even accurate up to 160/spl lambda/ provided the variation of the spectral kernel is large enough and we have accounted for a sufficient number of complex images.

Closed-form Expressions for Layered Media Green's Functions That are Reliable Both in the Near Field and in the Far Field

The authors have developed an algorithm for the determination of accurate closed- form expressions of Green's functions for multilayered media. The algorithm is based on the fltting of the spectral domain Green's functions in terms of an asymptotic term plus a ratio of two polynomials. The fltting is carried out via the method of total least squares, which is a non-iterative method demanding very few computational resources. The resulting closed-form expressions for the Green's functions consist of a quasistatic term plus a sum of cylindrical waves. The quasistatic term provides the near-fleld behavior and the cylindrical waves provide the farfleld behavior. As a consequence of this, the closed-form expressions are very accurate irrespective of the distance between the source point and the observation point. DOI: 10.2529/PIERS060807124124 The application of the method of moments (MoM) to the solution of mixed potential integral equations (MPIE) has proven to be an e-cient numerical tool for the analysis of planar circuits and antennas (1). In fact, several commercial software products that are currently used in the design of planar structures (such as \Ansoft Ensemble, \Zeland IE3D, and \Agilent Momentum) are based on the solution of MPIE by means of the MoM. In order to solve the MPIE arising from the analysis of planar structures, it is necessary to calculate the Green's functions (GF) for the scalar and vector potentials in multilayered media. These GF can be determined via numerical computation of inflnite integrals that are commonly known as Sommerfeld integrals (SI). However, the highly-oscillatory nature of the integrands involved makes the numerical computation of SI cumbersome and time consuming (1). Some researches have developed speciflc techniques that make it possible to accelerate the nu- merical computation of SI (2,3). Unfortunately, these techniques have the drawback that they have to be repeatedly used every time the distance between the source and observation points changes. One technique for the computation of multilayered media GFs that has received much attention in the last flfteen years is the discrete complex image method (DCIM) (4). This technique makes it possible to obtain closed-form expressions of the GFs without requiring numerical integration. However, the closed-form expressions have been recently found to produce unpredictable errors in the far-fleld computation of the GFs (5). Although it is possible to raise the threshold value of the distance between source and observation points that marks the onset of numerical errors, this is achieved at the expense of a considerable CPU time consumption (5). The sensitivity of the DCIM to far-fleld numerical errors seems to decrease when a surface waves term is included in the closed-form expression of the GFs (4,6). Unfortunately, the surface-waves term contains poles of the spectral domain GFs as well as residues of the spectral domain GFs at these poles, and the accurate determination of both the poles and the residues requires time-consuming algorithms (6). Very recently, the rational function fltting method (RFFM) has been proposed as an alternative technique to DCIM for the determination of closed-form expressions of multilayered media GFs (7). In the new technique the GFs are expressed in terms of a quasistatic term plus a linear com- bination of cylindrical waves. The amplitudes and propagation constants of the cylindrical waves are obtained in the spectral domain by means of a vector fltting algorithm, which is an iterative algorithm. The main drawback of the RFFM is that the closed-form expressions for the GFs in- troduce unacceptable errors in the near-fleld (7). These errors are caused by the Hankel functions representing the cylindrical waves, and in particular, by the non-physical near-fleld singularities present in these Hankel functions. In this paper, we present a revised version of the RFFM which substantially improves the original approach published in (7). In one hand, the determination of

Singularity subtraction for evaluation of Green's functions for multilayer media

This paper presents an efficient method to evaluate the two- and three-dimensional multilayered medium Green's functions for general electric and magnetic sources. Without finding any surface poles or steepest descent path, a special subtraction procedure is applied to each term of the Sommerfeld integrands to make them rapidly decreasing functions of k/sub /spl rho//. The contributions of the subtracted terms are calculated analytically. The remaining integrals are computed adaptively by using Gaussian quadratures. The accuracy of the method has been confirmed by comparison with many examples in literature, and the high efficiency has been verified.

Calculation of spatial-domain Green functions for multilayered media using DCIM with automatic handling of surface wave poles

The discrete complex image method (DCIM) has been used extensively for the calculation of spatial-domain Green functions for one-layer or two-layer media. However, one difficulty in applying DCIM to general multilayered media is the lack of a reliable procedure for the extraction of surface wave components. In the paper, the spectral-domain potential Green functions for a general multilayered medium are reformulated so that their denominators are obtained in an iterative form. A two-stage root-searching procedure is proposed for seeking the roots of these denominators. The residuals associated with the surface wave poles are calculated through contour integration. Special methods for handling the branch cuts close to the surface wave poles are discussed. Numerical examples of different geometries are given to reveal the behaviour of the surface wave poles and verify the method.

Time domain Green's functions for lossy and dispersive multilayered media

We have introduced a fast method of calculating the time domain Green's functions for multilayered media. In this paper, we demonstrate the use of this method to compute the scalar potential Green's function for a multilayer lossy dispersive medium on a PEC ground. The strength of the method lies in obtaining the Green's function for many source-to-field distances /spl rho/ and time instances t simultaneously. It only takes 6 min 28 s to compute 100/spl times/336=33 600 space time Green's function points in Matlab on a Pentium III 867 MHz processor with 1 GB of RAM for a multilayered lossy dispersive medium.

A Closed-Form Expression of the Nonsymmetrical Components of Green's Function for Multilayered Media

The Green's function for multilayered media is expressed in terms of Sommerfeld integrals. The discrete complex image method is an appealing technique in handling such integrals. However, the results of the nonsymmetrical components lacks sufficient accuracy in the near-field region. This is due to the fact that these components have slowly varying spectral-domain behavior. In this work, the quasi-dynamic contribution is explicitly extracted. The remaining part has fast decaying behavior. The generalized pencil-of-function method is used to recast this part into a set of exponentials. Using a special identity, a closed-form expression is obtained that is valid in the near-field region. The method is demonstrated to yield accurate results for microstrip structures.

Application of DCIM to MPIE-MoM analysis of 3D PEC objects in multilayered media

The Formulation-C Green's functions for multilayered media are reformulated in this paper to extract z-dependent part when the source and observation points are in different layers. The discrete complex image method (DCIM), is applied to obtain complex images independent on z but dependent on z/spl acute/. For simulation of three-dimensional (3-D) perfectly electrical conduction (PEC) objects penetrating two or more layers, tables of complex images are built in a z/spl acute/-grid. During the matrix-filling stage of the mixed-potential integral equation, together with method of moments (MPIE-MoM), the spatial-domain Green's functions are interpolated from values in the z/spl acute/-grid, while these values are calculated from complex images in the z/spl acute/-grid. This interpolation scheme is more efficient than those directly storing the spatial-domain Green's functions. Numerical examples are given for analyzing a dipole in a two-layered media.

High‐order window functions and fast algorithms for calculating dyadic electromagnetic Green's functions in multilayered media

A type of bell‐shaped compact high‐order window function ψ( x, y ) is studied, and closed‐form and approximation formulas are derived for its Hankel transforms. Applications of these results are presented as fast algorithms for calculating dyadic Green's functions for electromagnetic scattering in multilayered media. Numerical results in electromagnetics are provided to demonstrate the accuracy and efficiency of the algorithms.

An accurate computation of Green's functions for multilayered media in the near‐field region

AbstractThe discrete complex image method is one of the most efficient techniques used to evaluate the Green's functions of multilayered media. The usual extraction of surface waves may limit the validity of this method in the near‐field region. The aim of this work is to handle this problem such that the representation is valid for all field regions. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 130–131, 2001.

Resonant Behaviours of Microstrip Antenna in Multilayered Media: an Efficient Full-Wave Analysis - Abstract

This paper presents an efficient analysis of a microstrip antenna in multilayered media using the method of moments (MoM). The general forms of spectral-domain Green's functions for multilayered media are converted into the spatial-domain Green's functions using the discrete complex image method (DCIM). With the spatial-domain Green's functions, the mixed potential integral equation (MPIE) is discretized in spatial domain, and the resultant system of equations is then solved using the biconjugate gradient (BCG) method. As applications, resonant frequencies of microstrip antennas in multilayered media are analysed. The numerical results show that the present method is an efficient and accurate scheme for analysing microstrip antennas in multilayered media.

An efficient evaluation of the nonsymmetrical components of the Green's function for multilayered media

This paper is concerned with the evaluation of nonsymmetrical components of the Green's function of a Hertzian dipole present in a multilayered medium. The integrand of these components has a slowly varying tail which makes the discrete complex image method inefficient in representing the near field. In this work, the slowly varying tail is represented using real images whose locations are determined a priori. The amplitudes of these images are evaluated using a simple least square algorithm. The near field computed by this method is shown to yield good results for a half space and microstrip structures. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 28: 199–202 (2001).